TSTP Solution File: ITP268_1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP268_1 : TPTP v8.1.2. Released v8.0.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n028.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 03:28:59 EDT 2023
% Result : Theorem 26.68s 26.89s
% Output : Proof 26.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 8.88/9.05 % Problem : ITP268_1 : TPTP v8.1.2. Released v8.0.0.
% 8.88/9.06 % Command : do_cvc5 %s %d
% 9.10/9.27 % Computer : n028.cluster.edu
% 9.10/9.27 % Model : x86_64 x86_64
% 9.10/9.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 9.10/9.27 % Memory : 8042.1875MB
% 9.10/9.27 % OS : Linux 3.10.0-693.el7.x86_64
% 9.10/9.27 % CPULimit : 300
% 9.10/9.27 % WCLimit : 300
% 9.10/9.27 % DateTime : Sun Aug 27 16:03:33 EDT 2023
% 9.10/9.27 % CPUTime :
% 20.98/21.15 %----Proving TF0_NAR, FOF, or CNF
% 26.68/26.89 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.kG4gpB3iW9/cvc5---1.0.5_26155.p...
% 26.68/26.89 ------- get file name : TPTP file name is ITP268_1
% 26.68/26.89 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_26155.smt2...
% 26.68/26.89 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 26.68/26.89 % SZS status Theorem for ITP268_1
% 26.68/26.89 % SZS output start Proof for ITP268_1
% 26.68/26.89 (
% 26.68/26.89 (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_fun_nat_nat tptp.power_power_nat _let_2))) (let ((_let_4 (tptp.aa_nat_nat _let_3 tptp.na))) (let ((_let_5 (tptp.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.summin) _let_4)) tptp.lx))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_5) tptp.na))) (let ((_let_7 (tptp.vEBT_vebt_delete tptp.summary _let_6))) (let ((_let_8 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_5) tptp.na))) (let ((_let_9 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_6) _let_8))) (let ((_let_10 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_6 _let_9))) (let ((_let_11 (tptp.vEBT_vebt_maxt _let_7))) (let ((_let_12 (tptp.the_nat _let_11))) (let ((_let_13 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) _let_2))) (let ((_let_14 (tptp.aa_nat_nat _let_3 _let_13))) (let ((_let_15 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_11) tptp.none_nat)) _let_5) (tptp.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_14) _let_12)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_10 _let_12))))))) (let ((_let_16 (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 _let_5) tptp.ma)) _let_15) tptp.ma))) (let ((_let_17 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat _let_5) _let_16)) tptp.deg _let_10 _let_7))) (let ((_let_18 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_17) tptp.deg)))) (let ((_let_19 (not _let_18))) (let ((_let_20 (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (let ((_let_21 (tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat tptp.top_top_set_nat))) (let ((_let_22 (tptp.image_nat_set_nat tptp.set_ord_lessThan_nat tptp.top_top_set_nat))) (let ((_let_23 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (let ((_let_24 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi))) (let ((_let_25 (tptp.aa_real_real _let_24 _let_23))) (let ((_let_26 (tptp.topolo2177554685111907308n_real tptp.zero_zero_real _let_20))) (let ((_let_27 (tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (let ((_let_28 (tptp.aa_real_real tptp.uminus_uminus_real _let_25))) (let ((_let_29 (tptp.image_nat_nat tptp.suc tptp.top_top_set_nat))) (let ((_let_30 (tptp.aa_num_num tptp.bit0 _let_1))) (let ((_let_31 (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_30))))))))) (let ((_let_32 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat _let_31))) (let ((_let_33 (tptp.comp_nat_nat_nat tptp.suc tptp.suc))) (let ((_let_34 (tptp.map_fu3667384564859982768at_int tptp.rep_Integ tptp.abs_Integ))) (let ((_let_35 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1))) (let ((_let_36 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_37 (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_38 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_39 (tptp.aa_nat_nat tptp.suc _let_38))) (let ((_let_40 (tptp.aa_num_int tptp.numeral_numeral_int _let_1))) (let ((_let_41 (tptp.aa_int_nat tptp.nat2 tptp.one_one_int))) (let ((_let_42 (tptp.the_real tptp.aTP_Lamm_aaf))) (let ((_let_43 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_23))) (let ((_let_44 (tptp.aa_real_real tptp.sqrt _let_23))) (let ((_let_45 (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_46 (tptp.numera6690914467698888265omplex _let_1))) (let ((_let_47 (tptp.aa_real_complex tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_48 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_47))) (let ((_let_49 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit))) (let ((_let_50 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_51 (tptp.aa_real_real _let_43 tptp.pi))) (let ((_let_52 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_53 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_54 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_55 (tptp.aa_num_real tptp.numeral_numeral_real _let_54))) (let ((_let_56 (tptp.aa_real_real tptp.sqrt _let_55))) (let ((_let_57 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real))) (let ((_let_58 (tptp.aa_real_real _let_24 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 _let_54))))) (let ((_let_59 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_56) _let_23))) (let ((_let_60 (tptp.aa_real_real _let_24 _let_55))) (let ((_let_61 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_44) _let_23))) (let ((_let_62 (tptp.aa_num_real tptp.numeral_numeral_real _let_30))) (let ((_let_63 (tptp.aa_real_real _let_24 _let_62))) (let ((_let_64 (tptp.aa_real_real _let_57 _let_23))) (let ((_let_65 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (let ((_let_66 (tptp.aa_real_real tptp.cos_real _let_23))) (let ((_let_67 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_55))) (let ((_let_68 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_67 _let_23)) tptp.pi))) (let ((_let_69 (tptp.aa_num_num tptp.bit1 _let_54))) (let ((_let_70 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 _let_1)))) (let ((_let_71 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_72 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_73 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.zero_zero_complex))) (let ((_let_74 (tptp.aa_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int))) (let ((_let_75 (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real))) (let ((_let_76 (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_77 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_78 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_79 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_80 (tptp.aa_num_int tptp.numeral_numeral_int _let_54))) (let ((_let_81 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_54))) (let ((_let_82 (tptp.numera6690914467698888265omplex _let_54))) (let ((_let_83 (= (tptp.aa_int_int tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_84 (= (tptp.aa_rat_rat tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_85 (= (tptp.aa_real_real tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_86 (= (tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (let ((_let_87 (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one))) (let ((_let_88 (tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_89 (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (let ((_let_90 (tptp.aa_num_real tptp.numeral_numeral_real tptp.one))) (let ((_let_91 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_77))) (let ((_let_92 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_78))) (let ((_let_93 (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_79))) (let ((_let_94 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_53))) (let ((_let_95 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_96 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_97 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_79))) (let ((_let_98 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_78))) (let ((_let_99 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_77))) (let ((_let_100 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_53))) (let ((_let_101 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_102 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_103 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_104 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int))) (let ((_let_105 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real))) (let ((_let_106 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_107 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_108 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_109 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_35))) (let ((_let_110 (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_65))) (let ((_let_111 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_46))) (let ((_let_112 (tptp.aa_int_int tptp.uminus_uminus_int _let_40))) (let ((_let_113 (tptp.aa_real_real tptp.uminus_uminus_real _let_23))) (let ((_let_114 (= (tptp.modulo364778990260209775nteger _let_77 _let_35) tptp.one_one_Code_integer))) (let ((_let_115 (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int _let_79) _let_40) tptp.one_one_int))) (let ((_let_116 (tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_117 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_118 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (let ((_let_119 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_120 (tptp.minus_minus_rat _let_78))) (let ((_let_121 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex _let_50))) (let ((_let_122 (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_79))) (let ((_let_123 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_53))) (let ((_let_124 (tptp.plus_plus_rat _let_78))) (let ((_let_125 (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_50))) (let ((_let_126 (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_79))) (let ((_let_127 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_53))) (let ((_let_128 (tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_129 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (let ((_let_130 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real))) (let ((_let_131 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_40))) (let ((_let_132 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2))) (let ((_let_133 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_35))) (let ((_let_134 (tptp.pp (tptp.aa_int_bool _let_101 tptp.zero_zero_int)))) (let ((_let_135 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_136 (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one))) (let ((_let_137 (tptp.aa_int_int _let_129 tptp.one_one_int))) (let ((_let_138 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_139 (tptp.aa_nat_nat _let_138 tptp.one_one_nat))) (let ((_let_140 (tptp.aa_rat_rat _let_128 tptp.one_one_rat))) (let ((_let_141 (tptp.aa_real_real _let_130 tptp.one_one_real))) (let ((_let_142 (tptp.pp (tptp.aa_int_bool _let_96 tptp.one_one_int)))) (let ((_let_143 (tptp.pp (tptp.aa_nat_bool _let_135 tptp.one_one_nat)))) (let ((_let_144 (tptp.pp (tptp.aa_rat_bool _let_95 tptp.one_one_rat)))) (let ((_let_145 (tptp.pp (tptp.aa_real_bool _let_72 tptp.one_one_real)))) (let ((_let_146 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_147 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_148 (tptp.pp (tptp.aa_int_bool _let_101 tptp.one_one_int)))) (let ((_let_149 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_150 (tptp.pp (tptp.aa_nat_bool _let_149 tptp.one_one_nat)))) (let ((_let_151 (tptp.pp (tptp.aa_rat_bool _let_102 tptp.one_one_rat)))) (let ((_let_152 (tptp.pp (tptp.aa_real_bool _let_71 tptp.one_one_real)))) (let ((_let_153 (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (let ((_let_154 (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) _let_40) tptp.zero_zero_int))) (let ((_let_155 (= (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_156 (= (tptp.modulo364778990260209775nteger tptp.one_one_Code_integer _let_35) tptp.one_one_Code_integer))) (let ((_let_157 (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int tptp.one_one_int) _let_40) tptp.one_one_int))) (let ((_let_158 (= (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_159 (= _let_139 _let_2))) (let ((_let_160 (= _let_136 tptp.one_one_nat))) (let ((_let_161 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high tptp.ma) tptp.na))) (let ((_let_162 (tptp.nth_VEBT_VEBT tptp.treeList tptp.summin))) (let ((_let_163 (= tptp.xa tptp.mi))) (let ((_let_164 (not _let_163))) (let ((_let_165 (tptp.vEBT_vebt_mint tptp.summary))) (let ((_let_166 (tptp.the_nat _let_165))) (let ((_let_167 (tptp.aa_nat_nat _let_3 tptp.deg))) (let ((_let_168 (= tptp.mi tptp.ma))) (let ((_let_169 (not _let_168))) (let ((_let_170 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.ma) _let_167)))) (let ((_let_171 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.mi))) (let ((_let_172 (tptp.pp (tptp.aa_nat_bool _let_171 tptp.ma)))) (let ((_let_173 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.mi) tptp.ma)) tptp.deg tptp.treeList tptp.summary))) (let ((_let_174 (= _let_5 tptp.ma))) (let ((_let_175 (= _let_5 _let_15))) (let ((_let_176 (and (=> _let_174 _let_175) (=> (not _let_174) _let_174)))) (let ((_let_177 (not _let_176))) (let ((_let_178 (=> _let_177 (forall ((I 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 (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.summin) (tptp.aa_nat_nat _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (tptp.vEBT_vebt_maxt (tptp.vEBT_vebt_delete tptp.summary _let_4)))) (let ((_let_6 (tptp.the_nat _let_5))) (let ((_let_7 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_4 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_3) tptp.na))))) (let ((_let_8 (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 _let_3) tptp.ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat)) _let_3) (tptp.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 _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) _let_1))) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_7 _let_6)))))) tptp.ma))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.aa_nat_nat _let_2 tptp.m))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_8) tptp.na) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT _let_7 I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_8) tptp.na)))) (forall ((Y2 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 (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.summin) (tptp.aa_nat_nat _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (tptp.vEBT_vebt_maxt (tptp.vEBT_vebt_delete tptp.summary _let_4)))) (let ((_let_6 (tptp.the_nat _let_5))) (let ((_let_7 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_4 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_3) tptp.na))))) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Y2) tptp.na) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT _let_7 I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Y2) tptp.na)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) Y2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y2) (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 _let_3) tptp.ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat)) _let_3) (tptp.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 _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) _let_1))) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_7 _let_6)))))) tptp.ma))))))))))))))))))))))))))) (let ((_let_179 (forall ((I 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 I) (tptp.aa_nat_nat _let_1 tptp.m))) (= (exists ((X_12 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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na))) I)) X_12))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_vebt_delete tptp.summary (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.summin) (tptp.aa_nat_nat _let_1 tptp.na))) tptp.lx)) tptp.na))) I)))))))) (let ((_let_180 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_16) _let_167)))) (let ((_let_181 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_5) _let_16)))) (let ((_let_182 (= tptp.deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.na) tptp.m)))) (let ((_let_183 (tptp.aa_nat_nat tptp.suc tptp.na))) (let ((_let_184 (= tptp.m _let_183))) (let ((_let_185 (tptp.aa_nat_nat _let_3 tptp.m))) (let ((_let_186 (tptp.size_s6755466524823107622T_VEBT _let_10))) (let ((_let_187 (= _let_186 _let_185))) (let ((_let_188 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_7) tptp.m)))) (let ((_let_189 (=> (forall ((X3 tptp.vEBT_VEBT)) (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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X3) tptp.na)))))) (=> _let_188 (=> _let_187 (=> _let_184 (=> _let_182 (=> (forall ((I3 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 I3) (tptp.aa_nat_nat _let_1 tptp.m))) (= (exists ((X_12 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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na))) I3)) X_12))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_vebt_delete tptp.summary (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.summin) (tptp.aa_nat_nat _let_1 tptp.na))) tptp.lx)) tptp.na))) I3)))))) (=> (=> _let_176 (forall ((X3 tptp.vEBT_VEBT)) (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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na)))))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1))))))))) (=> _let_181 (=> _let_180 (=> (=> _let_177 (forall ((I3 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 (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.summin) (tptp.aa_nat_nat _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (tptp.vEBT_vebt_maxt (tptp.vEBT_vebt_delete tptp.summary _let_4)))) (let ((_let_6 (tptp.the_nat _let_5))) (let ((_let_7 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_4 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_3) tptp.na))))) (let ((_let_8 (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 _let_3) tptp.ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat)) _let_3) (tptp.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 _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) _let_1))) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_7 _let_6)))))) tptp.ma))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat _let_2 tptp.m))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_8) tptp.na) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT _let_7 I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_8) tptp.na)))) (forall ((X3 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 (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.summin) (tptp.aa_nat_nat _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (tptp.vEBT_vebt_maxt (tptp.vEBT_vebt_delete tptp.summary _let_4)))) (let ((_let_6 (tptp.the_nat _let_5))) (let ((_let_7 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_4 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_3) tptp.na))))) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X3) tptp.na) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT _let_7 I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X3) tptp.na)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) (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 _let_3) tptp.ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat)) _let_3) (tptp.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 _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) _let_1))) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_7 _let_6)))))) tptp.ma))))))))))))))))))))))))) _let_18)))))))))))) (let ((_let_190 (=> _let_176 (forall ((X2 tptp.vEBT_VEBT)) (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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na)))))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X2) X_13))))))))))) (let ((_let_191 (and _let_180 _let_181))) (let ((_let_192 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_6))) (let ((_let_193 (tptp.size_s6755466524823107622T_VEBT tptp.treeList))) (let ((_let_194 (forall ((X2 tptp.vEBT_VEBT)) (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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X2) tptp.na)))))))) (let ((_let_195 (= _let_183 tptp.m))) (let ((_let_196 (forall ((I3 tptp.nat) (BOUND_VARIABLE_177448 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 (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.summin) (tptp.aa_nat_nat _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (tptp.vEBT_vebt_maxt (tptp.vEBT_vebt_delete tptp.summary _let_4)))) (let ((_let_6 (tptp.the_nat _let_5))) (let ((_let_7 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_4 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_3) tptp.na))))) (let ((_let_8 (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 _let_3) tptp.ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat)) _let_3) (tptp.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 _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) _let_1))) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_7 _let_6)))))) tptp.ma))) (let ((_let_9 (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT _let_7 I3)))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat _let_2 tptp.m)))) (and (or (not (= I3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_8) tptp.na))) (tptp.pp (tptp.aa_nat_bool _let_9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_8) tptp.na)))) (or (not (= I3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high BOUND_VARIABLE_177448) tptp.na))) (not (tptp.pp (tptp.aa_nat_bool _let_9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low BOUND_VARIABLE_177448) tptp.na)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) BOUND_VARIABLE_177448)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat BOUND_VARIABLE_177448) _let_8)))))))))))))))))) (let ((_let_197 (= tptp.ma _let_5))) (let ((_let_198 (and (=> _let_197 _let_175) (=> (not _let_197) _let_197)))) (let ((_let_199 (not _let_198))) (let ((_let_200 (=> _let_199 _let_196))) (let ((_let_201 (=> _let_200 _let_18))) (let ((_let_202 (=> _let_180 _let_201))) (let ((_let_203 (=> _let_181 _let_202))) (let ((_let_204 (ASSUME :args (_let_191)))) (let ((_let_205 (AND_ELIM _let_204 :args (1)))) (let ((_let_206 (not _let_202))) (let ((_let_207 (AND_ELIM _let_204 :args (0)))) (let ((_let_208 (not _let_201))) (let ((_let_209 (forall ((X3 tptp.vEBT_VEBT) (BOUND_VARIABLE_177417 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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (or (not (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na))))))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) BOUND_VARIABLE_177417))))))))) (let ((_let_210 (=> _let_198 _let_209))) (let ((_let_211 (forall ((I tptp.nat) (BOUND_VARIABLE_177512 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 (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.summin) (tptp.aa_nat_nat _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (tptp.vEBT_vebt_maxt (tptp.vEBT_vebt_delete tptp.summary _let_4)))) (let ((_let_6 (tptp.the_nat _let_5))) (let ((_let_7 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_4 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_3) tptp.na))))) (let ((_let_8 (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 _let_3) tptp.ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat)) _let_3) (tptp.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 _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) _let_1))) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_7 _let_6)))))) tptp.ma))) (let ((_let_9 (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT _let_7 I)))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.aa_nat_nat _let_2 tptp.m)))) (and (or (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_8) tptp.na) I)) (tptp.pp (tptp.aa_nat_bool _let_9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_8) tptp.na)))) (or (not (= I (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high BOUND_VARIABLE_177512) tptp.na))) (not (tptp.pp (tptp.aa_nat_bool _let_9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low BOUND_VARIABLE_177512) tptp.na)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) BOUND_VARIABLE_177512)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat BOUND_VARIABLE_177512) _let_8)))))))))))))))))) (let ((_let_212 (=> _let_210 _let_203))) (let ((_let_213 (_let_210))) (let ((_let_214 (forall ((I3 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))))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat _let_1 tptp.m)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_vebt_delete tptp.summary (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.summin) (tptp.aa_nat_nat _let_1 tptp.na))) tptp.lx)) tptp.na))) I3)) (not (forall ((X_12 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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na))) I3)) X_12))))))))))))) (let ((_let_215 (=> _let_214 _let_212))) (let ((_let_216 (=> _let_182 _let_215))) (let ((_let_217 (=> _let_184 _let_216))) (let ((_let_218 (= _let_185 _let_186))) (let ((_let_219 (=> _let_218 _let_217))) (let ((_let_220 (=> _let_188 _let_219))) (let ((_let_221 (forall ((X3 tptp.vEBT_VEBT)) (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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (or (not (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X3) tptp.na)))))))) (let ((_let_222 (forall ((X2 tptp.vEBT_VEBT)) (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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (or (not (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X2) tptp.na)))))))) (let ((_let_223 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_POS :args (_let_215)) :args ((or _let_212 (not _let_214) (not _let_215)))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_214 (= X_12 X_12) (= I3 I)))) (EQ_RESOLVE (ASSUME :args (_let_179)) (MACRO_SR_EQ_INTRO :args (_let_179 SB_DEFAULT SBA_FIXPOINT))) :args (_let_214 false (forall ((I 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))))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.aa_nat_nat _let_1 tptp.m)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_vebt_delete tptp.summary (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.summin) (tptp.aa_nat_nat _let_1 tptp.na))) tptp.lx)) tptp.na))) I)) (not (forall ((X_12 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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na))) I)) X_12))))))))))))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_POS :args (_let_216)) :args ((or _let_215 (not _let_182) (not _let_216)))) (ASSUME :args (_let_182)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_POS :args (_let_217)) :args ((or _let_216 (not _let_184) (not _let_217)))) (SYMM (ASSUME :args (_let_195))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_POS :args (_let_219)) :args ((or _let_217 (not _let_218) (not _let_219)))) (SYMM (ASSUME :args (_let_187))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_POS :args (_let_220)) :args ((or _let_219 (not _let_188) (not _let_220)))) (ASSUME :args (_let_188)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_189)) (MACRO_SR_EQ_INTRO :args (_let_189 SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_220 (not _let_221)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_222 (= X2 X3)))) :args ((or _let_221 (not _let_222)))) (EQ_RESOLVE (ASSUME :args (_let_194)) (MACRO_SR_EQ_INTRO :args (_let_194 SB_DEFAULT SBA_FIXPOINT))) :args (_let_221 false _let_222)) :args (_let_220 false _let_221)) :args (_let_219 false _let_188 false _let_220)) :args (_let_217 false _let_218 false _let_219)) :args (_let_216 false _let_184 false _let_217)) :args (_let_215 false _let_182 false _let_216)) :args (_let_212 false _let_214 false _let_215)))) (let ((_let_224 (REORDERING (CNF_IMPLIES_POS :args (_let_212)) :args ((or _let_203 (not _let_210) (not _let_212)))))) (let ((_let_225 (REORDERING (CNF_IMPLIES_POS :args (_let_203)) :args ((or _let_202 (not _let_181) (not _let_203)))))) (let ((_let_226 (_let_200))) (let ((_let_227 (REORDERING (CNF_IMPLIES_POS :args (_let_202)) :args ((or _let_201 (not _let_180) _let_206))))) (let ((_let_228 (ASSUME :args (_let_19)))) (let ((_let_229 (REORDERING (CNF_IMPLIES_POS :args (_let_201)) :args ((or _let_18 (not _let_200) _let_208))))) (let ((_let_230 (MACRO_RESOLUTION_TRUST _let_229 _let_228 _let_227 _let_207 (CNF_IMPLIES_NEG2 :args _let_226) _let_225 _let_205 (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_196 (= I3 I) (= BOUND_VARIABLE_177448 BOUND_VARIABLE_177512))) (MACRO_SR_PRED_INTRO :args ((= (forall ((I tptp.nat) (BOUND_VARIABLE_177512 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 (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.summin) (tptp.aa_nat_nat _let_2 tptp.na))) tptp.lx))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_3) tptp.na))) (let ((_let_5 (tptp.vEBT_vebt_maxt (tptp.vEBT_vebt_delete tptp.summary _let_4)))) (let ((_let_6 (tptp.the_nat _let_5))) (let ((_let_7 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_4 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_3) tptp.na))))) (let ((_let_8 (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 _let_3) tptp.ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat)) _let_3) (tptp.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 _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.deg) _let_1))) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_7 _let_6)))))) tptp.ma))) (let ((_let_9 (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT _let_7 I)))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) (tptp.aa_nat_nat _let_2 tptp.m)))) (and (or (not (= I (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_8) tptp.na))) (tptp.pp (tptp.aa_nat_bool _let_9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_8) tptp.na)))) (or (not (= I (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high BOUND_VARIABLE_177512) tptp.na))) (not (tptp.pp (tptp.aa_nat_bool _let_9 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low BOUND_VARIABLE_177512) tptp.na)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) BOUND_VARIABLE_177512)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat BOUND_VARIABLE_177512) _let_8)))))))))))))))) _let_211) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) _let_224 _let_223 (EQ_RESOLVE (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_178)) (MACRO_SR_EQ_INTRO :args (_let_178 SB_DEFAULT SBA_FIXPOINT)))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_199) _let_198))) (REFL :args (_let_211)) :args (or))) (REORDERING (CNF_IMPLIES_NEG1 :args _let_213) :args ((or _let_198 _let_210))) :args (_let_198 true _let_18 false _let_201 false _let_180 false _let_200 false _let_202 false _let_181 false _let_196 false _let_203 false _let_212 false _let_211 false _let_210)))) (let ((_let_231 (forall ((X2 tptp.vEBT_VEBT) (BOUND_VARIABLE_177385 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.summin) (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.na))) tptp.lx))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_1) tptp.na))) (or (not (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_2 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_1) tptp.na))))))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X2) BOUND_VARIABLE_177385))))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST _let_225 (MACRO_RESOLUTION_TRUST _let_224 (MACRO_RESOLUTION_TRUST (CNF_IMPLIES_NEG2 :args _let_213) (MACRO_RESOLUTION_TRUST (REORDERING (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_231 (= BOUND_VARIABLE_177385 BOUND_VARIABLE_177417) (= X2 X3)))) :args ((or _let_209 (not _let_231)))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_190)) (MACRO_SR_EQ_INTRO :args (_let_190 SB_DEFAULT SBA_FIXPOINT)))) :args ((or _let_231 _let_199))) _let_230 :args (_let_231 false _let_198)) :args (_let_209 false _let_231)) :args (_let_210 false _let_209)) _let_223 :args (_let_203 false _let_210 false _let_212)) (MACRO_RESOLUTION_TRUST _let_227 (MACRO_RESOLUTION_TRUST _let_229 _let_228 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_IMPLIES_NEG1 :args _let_226) :args ((or _let_199 _let_200))) _let_230 :args (_let_200 false _let_198)) :args (_let_208 true _let_18 false _let_200)) _let_207 :args (_let_206 true _let_201 false _let_180)) _let_205 :args (false false _let_203 true _let_202 false _let_181)) :args ((tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt tptp.summary) tptp.m)) (forall ((X tptp.nat)) (=> (forall ((N tptp.nat)) (not (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) N)))) (not (forall ((N tptp.nat)) (not (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) (tptp.aa_nat_nat tptp.suc N)))))))) (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node Info Deg TreeList Summary)) N2)) (= Deg N2))) _let_182 (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 tptp.treeList))) (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X2) tptp.na)) (forall ((Xa tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_vebt_delete X2 Xa)) tptp.na)))))) (forall ((Tree tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Tree) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N2)))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (= Tree (tptp.vEBT_Node Info2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N2)) TreeList2 S))))) (forall ((X tptp.nat) (D tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.vEBT_VEBT_bit_concat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) D)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) D)) D) X)) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_vebt_delete T X)) Y)) (and (not (= X Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) Y)))))) _let_170 (= _let_193 _let_185) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))) (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B)))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) N2) (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))) N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_162) tptp.na)) (= _let_13 tptp.na) (forall ((X tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_vebt_delete tptp.summary X)) tptp.m))) (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 tptp.treeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X2) tptp.na)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) tptp.deg)) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList tptp.summin)) X_1))) (forall ((Ma tptp.nat) (N2 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 N2) 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) N2)) (tptp.aa_nat_nat _let_1 M)))))) (forall ((H tptp.nat) (L tptp.nat) (D tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.vEBT_VEBT_bit_concat H) L) D) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat H) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) D))) L))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions tptp.summary) _let_161)) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) Deg)) (=> (not (= Mi Ma)) (= (tptp.the_nat (tptp.vEBT_vebt_maxt Summary)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Ma) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y) _let_1)) X)) N2) Y)))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y) _let_1)) X)) N2) X)))) _let_195 (forall ((I 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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.m))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList I)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions tptp.summary) I))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList _let_161)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_9) tptp.na)) (= (tptp.nth_VEBT_VEBT _let_10 _let_6) _let_9) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_5) _let_167)) _let_188 (= _let_193 _let_186) _let_194 (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) Deg)) (=> (= Mi Ma) (and (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X2) X_13)))))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) X_13)))))))) (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_9)) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary))) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)) (= (tptp.vEBT_vebt_delete _let_1 X) _let_1))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.summin) _let_185)) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) N2)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) Ma)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)))))) _let_181 _let_180 (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.vEBT_Node Info Deg TreeList Summary))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_1) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2) Deg))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_3))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions _let_1) X))))))))) (tptp.pp (tptp.aa_nat_bool _let_192 _let_193)) (and (tptp.pp (tptp.aa_nat_bool _let_192 _let_185)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_8) _let_4))) (forall ((I2 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 (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.summin) (tptp.aa_nat_nat _let_1 tptp.na))) tptp.lx))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_2) tptp.na))) (=> (and (not (= I2 _let_3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat _let_1 tptp.m)))) (= (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT tptp.treeList _let_3 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT tptp.treeList _let_3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_2) tptp.na))) I2) (tptp.nth_VEBT_VEBT tptp.treeList I2))))))) _let_187 (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.product_prod_int_int) (P tptp.fun_Pr803113274115125473t_bool)) (= (tptp.member5262025264175285858nt_int A (tptp.collec213857154873943460nt_int P)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P A)))) (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.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_real)) (= (tptp.collect_real (tptp.aTP_Lamm_a A2)) A2)) (forall ((A2 tptp.set_Pr958786334691620121nt_int)) (= (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_aa A2)) A2)) (forall ((A2 tptp.set_complex)) (= (tptp.collect_complex (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_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (=> (forall ((X3 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q X3)))) (= (tptp.collec213857154873943460nt_int P) (tptp.collec213857154873943460nt_int Q)))) (forall ((P tptp.fun_complex_bool) (Q tptp.fun_complex_bool)) (=> (forall ((X3 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool P X3)) (tptp.pp (tptp.aa_complex_bool Q X3)))) (= (tptp.collect_complex P) (tptp.collect_complex 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)))) _let_191 _let_190 _let_189 _let_179 _let_178 (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)) _let_172 (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions _let_173) _let_5)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_173) tptp.deg)) (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (tptp.some_P7363390416028606310at_nat (tptp.the_Pr8591224930841456533at_nat Option)) Option))) (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (tptp.some_nat (tptp.the_nat Option)) Option))) (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (tptp.some_num (tptp.the_num Option)) Option))) (= (tptp.vEBT_vebt_delete _let_173 tptp.xa) _let_17) (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex V)))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex B) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex _let_1 B)) (tptp.aa_complex_complex _let_1 C))))) (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real V)))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 C))))) (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat B) C)) (tptp.aa_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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) _let_1))))) (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real V))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) _let_1))))) (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) _let_1) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1)) (tptp.aa_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 ((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.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y)) _let_2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) _let_2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Y) _let_2))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) Y)) _let_2) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_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.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)) X)) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) X)) Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_int_fun_nat_int tptp.power_power_int X) _let_2)) (tptp.aa_nat_int (tptp.aa_int_fun_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)))))) _let_163 (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) Y) Z) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_power (tptp.some_nat X)) (tptp.some_nat Y)) (tptp.some_nat Z)))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X)))) (forall ((T tptp.vEBT_VEBT)) (=> (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull T))) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X_1))))) (forall ((Xs tptp.set_nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_min_in_set Xs) X)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) Xs)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) X4))))))) (forall ((Xs tptp.set_nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_max_in_set Xs) X)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) Xs)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) X))))))) (=> _let_168 (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 tptp.treeList))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X2) X_13))))))) (forall ((Xs tptp.list_complex) (P tptp.fun_complex_bool) (N2 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 N2) (tptp.size_s3451745648224563538omplex Xs))) (tptp.pp (tptp.aa_complex_bool P (tptp.aa_nat_complex (tptp.nth_complex Xs) N2)))))) (forall ((Xs tptp.list_real) (P tptp.fun_real_bool) (N2 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 N2) (tptp.size_size_list_real Xs))) (tptp.pp (tptp.aa_real_bool P (tptp.aa_nat_real (tptp.nth_real Xs) N2)))))) (forall ((Xs tptp.list_set_nat) (P tptp.fun_set_nat_bool) (N2 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 N2) (tptp.size_s3254054031482475050et_nat Xs))) (tptp.pp (tptp.aa_set_nat_bool P (tptp.nth_set_nat Xs N2)))))) (forall ((Xs tptp.list_nat) (P tptp.fun_nat_bool) (N2 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 N2) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat Xs) N2)))))) (forall ((Xs tptp.list_VEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool) (N2 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 N2) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT Xs N2)))))) (forall ((Xs tptp.list_bool) (P tptp.fun_bool_bool) (N2 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 N2) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool P (tptp.aa_nat_bool (tptp.nth_bool Xs) N2)))))) (forall ((Xs tptp.list_int) (P tptp.fun_int_bool) (N2 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 N2) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int Xs) N2)))))) _let_163 (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.numera6690914467698888265omplex M) (tptp.numera6690914467698888265omplex N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.aa_num_real tptp.numeral_numeral_real M) (tptp.aa_num_real tptp.numeral_numeral_real N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.aa_num_rat tptp.numeral_numeral_rat M) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.aa_num_nat tptp.numeral_numeral_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.aa_num_int tptp.numeral_numeral_int M) (tptp.aa_num_int tptp.numeral_numeral_int N2)) (= M N2))) (forall ((X22 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (tptp.some_P7363390416028606310at_nat X22) (tptp.some_P7363390416028606310at_nat Y22)) (= X22 Y22))) (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (tptp.some_nat X22) (tptp.some_nat Y22)) (= X22 Y22))) (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (tptp.some_num X22) (tptp.some_num Y22)) (= X22 Y22))) (or _let_164 (not (= tptp.xa tptp.ma))) (and (tptp.pp (tptp.aa_nat_bool _let_171 tptp.xa)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.xa) tptp.ma))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 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 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 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 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 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 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 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 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex V)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real V)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real W)) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)) Z)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat W)) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int W)) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Z))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex M)) (tptp.numera6690914467698888265omplex N2)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N2)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 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 N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 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 N2)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.numera6690914467698888265omplex V)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.numera6690914467698888265omplex W)) Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real V)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real W)) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)) Z)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat W)) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int W)) Z)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Z))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.numera6690914467698888265omplex M)) (tptp.numera6690914467698888265omplex N2)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N2)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 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 N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 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 N2)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit0 tptp.one)) N2) (tptp.aa_num_num tptp.bit0 N2))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (and (= X Mi) (= X Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)) (= (tptp.vEBT_vebt_delete (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList Summary))))) (forall ((A tptp.nat) (M tptp.num) (N2 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 N2)) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))))) (forall ((A tptp.real) (M tptp.num) (N2 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 N2)) (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))))) (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (= (tptp.aa_nat_int (tptp.aa_int_fun_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 N2)) (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))))) (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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 N2)) (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))))) (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y3 tptp.product_prod_nat_nat)) (not (= X (tptp.some_P7363390416028606310at_nat Y3)))) (= X tptp.none_P5556105721700978146at_nat))) (forall ((X tptp.option_nat)) (= (forall ((Y3 tptp.nat)) (not (= X (tptp.some_nat Y3)))) (= X tptp.none_nat))) (forall ((X tptp.option_num)) (= (forall ((Y3 tptp.num)) (not (= X (tptp.some_num Y3)))) (= X tptp.none_num))) (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y3 tptp.product_prod_nat_nat)) (= X (tptp.some_P7363390416028606310at_nat Y3))))) (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y3 tptp.nat)) (= X (tptp.some_nat Y3))))) (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y3 tptp.num)) (= X (tptp.some_num Y3))))) (=> _let_169 (forall ((I 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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.m))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low tptp.ma) tptp.na)))) (forall ((Y2 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Y2) tptp.na) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Y2) tptp.na)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.mi) Y2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y2) tptp.ma))))))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_lesseq (tptp.some_nat X)) (tptp.some_nat Y))))) (and _let_172 _let_170) (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num) (B tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.real) (M tptp.num) (N2 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 N2))) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.rat) (M tptp.num) (N2 tptp.num) (B tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_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.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) B)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.nat) (M tptp.num) (N2 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 N2))) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.int) (M tptp.num) (N2 tptp.num) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2))) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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 N2))) (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((A tptp.real) (M tptp.num) (N2 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 N2))) (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((A tptp.rat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_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 N2))) (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((A tptp.nat) (M tptp.num) (N2 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 N2))) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2))) (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N2) tptp.one)))) (and _let_169 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.xa) _let_167))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) B))))) (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1)) B))))) (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1)))))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) B))))) (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1)) B))))) (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1)))))) (= (tptp.some_nat tptp.summin) _let_165) (forall ((N2 tptp.nat)) (= (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.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N2)))) (forall ((N2 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))) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N2)))) (forall ((Y 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 (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Y) tptp.na))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Y) tptp.na))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList _let_3)) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.aa_nat_nat _let_1 tptp.m))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.mi) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) tptp.ma)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.aa_nat_nat _let_1 tptp.na)))))))))) (forall ((I 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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.m))) (and (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high tptp.ma) tptp.na) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low tptp.ma) tptp.na)))) (forall ((Y2 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Y2) tptp.na) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT tptp.treeList I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Y2) tptp.na)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.mi) Y2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y2) tptp.ma)))))))) (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 ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.product_Pair_nat_nat Mi))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (= _let_4 H) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2) L) (=> (= Newnode (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList H) L)) (=> (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull Newnode))) (=> (= Newlist (tptp.list_u1324408373059187874T_VEBT TreeList H Newnode)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList))) (= (tptp.vEBT_vebt_delete (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_3 Ma)) Deg TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_3 (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 X) Ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat H) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT Newlist H))))) Ma))) Deg Newlist Summary)))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList H) L))) (let ((_let_2 (tptp.list_u1324408373059187874T_VEBT TreeList H _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Ma)))) (let ((_let_7 (tptp.product_Pair_nat_nat Mi))) (let ((_let_8 (tptp.vEBT_vebt_delete Summary H))) (let ((_let_9 (tptp.vEBT_vebt_maxt _let_8))) (let ((_let_10 (tptp.the_nat _let_9))) (let ((_let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_4))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) Deg)) (=> (= _let_11 H) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_4) L) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_11) (tptp.size_s6755466524823107622T_VEBT TreeList))) (= (tptp.vEBT_vebt_delete (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_7 Ma)) Deg TreeList Summary) X) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_1) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat)) Mi) (tptp.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_5) _let_10)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_2 _let_10)))))) Ma))) Deg _let_2 _let_8) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat H) _let_5)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_2 H))))) Ma))) Deg _let_2 Summary))))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT) (Summary tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (tptp.the_nat _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (tptp.product_Pair_nat_nat Mi))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_4))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) Deg)) (=> (= _let_6 H) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_4) L) (=> (= Newnode (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList H) L)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull Newnode)) (=> (= Sn (tptp.vEBT_vebt_delete Summary H)) (=> (= Newlist (tptp.list_u1324408373059187874T_VEBT TreeList H Newnode)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_6) (tptp.size_s6755466524823107622T_VEBT TreeList))) (= (tptp.vEBT_vebt_delete (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 Ma)) Deg TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_1) tptp.none_nat)) Mi) (tptp.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.power_power_nat _let_3) _let_4)) _let_2)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT Newlist _let_2)))))) Ma))) Deg Newlist Sn))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H tptp.nat) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))) (let ((_let_4 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Ma)))) (let ((_let_5 (tptp.product_Pair_nat_nat Mi))) (let ((_let_6 (tptp.vEBT_vebt_delete (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 Ma)) Deg TreeList Summary) X))) (let ((_let_7 (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull Newnode)))) (let ((_let_8 (tptp.vEBT_vebt_delete Summary H))) (let ((_let_9 (tptp.vEBT_vebt_maxt _let_8))) (let ((_let_10 (tptp.the_nat _let_9))) (let ((_let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (= _let_11 H) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2) L) (=> (= Newnode (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList H) L)) (=> (= Newlist (tptp.list_u1324408373059187874T_VEBT TreeList H Newnode)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_11) (tptp.size_s6755466524823107622T_VEBT TreeList))) (and (=> _let_7 (= _let_6 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat)) Mi) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) _let_10)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT Newlist _let_10)))))) Ma))) Deg Newlist _let_8))) (=> (not _let_7) (= _let_6 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat H) _let_3)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT Newlist H))))) Ma))) Deg Newlist Summary)))))))))))))))))))))))) (= (tptp.some_nat tptp.lx) (tptp.vEBT_vebt_mint _let_162)) (forall ((N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N2) tptp.one))) (forall ((M tptp.nat) (N2 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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc M)) N2)))) (forall ((A tptp.nat) (K tptp.num) (L tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num K) L)))))) (forall ((A tptp.int) (K tptp.num) (L tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int L)) (tptp.aa_int_int _let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num K) L)))))) (forall ((V tptp.num) (N2 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)) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) tptp.one))) N2))) (forall ((M tptp.nat) (N2 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) N2)) M))) (forall ((M tptp.nat) (N2 tptp.nat) (K 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 (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 N2) K))))) (forall ((N2 tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2))) (=> (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) N2) Q2))))) (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.plus_plus_rat A))) (= (tptp.aa_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.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 ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 N2)) A)))) (forall ((A tptp.real) (N2 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 N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 N2)) A)))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_1 N2)) A)))) (forall ((A tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N2)) A)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N2)) A)))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_nat_complex _let_1 N2))))) (forall ((A tptp.real) (N2 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 N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real _let_1 N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.times_times_rat A) (tptp.aa_nat_rat _let_1 N2))))) (forall ((A tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat _let_1 N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int _let_1 N2))))) (forall ((M tptp.nat) (I2 tptp.nat) (N2 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 I2) N2))) (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) N2)) I2)))) (forall ((N2 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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) M))) (forall ((M tptp.nat) (N2 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) N2)) N2)) M))) (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2))) (let ((_let_2 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Y))) (=> (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y) (tptp.aa_complex_complex _let_2 X)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) Y) (tptp.aa_complex_complex _let_2 _let_1)))))) (forall ((X tptp.real) (Y tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2))) (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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat X) N2))) (let ((_let_2 (tptp.times_times_rat Y))) (=> (= (tptp.aa_rat_rat (tptp.times_times_rat X) Y) (tptp.aa_rat_rat _let_2 X)) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat _let_2 _let_1)))))) (forall ((X tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) N2))) (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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2))) (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) (N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B)) N2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex B) N2)))) (forall ((A tptp.real) (B tptp.real) (N2 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)) N2) (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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2)))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.times_times_rat A) B)) N2) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 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)) N2) (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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) _let_1)))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))) (= (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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_1) A) (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1)))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))) (= (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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)))) (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) N2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex B) N2)))) (forall ((A tptp.real) (B tptp.real) (N2 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)) N2) (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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2)))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) N2) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)))) (forall ((A tptp.nat) (M tptp.nat) (N2 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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_1 M)) N2)))) (forall ((A tptp.real) (M tptp.nat) (N2 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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real _let_1 M)) N2)))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int _let_1 M)) N2)))) (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex 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) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_nat_complex _let_1 M)) N2)))) (forall ((X tptp.option4927543243414619207at_nat) (P tptp.fun_op5682630191948829869t_bool) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt7606875699174042974t_bool P X) Y)))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (=> (= X (tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (tptp.some_P7363390416028606310at_nat B2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt7606875699174042974t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option4927543243414619207at_nat) (P tptp.fun_op9100744243108201484t_bool) (Y tptp.option_nat)) (let ((_let_1 (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt5915962183577952389t_bool P X) Y)))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.nat)) (=> (= X (tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (tptp.some_nat B2)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt5915962183577952389t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option4927543243414619207at_nat) (P tptp.fun_op775672374849087042m_bool) (Y tptp.option_num)) (let ((_let_1 (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt9110142220287573435m_bool P X) Y)))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.product_prod_nat_nat) (B2 tptp.num)) (=> (= X (tptp.some_P7363390416028606310at_nat A3)) (=> (= Y (tptp.some_num B2)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt9110142220287573435m_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_nat) (P tptp.fun_op5698422665285572208t_bool) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt9009324110926966577t_bool P X) Y)))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.product_prod_nat_nat)) (=> (= X (tptp.some_nat A3)) (=> (= Y (tptp.some_P7363390416028606310at_nat B2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt9009324110926966577t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_nat) (P tptp.fun_op7792301606653096457t_bool) (Y tptp.option_nat)) (let ((_let_1 (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool P X) Y)))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= X (tptp.some_nat A3)) (=> (= Y (tptp.some_nat B2)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_nat) (P tptp.fun_op8690601775248757823m_bool) (Y tptp.option_num)) (let ((_let_1 (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt1914333813751119784m_bool P X) Y)))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= X (tptp.some_nat A3)) (=> (= Y (tptp.some_num B2)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt1914333813751119784m_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num) (P tptp.fun_op7732454363416259258t_bool) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt1819983772202877819t_bool P X) Y)))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.product_prod_nat_nat)) (=> (= X (tptp.some_num A3)) (=> (= Y (tptp.some_P7363390416028606310at_nat B2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.aa_opt1819983772202877819t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num) (P tptp.fun_op1064277265382982207t_bool) (Y tptp.option_nat)) (let ((_let_1 (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt1215501472626160296t_bool P X) Y)))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.nat)) (=> (= X (tptp.some_num A3)) (=> (= Y (tptp.some_nat B2)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt1215501472626160296t_bool P X) Y))))) _let_1))))) (forall ((X tptp.option_num) (P tptp.fun_op1962577433978643573m_bool) (Y tptp.option_num)) (let ((_let_1 (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool P X) Y)))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= X (tptp.some_num A3)) (=> (= Y (tptp.some_num B2)) (tptp.pp (tptp.aa_option_num_bool (tptp.aa_opt4409681509335781342m_bool P X) Y))))) _let_1))))) (forall ((P tptp.fun_op2627489687811228755t_bool)) (= (forall ((X_12 tptp.option4927543243414619207at_nat)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool P X_12))) (and (tptp.pp (tptp.aa_opt6800557945374683724t_bool P tptp.none_P5556105721700978146at_nat)) (forall ((X4 tptp.product_prod_nat_nat)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool P (tptp.some_P7363390416028606310at_nat X4))))))) (forall ((P tptp.fun_option_nat_bool)) (= (forall ((X_12 tptp.option_nat)) (tptp.pp (tptp.aa_option_nat_bool P X_12))) (and (tptp.pp (tptp.aa_option_nat_bool P tptp.none_nat)) (forall ((X4 tptp.nat)) (tptp.pp (tptp.aa_option_nat_bool P (tptp.some_nat X4))))))) (forall ((P tptp.fun_option_num_bool)) (= (forall ((X_12 tptp.option_num)) (tptp.pp (tptp.aa_option_num_bool P X_12))) (and (tptp.pp (tptp.aa_option_num_bool P tptp.none_num)) (forall ((X4 tptp.num)) (tptp.pp (tptp.aa_option_num_bool P (tptp.some_num X4))))))) (forall ((P tptp.fun_op2627489687811228755t_bool)) (= (exists ((X_12 tptp.option4927543243414619207at_nat)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool P X_12))) (or (tptp.pp (tptp.aa_opt6800557945374683724t_bool P tptp.none_P5556105721700978146at_nat)) (exists ((X4 tptp.product_prod_nat_nat)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool P (tptp.some_P7363390416028606310at_nat X4))))))) (forall ((P tptp.fun_option_nat_bool)) (= (exists ((X_12 tptp.option_nat)) (tptp.pp (tptp.aa_option_nat_bool P X_12))) (or (tptp.pp (tptp.aa_option_nat_bool P tptp.none_nat)) (exists ((X4 tptp.nat)) (tptp.pp (tptp.aa_option_nat_bool P (tptp.some_nat X4))))))) (forall ((P tptp.fun_option_num_bool)) (= (exists ((X_12 tptp.option_num)) (tptp.pp (tptp.aa_option_num_bool P X_12))) (or (tptp.pp (tptp.aa_option_num_bool P tptp.none_num)) (exists ((X4 tptp.num)) (tptp.pp (tptp.aa_option_num_bool P (tptp.some_num X4))))))) (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y (tptp.some_P7363390416028606310at_nat X23))))))) (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y (tptp.some_nat X23))))))) (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (tptp.some_num X23))))))) (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))) (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (tptp.some_nat X22)) (not (= Option tptp.none_nat)))) (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (tptp.some_num X22)) (not (= Option tptp.none_num)))) (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (tptp.some_P7363390416028606310at_nat X22)))) (forall ((X22 tptp.nat)) (not (= tptp.none_nat (tptp.some_nat X22)))) (forall ((X22 tptp.num)) (not (= tptp.none_num (tptp.some_num X22)))) (forall ((M tptp.nat) (N2 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 N2) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 N2)) Q2)))) (forall ((X22 tptp.product_prod_nat_nat)) (= (tptp.the_Pr8591224930841456533at_nat (tptp.some_P7363390416028606310at_nat X22)) X22)) (forall ((X22 tptp.nat)) (= (tptp.the_nat (tptp.some_nat X22)) X22)) (forall ((X22 tptp.num)) (= (tptp.the_num (tptp.some_num X22)) X22)) (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (tptp.the_nat Option) (tptp.the_nat Option2)))) (= Option Option2)))))) (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (tptp.the_Pr8591224930841456533at_nat Option) (tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))) (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (tptp.the_num Option) (tptp.the_num Option2)))) (= Option Option2)))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (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))) N2)))) (forall ((M tptp.nat) (N2 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)))) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2) _let_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))) (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 ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_num_real tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one)) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex tptp.one)) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real tptp.one)) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one)) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) A) A)) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N2))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N2))) (= (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) (tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_num_real tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one)) A)) (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex 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) N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 N2))))) (forall ((A tptp.real) (M tptp.nat) (N2 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) N2)) (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 N2))))) (forall ((A tptp.rat) (M tptp.nat) (N2 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) N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 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) N2)) (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 N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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) N2)) (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 N2))))) (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (tptp.some_P7363390416028606310at_nat (tptp.the_Pr8591224930841456533at_nat Option))))) (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (tptp.some_nat (tptp.the_nat Option))))) (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (tptp.some_num (tptp.the_num Option))))) (forall ((A tptp.complex) (N2 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_com8181001469867462503omplex 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) N2))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_nat_complex _let_2 N2)) _let_1)))))) (forall ((A tptp.real) (N2 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) N2))) (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 N2)) _let_1)))))) (forall ((A tptp.rat) (N2 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) N2))) (tptp.aa_rat_rat (tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_nat_rat _let_2 N2)) _let_1)))))) (forall ((A tptp.nat) (N2 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) N2))) (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 N2)) _let_1)))))) (forall ((A tptp.int) (N2 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_int_fun_nat_int 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) N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int _let_2 N2)) _let_1)))))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N2))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N2))) (= (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)))) (forall ((N2 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 N2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (forall ((N2 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 N2))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_int tptp.numeral_numeral_int N2))) (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Z))) (let ((_let_2 (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_2) _let_2))))) (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real Z))) (let ((_let_2 (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_2))))) (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.power_power_rat Z))) (let ((_let_2 (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_rat_rat (tptp.times_times_rat _let_2) _let_2))))) (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Z))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) _let_2))))) (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int Z))) (let ((_let_2 (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_2))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex _let_1 B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A)) B)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Z) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Z) Z))) (forall ((Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat Z) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_rat_rat (tptp.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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Z) Z))) (forall ((Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (tptp.aa_rat_rat (tptp.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 ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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.aa_com3342990543769683525omplex 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.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.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A))) (forall ((X tptp.complex)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_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.aa_int_fun_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.nat) (N2 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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat _let_2 N2)) _let_1))))) (forall ((A tptp.real) (N2 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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real _let_2 N2)) _let_1))))) (forall ((A tptp.int) (N2 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_int_fun_nat_int 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) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int _let_2 N2)) _let_1))))) (forall ((A tptp.complex) (N2 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_com8181001469867462503omplex 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) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_nat_complex _let_2 N2)) _let_1))))) (forall ((N2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5917875025757280293ildren N2 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) N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) N2))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((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) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat _let_2 M)) (=> (= M (tptp.aa_nat_nat tptp.suc N2)) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat _let_2 Deg))) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.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) N2) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma) N2)))) (forall ((X3 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X3) N2) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X3) N2)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Ma))))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) Deg))))))))))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((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) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat _let_2 M)) (=> (= M N2) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) (tptp.aa_nat_nat _let_2 Deg))) (=> (=> (not _let_1) (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.aa_nat_nat (tptp.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) N2) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma) N2)))) (forall ((X3 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X3) N2) I3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList I3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X3) N2)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Ma))))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) Deg))))))))))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (= (tptp.vEBT_vebt_succ (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) tptp.none_nat)))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) tptp.none_nat)))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (tptp.the_nat (tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2) _let_3))) (let ((_let_6 (tptp.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_4) _let_5)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList _let_4)))))) (let ((_let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_6) _let_3))) (let ((_let_8 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList _let_7) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_6) _let_3)))) (let ((_let_9 (tptp.list_u1324408373059187874T_VEBT TreeList _let_7 _let_8))) (let ((_let_10 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat _let_6) Ma)))) (let ((_let_11 (tptp.product_Pair_nat_nat _let_6))) (let ((_let_12 (tptp.vEBT_vebt_delete Summary _let_7))) (let ((_let_13 (tptp.vEBT_vebt_maxt _let_12))) (let ((_let_14 (tptp.the_nat _let_13))) (=> (and (= X Mi) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) Deg)) (= (tptp.vEBT_vebt_delete _let_1 X) (tptp.if_VEBT_VEBT (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_7) (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_8) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_10 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_13) tptp.none_nat)) _let_6) (tptp.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_5) _let_14)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_9 _let_14)))))) Ma))) Deg _let_9 _let_12) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_10 (tptp.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_7) _let_5)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_9 _let_7))))) Ma))) Deg _let_9 Summary)) _let_1)))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (tptp.the_nat _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xn) _let_4))) (let ((_let_7 (tptp.the_nat (tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) Deg)) (=> (= _let_6 H) (=> (= Xn (tptp.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_7) _let_5)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList _let_7))))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xn) _let_4) L) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_6) (tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (= Newnode (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList H) L)) (=> (= Newlist (tptp.list_u1324408373059187874T_VEBT TreeList H Newnode)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull Newnode)) (=> (= Sn (tptp.vEBT_vebt_delete Summary H)) (= (tptp.vEBT_vebt_delete (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xn) (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 Xn) Ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_1) tptp.none_nat)) Xn) (tptp.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_5) _let_2)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT Newlist _let_2)))))) Ma))) Deg Newlist Sn))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))) (let ((_let_4 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Xn) Ma)))) (let ((_let_5 (tptp.product_Pair_nat_nat Xn))) (let ((_let_6 (tptp.vEBT_vebt_delete (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X))) (let ((_let_7 (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull Newnode)))) (let ((_let_8 (tptp.vEBT_vebt_delete Summary H))) (let ((_let_9 (tptp.vEBT_vebt_maxt _let_8))) (let ((_let_10 (tptp.the_nat _let_9))) (let ((_let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xn) _let_2))) (let ((_let_12 (tptp.the_nat (tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (= _let_11 H) (=> (= Xn (tptp.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_12) _let_3)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList _let_12))))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xn) _let_2) L) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_11) (tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (= Newnode (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList H) L)) (=> (= Newlist (tptp.list_u1324408373059187874T_VEBT TreeList H Newnode)) (and (=> _let_7 (= _let_6 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat)) Xn) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) _let_10)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT Newlist _let_10)))))) Ma))) Deg Newlist _let_8))) (=> (not _let_7) (= _let_6 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat H) _let_3)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT Newlist H))))) Ma))) Deg Newlist Summary)))))))))))))))))))))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat)) (let ((_let_1 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList H) L))) (let ((_let_2 (tptp.list_u1324408373059187874T_VEBT TreeList H _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Xn) Ma)))) (let ((_let_7 (tptp.product_Pair_nat_nat Xn))) (let ((_let_8 (tptp.vEBT_vebt_delete Summary H))) (let ((_let_9 (tptp.vEBT_vebt_maxt _let_8))) (let ((_let_10 (tptp.the_nat _let_9))) (let ((_let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xn) _let_4))) (let ((_let_12 (tptp.the_nat (tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) Deg)) (=> (= _let_11 H) (=> (= Xn (tptp.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_12) _let_5)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList _let_12))))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xn) _let_4) L) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_11) (tptp.size_s6755466524823107622T_VEBT TreeList))) (= (tptp.vEBT_vebt_delete (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_1) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat)) Xn) (tptp.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_5) _let_10)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_2 _let_10)))))) Ma))) Deg _let_2 _let_8) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat H) _let_5)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_2 H))))) Ma))) Deg _let_2 Summary))))))))))))))))))))))) (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (tptp.the_nat (tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2) _let_3))) (let ((_let_6 (tptp.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_4) _let_5)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList _let_4)))))) (let ((_let_7 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X))) (let ((_let_8 (tptp.aa_nat_bool _let_7 Mi))) (let ((_let_9 (tptp.if_nat _let_8))) (let ((_let_10 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_9 _let_6) X))) (let ((_let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_10) _let_3))) (let ((_let_12 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList _let_11) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_10) _let_3)))) (let ((_let_13 (tptp.list_u1324408373059187874T_VEBT TreeList _let_11 _let_12))) (let ((_let_14 (tptp.if_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies _let_8) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat _let_6) Ma))) (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies (tptp.aa_bool_bool tptp.fNot _let_8)) (tptp.aa_nat_bool _let_7 Ma)))))) (let ((_let_15 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_9 _let_10) Mi))) (let ((_let_16 (tptp.product_Pair_nat_nat _let_15))) (let ((_let_17 (tptp.vEBT_vebt_delete Summary _let_11))) (let ((_let_18 (tptp.vEBT_vebt_maxt _let_17))) (let ((_let_19 (tptp.the_nat _let_18))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) Deg)) (= (tptp.vEBT_vebt_delete _let_1 X) (tptp.if_VEBT_VEBT (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_11) (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_12) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_16 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_14 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_18) tptp.none_nat)) _let_15) (tptp.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_5) _let_19)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_13 _let_19)))))) Ma))) Deg _let_13 _let_17) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_16 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_14 (tptp.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_11) _let_5)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_13 _let_11))))) Ma))) Deg _let_13 Summary)) _let_1))))))))))))))))))))))))) (and (=> _let_163 (= _let_5 (tptp.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_166) _let_14)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT tptp.treeList _let_166)))))) (=> _let_164 (= _let_5 tptp.xa))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList tptp.list_VEBT_VEBT) (L tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xn) _let_2))) (let ((_let_5 (tptp.the_nat (tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Ma))) (=> (not (= Mi Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (= _let_4 H) (=> (= Xn (tptp.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_5) _let_3)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList _let_5))))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xn) _let_2) L) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (= Newnode (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList H) L)) (=> (= Newlist (tptp.list_u1324408373059187874T_VEBT TreeList H Newnode)) (=> (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull Newnode))) (= (tptp.vEBT_vebt_delete (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xn) (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 Xn) Ma)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat H) _let_3)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT Newlist H))))) Ma))) Deg Newlist Summary)))))))))))))))))) (forall ((T tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull T)) (= (tptp.vEBT_vebt_mint T) tptp.none_nat))) (forall ((T tptp.vEBT_VEBT)) (=> (= (tptp.vEBT_vebt_mint T) tptp.none_nat) (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull T)))) (not (forall ((Summin tptp.nat)) (not (= (tptp.some_nat Summin) (tptp.vEBT_vebt_mint tptp.summary))))) (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)))) (not (forall ((Lx tptp.nat)) (not (= (tptp.some_nat Lx) (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT tptp.treeList tptp.summin)))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt _let_1) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Ma) X)) (= (tptp.vEBT_vebt_succ _let_1 X) tptp.none_nat))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.some_nat M) (tptp.vEBT_vebt_mint T)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_succ T X) (tptp.some_nat Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) (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))) N2)))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_pred T X) (tptp.some_nat Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) (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))) N2)))))) (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) X)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.some_nat Ma))))) (forall ((Deg tptp.nat) (X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi)) (= (tptp.vEBT_vebt_succ (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.some_nat Mi))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat) (Va tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (tptp.the_nat (tptp.vEBT_vebt_mint Summary)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) N2)) (=> (= N2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) Mi))) (=> (not (= Ma Mi)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)))) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList _let_3))))) (tptp.aa_nat_nat tptp.suc _let_2))) (tptp.size_s6755466524823107622T_VEBT TreeList))))))))))) (= tptp.vEBT_VEBT_power (tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)) (forall ((X tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) tptp.one)) (= X tptp.one))) (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X3) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (=> (= M N2) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) X_1)))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList Summary)) Deg)))))))))) (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X3) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary) M)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (=> (= M (tptp.aa_nat_nat tptp.suc N2)) (=> (= Deg (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary) X_1)))) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList))) (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X3) X_1)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList Summary)) Deg)))))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_mint T) (tptp.some_nat X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_min_in_set (tptp.vEBT_VEBT_set_vebt T)) X))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_min_in_set (tptp.vEBT_VEBT_set_vebt T)) X)) (= (tptp.vEBT_vebt_mint T) (tptp.some_nat X))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_max_in_set (tptp.vEBT_VEBT_set_vebt T)) X))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_max_in_set (tptp.vEBT_VEBT_set_vebt T)) X)) (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat X))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_1 TreeList Summary))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (tptp.the_nat (tptp.vEBT_vebt_mint Summary)))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (let ((_let_7 (tptp.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_5) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList _let_5)))))) (let ((_let_8 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X))) (let ((_let_9 (tptp.aa_nat_bool _let_8 Mi))) (let ((_let_10 (tptp.if_nat _let_9))) (let ((_let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_10 _let_7) X))) (let ((_let_12 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList _let_12) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (tptp.list_u1324408373059187874T_VEBT TreeList _let_12 _let_13))) (let ((_let_15 (tptp.if_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies _let_9) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat _let_7) Ma))) (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies (tptp.aa_bool_bool tptp.fNot _let_9)) (tptp.aa_nat_bool _let_8 Ma)))))) (let ((_let_16 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_10 _let_11) Mi))) (let ((_let_17 (tptp.product_Pair_nat_nat _let_16))) (let ((_let_18 (tptp.vEBT_vebt_delete Summary _let_12))) (let ((_let_19 (tptp.vEBT_vebt_maxt _let_18))) (let ((_let_20 (tptp.the_nat _let_19))) (let ((_let_21 (tptp.vEBT_vebt_delete _let_2 X))) (let ((_let_22 (and (= X Mi) (= X Ma)))) (let ((_let_23 (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) X))))) (and (=> _let_23 (= _let_21 _let_2)) (=> (not _let_23) (and (=> _let_22 (= _let_21 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList Summary))) (=> (not _let_22) (= _let_21 (tptp.if_VEBT_VEBT (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_12) (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_13) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_17 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_15 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_19) tptp.none_nat)) _let_16) (tptp.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_6) _let_20)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_14 _let_20)))))) Ma))) _let_1 _let_14 _let_18) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_17 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_15 (tptp.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_12) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_14 _let_12))))) Ma))) _let_1 _let_14 Summary)) _let_2)))))))))))))))))))))))))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_vebt_insert T X)) X))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_vebt_insert T Y)) X)))))))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary))) (=> (or (= X Mi) (= X Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Deg)) (= (tptp.vEBT_vebt_insert _let_1 X) _let_1))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) X)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (or (= X Mi) (= X Ma) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Ma)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))))))))))) (forall ((I2 tptp.nat) (Xs tptp.list_nat) (J tptp.nat)) (let ((_let_1 (tptp.nth_nat Xs))) (let ((_let_2 (tptp.size_size_list_nat Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) _let_2)) (= (tptp.set_nat2 (tptp.list_update_nat (tptp.list_update_nat Xs I2 (tptp.aa_nat_nat _let_1 J)) J (tptp.aa_nat_nat _let_1 I2))) (tptp.set_nat2 Xs))))))) (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat)) (let ((_let_1 (tptp.size_s6755466524823107622T_VEBT Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) _let_1)) (= (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I2 (tptp.nth_VEBT_VEBT Xs J)) J (tptp.nth_VEBT_VEBT Xs I2))) (tptp.set_VEBT_VEBT2 Xs)))))) (forall ((I2 tptp.nat) (Xs tptp.list_bool) (J tptp.nat)) (let ((_let_1 (tptp.nth_bool Xs))) (let ((_let_2 (tptp.size_size_list_bool Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) _let_2)) (= (tptp.set_bool2 (tptp.list_update_bool (tptp.list_update_bool Xs I2 (tptp.aa_nat_bool _let_1 J)) J (tptp.aa_nat_bool _let_1 I2))) (tptp.set_bool2 Xs))))))) (forall ((I2 tptp.nat) (Xs tptp.list_int) (J tptp.nat)) (let ((_let_1 (tptp.nth_int Xs))) (let ((_let_2 (tptp.size_size_list_int Xs))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) _let_2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J) _let_2)) (= (tptp.set_int2 (tptp.list_update_int (tptp.list_update_int Xs I2 (tptp.aa_nat_int _let_1 J)) J (tptp.aa_nat_int _let_1 I2))) (tptp.set_int2 Xs))))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_1))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) X)))))))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull T)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X))))) (forall ((T tptp.vEBT_VEBT)) (= (tptp.vEBT_VEBT_set_vebt T) (tptp.collect_nat (tptp.vEBT_vebt_member T)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X))))) (tptp.pp (tptp.aa_nat_bool _let_147 tptp.na)) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat Maxi)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Maxi))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_mint T) (tptp.some_nat Maxi)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Maxi))))) (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (tptp.list_u1324408373059187874T_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I2 X) I2 Y) (tptp.list_u1324408373059187874T_VEBT Xs I2 Y))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_maxt T) (tptp.some_nat Maxi)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Maxi)))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_mint T) (tptp.some_nat Mini)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mini) X)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member _let_162) tptp.lx)) (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member Tree) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Tree) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member tptp.summary) _let_161)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.one_one_rat) N2) tptp.one_one_rat)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.one_one_nat) N2) tptp.one_one_nat)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.one_one_real) N2) tptp.one_one_real)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int tptp.one_one_int) N2) tptp.one_one_int)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.one_one_complex) N2) 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.aa_int_fun_nat_int tptp.power_power_int A) tptp.one_one_nat) A)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) tptp.one_one_nat) A)) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) _let_1)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_vebt_insert T X)) Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Y)) (= X Y)))))))) (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (= (tptp.size_s6755466524823107622T_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I2 X)) (tptp.size_s6755466524823107622T_VEBT Xs))) (forall ((Xs tptp.list_bool) (I2 tptp.nat) (X tptp.bool)) (= (tptp.size_size_list_bool (tptp.list_update_bool Xs I2 X)) (tptp.size_size_list_bool Xs))) (forall ((Xs tptp.list_int) (I2 tptp.nat) (X tptp.int)) (= (tptp.size_size_list_int (tptp.list_update_int Xs I2 X)) (tptp.size_size_list_int Xs))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) X)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.vEBT_set_vebt T)))))) (forall ((I2 tptp.nat) (J tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (not (= I2 J)) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.list_update_nat Xs I2 X)) J) (tptp.aa_nat_nat (tptp.nth_nat Xs) J)))) (forall ((I2 tptp.nat) (J tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (not (= I2 J)) (= (tptp.aa_nat_int (tptp.nth_int (tptp.list_update_int Xs I2 X)) J) (tptp.aa_nat_int (tptp.nth_int Xs) J)))) (forall ((I2 tptp.nat) (J tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (not (= I2 J)) (= (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I2 X) J) (tptp.nth_VEBT_VEBT Xs J)))) (forall ((Xs tptp.list_nat) (I2 tptp.nat)) (= (tptp.list_update_nat Xs I2 (tptp.aa_nat_nat (tptp.nth_nat Xs) I2)) Xs)) (forall ((Xs tptp.list_int) (I2 tptp.nat)) (= (tptp.list_update_int Xs I2 (tptp.aa_nat_int (tptp.nth_int Xs) I2)) Xs)) (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat)) (= (tptp.list_u1324408373059187874T_VEBT Xs I2 (tptp.nth_VEBT_VEBT Xs I2)) Xs)) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (tptp.vEBT_set_vebt T) (tptp.vEBT_VEBT_set_vebt T)))) (forall ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X3) N2)))) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2))))) (forall ((N2 tptp.num)) (= (= tptp.one_one_complex (tptp.numera6690914467698888265omplex N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_real (tptp.aa_num_real tptp.numeral_numeral_real N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= (tptp.numera6690914467698888265omplex N2) tptp.one_one_complex) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_num_real tptp.numeral_numeral_real N2) tptp.one_one_real) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_num_rat tptp.numeral_numeral_rat N2) tptp.one_one_rat) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_num_nat tptp.numeral_numeral_nat N2) tptp.one_one_nat) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_num_int tptp.numeral_numeral_int N2) tptp.one_one_int) (= N2 tptp.one))) (forall ((A tptp.real) (M tptp.nat) (N2 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 N2)) (= M N2))))) (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2)) (= M N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (= M N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2)) (= M N2))))) (forall ((Xs tptp.list_VEBT_VEBT) (I2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s6755466524823107622T_VEBT Xs)) I2)) (= (tptp.list_u1324408373059187874T_VEBT Xs I2 X) Xs))) (forall ((Xs tptp.list_bool) (I2 tptp.nat) (X tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_bool Xs)) I2)) (= (tptp.list_update_bool Xs I2 X) Xs))) (forall ((Xs tptp.list_int) (I2 tptp.nat) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_int Xs)) I2)) (= (tptp.list_update_int Xs I2 X) Xs))) (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) X)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_1))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_1))) (= X Mi) (= X Ma)))))) (forall ((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.aa_int_fun_nat_int 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 ((I2 tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.list_update_nat Xs I2 X)) I2) X))) (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I2 X) I2) X))) (forall ((I2 tptp.nat) (Xs tptp.list_bool) (X tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool (tptp.list_update_bool Xs I2 X)) I2)) (tptp.pp X)))) (forall ((I2 tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int (tptp.list_update_int Xs I2 X)) I2) X))) (= (tptp.aa_complex_complex _let_45 tptp.one_one_complex) _let_46) (= _let_141 _let_23) (= _let_140 _let_65) _let_159 (= _let_137 _let_40) (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.aa_int_fun_nat_int 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)))))) (= (tptp.aa_nat_nat tptp.suc tptp.one_one_nat) _let_2) (forall ((N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex tptp.one_one_complex) (tptp.numera6690914467698888265omplex N2)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real N2)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 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 N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 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 N2)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.numera6690914467698888265omplex N2)) tptp.one_one_complex) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_num_real tptp.numeral_numeral_real N2)) tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real N2)) tptp.one_one_real)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) tptp.one_one_rat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) tptp.one)))) (forall ((N2 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 N2)) tptp.one_one_nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) tptp.one)))) (forall ((N2 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 N2)) tptp.one_one_int)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N2)))) (forall ((N2 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 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N2)))) (forall ((N2 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 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) N2)))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set (tptp.vEBT_VEBT_set_vebt T)) X) Y)) (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (forall ((Z2 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Z2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z2) X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z2) Y))))))) (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_succ_in_set (tptp.vEBT_VEBT_set_vebt T)) X) Y)) (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (forall ((Z2 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member T) Z2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Z2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) Z2))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (= (tptp.vEBT_vebt_succ T X) (tptp.some_nat Sx)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_succ_in_set (tptp.vEBT_VEBT_set_vebt T)) X) Sx))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Px tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (= (tptp.vEBT_vebt_pred T X) (tptp.some_nat Px)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set (tptp.vEBT_VEBT_set_vebt T)) X) Px))))) (tptp.pp (tptp.aa_real_bool _let_108 tptp.one_one_real)) (tptp.pp (tptp.aa_rat_bool _let_107 tptp.one_one_rat)) (tptp.pp (tptp.aa_nat_bool _let_147 tptp.one_one_nat)) (tptp.pp (tptp.aa_int_bool _let_106 tptp.one_one_int)) (not (tptp.pp (tptp.aa_real_bool _let_105 tptp.one_one_real))) (not (tptp.pp (tptp.aa_rat_bool _let_103 tptp.one_one_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_146 tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool _let_104 tptp.one_one_int))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((N2 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 N2)))) (forall ((N2 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 N2)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real N2)) tptp.one_one_real)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) tptp.one_one_rat)))) (forall ((N2 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 N2)) tptp.one_one_nat)))) (forall ((N2 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 N2)) tptp.one_one_int)))) (= _let_88 tptp.one_one_complex) (= _let_90 tptp.one_one_real) (= _let_87 tptp.one_one_rat) _let_160 (= _let_89 tptp.one_one_int) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex X))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex tptp.one_one_complex) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) tptp.one_one_complex)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.plus_plus_rat tptp.one_one_rat) _let_1) (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) tptp.one_one_rat)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))) (forall ((A tptp.real) (N2 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) N2)))))) (forall ((A tptp.rat) (N2 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) N2)))))) (forall ((A tptp.nat) (N2 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) N2)))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) N2)))))) (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y) tptp.one_one_complex) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Y) N2)) tptp.one_one_complex))) (forall ((X tptp.real) (Y tptp.real) (N2 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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N2)) tptp.one_one_real))) (forall ((X tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (=> (= (tptp.aa_rat_rat (tptp.times_times_rat X) Y) tptp.one_one_rat) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat X) N2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) N2)) tptp.one_one_rat))) (forall ((X tptp.nat) (Y tptp.nat) (N2 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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) N2)) tptp.one_one_nat))) (forall ((X tptp.int) (Y tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int X) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) N2)) tptp.one_one_int))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex _let_1 A)) N2) (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2))))) (forall ((A tptp.real) (N2 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)) N2) (tptp.aa_real_real _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.divide_divide_rat tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat _let_1 A)) N2) (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))))) _let_160 (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))) (=> (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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (=> (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.times_times_rat A) _let_1)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))) (=> (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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_1)))))) (forall ((A tptp.real) (N2 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) N2))))))) (forall ((A tptp.rat) (N2 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.times_times_rat A) (tptp.aa_nat_rat (tptp.power_power_rat A) N2))))))) (forall ((A tptp.nat) (N2 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) N2))))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) N2))))))) (forall ((A tptp.real) (N2 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 N2))))))) (forall ((A tptp.rat) (N2 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 N2))))))) (forall ((A tptp.nat) (N2 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 N2))))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real _let_1 N2)) (tptp.aa_nat_real _let_1 N3))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_nat_rat _let_1 N3))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 N3))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 N2)) (tptp.aa_nat_int _let_1 N3))))))) (forall ((A tptp.real) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real _let_1 N2)) (tptp.aa_nat_real _let_1 N3))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_nat_rat _let_1 N3))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 N3))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 N2)) (tptp.aa_nat_int _let_1 N3))))))) (forall ((Xs tptp.list_complex) (B3 tptp.set_complex)) (= (tptp.ord_le211207098394363844omplex (tptp.set_complex2 Xs) B3) (forall ((X4 tptp.complex)) (=> (tptp.member_complex X4 (tptp.set_complex2 Xs)) (tptp.member_complex X4 B3))))) (forall ((Xs tptp.list_real) (B3 tptp.set_real)) (= (tptp.ord_less_eq_set_real (tptp.set_real2 Xs) B3) (forall ((X4 tptp.real)) (=> (tptp.member_real X4 (tptp.set_real2 Xs)) (tptp.member_real X4 B3))))) (forall ((Xs tptp.list_set_nat) (B3 tptp.set_set_nat)) (= (tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat2 Xs) B3) (forall ((X4 tptp.set_nat)) (=> (tptp.member_set_nat X4 (tptp.set_set_nat2 Xs)) (tptp.member_set_nat X4 B3))))) (forall ((Xs tptp.list_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 Xs)) B3)) (forall ((X4 tptp.nat)) (let ((_let_1 (tptp.member_nat X4))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((Xs tptp.list_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (= (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 Xs) B3) (forall ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4))) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool _let_1 (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_set8260762808118238015T_bool _let_1 B3))))))) (forall ((Xs tptp.list_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int (tptp.set_int2 Xs) B3) (forall ((X4 tptp.int)) (=> (tptp.member_int X4 (tptp.set_int2 Xs)) (tptp.member_int X4 B3))))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (tptp.size_s6755466524823107622T_VEBT Xs2) N2))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_bool)) (= (tptp.size_size_list_bool Xs2) N2))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (tptp.size_size_list_int Xs2) N2))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (tptp.size_s6755466524823107622T_VEBT Xs) (tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_bool)) (=> (not (= (tptp.size_size_list_bool Xs) (tptp.size_size_list_bool Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (tptp.size_size_list_int Xs) (tptp.size_size_list_int Ys))) (not (= Xs Ys)))) (forall ((I2 tptp.nat) (I4 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (X5 tptp.vEBT_VEBT)) (=> (not (= I2 I4)) (= (tptp.list_u1324408373059187874T_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I2 X) I4 X5) (tptp.list_u1324408373059187874T_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I4 X5) I2 X)))) (forall ((A tptp.real) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (= (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.aa_int_fun_nat_int tptp.power_power_int tptp.one_one_int) _let_2) tptp.one_one_int) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.one_one_complex) _let_2) tptp.one_one_complex) _let_159 (forall ((P tptp.fun_li6006399982103069984T_bool) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_s6755466524823107622T_VEBT Ys2)) (tptp.size_s6755466524823107622T_VEBT Xs2))) (tptp.pp (tptp.aa_lis2822252094023462681T_bool P Ys2)))) (tptp.pp (tptp.aa_lis2822252094023462681T_bool P Xs2)))) (tptp.pp (tptp.aa_lis2822252094023462681T_bool P Xs)))) (forall ((P tptp.fun_list_bool_bool) (Xs tptp.list_bool)) (=> (forall ((Xs2 tptp.list_bool)) (=> (forall ((Ys2 tptp.list_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_bool Ys2)) (tptp.size_size_list_bool Xs2))) (tptp.pp (tptp.aa_list_bool_bool P Ys2)))) (tptp.pp (tptp.aa_list_bool_bool P Xs2)))) (tptp.pp (tptp.aa_list_bool_bool P Xs)))) (forall ((P tptp.fun_list_int_bool) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_int Ys2)) (tptp.size_size_list_int Xs2))) (tptp.pp (tptp.aa_list_int_bool P Ys2)))) (tptp.pp (tptp.aa_list_int_bool P Xs2)))) (tptp.pp (tptp.aa_list_int_bool P Xs)))) (forall ((Xs tptp.list_complex) (A2 tptp.set_complex) (X tptp.complex) (I2 tptp.nat)) (=> (tptp.ord_le211207098394363844omplex (tptp.set_complex2 Xs) A2) (=> (tptp.member_complex X A2) (tptp.ord_le211207098394363844omplex (tptp.set_complex2 (tptp.list_update_complex Xs I2 X)) A2)))) (forall ((Xs tptp.list_real) (A2 tptp.set_real) (X tptp.real) (I2 tptp.nat)) (=> (tptp.ord_less_eq_set_real (tptp.set_real2 Xs) A2) (=> (tptp.member_real X A2) (tptp.ord_less_eq_set_real (tptp.set_real2 (tptp.list_update_real Xs I2 X)) A2)))) (forall ((Xs tptp.list_set_nat) (A2 tptp.set_set_nat) (X tptp.set_nat) (I2 tptp.nat)) (=> (tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat2 Xs) A2) (=> (tptp.member_set_nat X A2) (tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat2 (tptp.list_update_set_nat Xs I2 X)) A2)))) (forall ((Xs tptp.list_nat) (A2 tptp.set_nat) (X tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 Xs)) A2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) A2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 (tptp.list_update_nat Xs I2 X))) A2))))) (forall ((Xs tptp.list_VEBT_VEBT) (A2 tptp.set_VEBT_VEBT) (X tptp.vEBT_VEBT) (I2 tptp.nat)) (=> (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 Xs) A2) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) A2)) (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT Xs I2 X)) A2)))) (forall ((Xs tptp.list_int) (A2 tptp.set_int) (X tptp.int) (I2 tptp.nat)) (=> (tptp.ord_less_eq_set_int (tptp.set_int2 Xs) A2) (=> (tptp.member_int X A2) (tptp.ord_less_eq_set_int (tptp.set_int2 (tptp.list_update_int Xs I2 X)) A2)))) (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 ((N 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 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) (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 ((N 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 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 ((Xs tptp.list_nat) (Ys tptp.list_nat)) (= (= Xs Ys) (and (= (tptp.size_size_list_nat Xs) (tptp.size_size_list_nat Ys)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I5) (tptp.aa_nat_nat (tptp.nth_nat Ys) I5))))))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (= Xs Ys) (and (= (tptp.size_s6755466524823107622T_VEBT Xs) (tptp.size_s6755466524823107622T_VEBT Ys)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (tptp.nth_VEBT_VEBT Xs I5) (tptp.nth_VEBT_VEBT Ys I5))))))) (forall ((Xs tptp.list_bool) (Ys tptp.list_bool)) (= (= Xs Ys) (and (= (tptp.size_size_list_bool Xs) (tptp.size_size_list_bool Ys)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I5)) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Ys) I5)))))))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (= Xs Ys) (and (= (tptp.size_size_list_int Xs) (tptp.size_size_list_int Ys)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int Xs) I5) (tptp.aa_nat_int (tptp.nth_int Ys) I5))))))) (forall ((K tptp.nat) (P tptp.fun_nat_fun_nat_bool)) (= (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) K)) (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I5) X_12))))) (exists ((Xs3 tptp.list_nat)) (and (= (tptp.size_size_list_nat Xs3) K) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I5) (tptp.aa_nat_nat (tptp.nth_nat Xs3) I5))))))))) (forall ((K tptp.nat) (P tptp.fun_na2351039247863542899T_bool)) (= (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) K)) (exists ((X_12 tptp.vEBT_VEBT)) (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.aa_nat8029987864780243636T_bool P I5) X_12))))) (exists ((Xs3 tptp.list_VEBT_VEBT)) (and (= (tptp.size_s6755466524823107622T_VEBT Xs3) K) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) K)) (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.aa_nat8029987864780243636T_bool P I5) (tptp.nth_VEBT_VEBT Xs3 I5))))))))) (forall ((K tptp.nat) (P tptp.fun_na9137082442855928016l_bool)) (= (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) K)) (exists ((X_12 tptp.bool)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool P I5) X_12))))) (exists ((Xs3 tptp.list_bool)) (and (= (tptp.size_size_list_bool Xs3) K) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) K)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_nat_fun_bool_bool P I5) (tptp.aa_nat_bool (tptp.nth_bool Xs3) I5))))))))) (forall ((K tptp.nat) (P tptp.fun_nat_fun_int_bool)) (= (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) K)) (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool P I5) X_12))))) (exists ((Xs3 tptp.list_int)) (and (= (tptp.size_size_list_int Xs3) K) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool P I5) (tptp.aa_nat_int (tptp.nth_int Xs3) I5))))))))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (tptp.size_size_list_nat Xs) (tptp.size_size_list_nat Ys)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I3) (tptp.aa_nat_nat (tptp.nth_nat Ys) I3)))) (= Xs Ys)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (tptp.size_s6755466524823107622T_VEBT Xs) (tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (tptp.nth_VEBT_VEBT Xs I3) (tptp.nth_VEBT_VEBT Ys I3)))) (= Xs Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_bool)) (=> (= (tptp.size_size_list_bool Xs) (tptp.size_size_list_bool Ys)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Ys) I3))))) (= Xs Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (tptp.size_size_list_int Xs) (tptp.size_size_list_int Ys)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int Xs) I3) (tptp.aa_nat_int (tptp.nth_int Ys) I3)))) (= Xs Ys)))) (forall ((Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg TreeList Summary))) (= (tptp.vEBT_vebt_delete _let_1 Uu) _let_1))) (forall ((Xs tptp.list_nat) (P tptp.fun_nat_bool)) (= (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_nat_bool P X4)))) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat Xs) I5))))))) (forall ((Xs tptp.list_VEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X4)))) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT Xs I5))))))) (forall ((Xs tptp.list_bool) (P tptp.fun_bool_bool)) (= (forall ((X4 tptp.bool)) (=> (tptp.member_bool X4 (tptp.set_bool2 Xs)) (tptp.pp (tptp.aa_bool_bool P X4)))) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool P (tptp.aa_nat_bool (tptp.nth_bool Xs) I5))))))) (forall ((Xs tptp.list_int) (P tptp.fun_int_bool)) (= (forall ((X4 tptp.int)) (=> (tptp.member_int X4 (tptp.set_int2 Xs)) (tptp.pp (tptp.aa_int_bool P X4)))) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int Xs) I5))))))) (forall ((Xs tptp.list_complex) (P tptp.fun_complex_bool) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_s3451745648224563538omplex Xs))) (tptp.pp (tptp.aa_complex_bool P (tptp.aa_nat_complex (tptp.nth_complex Xs) I3))))) (=> (tptp.member_complex X (tptp.set_complex2 Xs)) (tptp.pp (tptp.aa_complex_bool P X))))) (forall ((Xs tptp.list_real) (P tptp.fun_real_bool) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_real Xs))) (tptp.pp (tptp.aa_real_bool P (tptp.aa_nat_real (tptp.nth_real Xs) I3))))) (=> (tptp.member_real X (tptp.set_real2 Xs)) (tptp.pp (tptp.aa_real_bool P X))))) (forall ((Xs tptp.list_set_nat) (P tptp.fun_set_nat_bool) (X tptp.set_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_s3254054031482475050et_nat Xs))) (tptp.pp (tptp.aa_set_nat_bool P (tptp.nth_set_nat Xs I3))))) (=> (tptp.member_set_nat X (tptp.set_set_nat2 Xs)) (tptp.pp (tptp.aa_set_nat_bool P X))))) (forall ((Xs tptp.list_nat) (P tptp.fun_nat_bool) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat Xs) I3))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 Xs))) (tptp.pp (tptp.aa_nat_bool P X))))) (forall ((Xs tptp.list_VEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool) (X tptp.vEBT_VEBT)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT Xs I3))))) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) (tptp.set_VEBT_VEBT2 Xs))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X))))) (forall ((Xs tptp.list_bool) (P tptp.fun_bool_bool) (X tptp.bool)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_bool Xs))) (tptp.pp (tptp.aa_bool_bool P (tptp.aa_nat_bool (tptp.nth_bool Xs) I3))))) (=> (tptp.member_bool X (tptp.set_bool2 Xs)) (tptp.pp (tptp.aa_bool_bool P X))))) (forall ((Xs tptp.list_int) (P tptp.fun_int_bool) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) (tptp.size_size_list_int Xs))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int Xs) I3))))) (=> (tptp.member_int X (tptp.set_int2 Xs)) (tptp.pp (tptp.aa_int_bool P X))))) (forall ((X tptp.complex) (Xs tptp.list_complex)) (= (tptp.member_complex X (tptp.set_complex2 Xs)) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_s3451745648224563538omplex Xs))) (= (tptp.aa_nat_complex (tptp.nth_complex Xs) I5) X))))) (forall ((X tptp.real) (Xs tptp.list_real)) (= (tptp.member_real X (tptp.set_real2 Xs)) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_real Xs))) (= (tptp.aa_nat_real (tptp.nth_real Xs) I5) X))))) (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (= (tptp.member_set_nat X (tptp.set_set_nat2 Xs)) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_s3254054031482475050et_nat Xs))) (= (tptp.nth_set_nat Xs I5) X))))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 Xs))) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_nat Xs))) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I5) X))))) (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) (tptp.set_VEBT_VEBT2 Xs))) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (tptp.nth_VEBT_VEBT Xs I5) X))))) (forall ((X tptp.bool) (Xs tptp.list_bool)) (= (tptp.member_bool X (tptp.set_bool2 Xs)) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I5)) (tptp.pp X)))))) (forall ((X tptp.int) (Xs tptp.list_int)) (= (tptp.member_int X (tptp.set_int2 Xs)) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.size_size_list_int Xs))) (= (tptp.aa_nat_int (tptp.nth_int Xs) I5) X))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_nat Xs))) (=> (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 P (tptp.aa_nat_nat (tptp.nth_nat Xs) N2)))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_s6755466524823107622T_VEBT Xs))) (=> (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_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT Xs N2)))))) (forall ((N2 tptp.nat) (Xs tptp.list_bool) (P tptp.fun_bool_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_bool Xs))) (=> (forall ((X3 tptp.bool)) (=> (tptp.member_bool X3 (tptp.set_bool2 Xs)) (tptp.pp (tptp.aa_bool_bool P X3)))) (tptp.pp (tptp.aa_bool_bool P (tptp.aa_nat_bool (tptp.nth_bool Xs) N2)))))) (forall ((N2 tptp.nat) (Xs tptp.list_int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_int Xs))) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.set_int2 Xs)) (tptp.pp (tptp.aa_int_bool P X3)))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int Xs) N2)))))) (forall ((N2 tptp.nat) (Xs tptp.list_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_s3451745648224563538omplex Xs))) (tptp.member_complex (tptp.aa_nat_complex (tptp.nth_complex Xs) N2) (tptp.set_complex2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_real Xs))) (tptp.member_real (tptp.aa_nat_real (tptp.nth_real Xs) N2) (tptp.set_real2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_set_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_s3254054031482475050et_nat Xs))) (tptp.member_set_nat (tptp.nth_set_nat Xs N2) (tptp.set_set_nat2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat (tptp.nth_nat Xs) N2)) (tptp.set_nat2 Xs))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT (tptp.nth_VEBT_VEBT Xs N2)) (tptp.set_VEBT_VEBT2 Xs))))) (forall ((N2 tptp.nat) (Xs tptp.list_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_bool Xs))) (tptp.member_bool (tptp.aa_nat_bool (tptp.nth_bool Xs) N2) (tptp.set_bool2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_int Xs))) (tptp.member_int (tptp.aa_nat_int (tptp.nth_int Xs) N2) (tptp.set_int2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_complex) (X tptp.complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_s3451745648224563538omplex Xs))) (tptp.member_complex X (tptp.set_complex2 (tptp.list_update_complex Xs N2 X))))) (forall ((N2 tptp.nat) (Xs tptp.list_real) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_real Xs))) (tptp.member_real X (tptp.set_real2 (tptp.list_update_real Xs N2 X))))) (forall ((N2 tptp.nat) (Xs tptp.list_set_nat) (X tptp.set_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_s3254054031482475050et_nat Xs))) (tptp.member_set_nat X (tptp.set_set_nat2 (tptp.list_update_set_nat Xs N2 X))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_nat Xs))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 (tptp.list_update_nat Xs N2 X)))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_s6755466524823107622T_VEBT Xs))) (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) (tptp.set_VEBT_VEBT2 (tptp.list_u1324408373059187874T_VEBT Xs N2 X)))))) (forall ((N2 tptp.nat) (Xs tptp.list_bool) (X tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_bool Xs))) (tptp.member_bool X (tptp.set_bool2 (tptp.list_update_bool Xs N2 X))))) (forall ((N2 tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.size_size_list_int Xs))) (tptp.member_int X (tptp.set_int2 (tptp.list_update_int Xs N2 X))))) (forall ((I2 tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_size_list_nat Xs))) (= (= (tptp.list_update_nat Xs I2 X) Xs) (= (tptp.aa_nat_nat (tptp.nth_nat Xs) I2) X)))) (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_s6755466524823107622T_VEBT Xs))) (= (= (tptp.list_u1324408373059187874T_VEBT Xs I2 X) Xs) (= (tptp.nth_VEBT_VEBT Xs I2) X)))) (forall ((I2 tptp.nat) (Xs tptp.list_bool) (X tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_size_list_bool Xs))) (= (= (tptp.list_update_bool Xs I2 X) Xs) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) I2)) (tptp.pp X))))) (forall ((I2 tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_size_list_int Xs))) (= (= (tptp.list_update_int Xs I2 X) Xs) (= (tptp.aa_nat_int (tptp.nth_int Xs) I2) X)))) (forall ((I2 tptp.nat) (Xs tptp.list_nat) (J tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.nth_nat (tptp.list_update_nat Xs I2 X)) J))) (let ((_let_2 (= I2 J))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_size_list_nat Xs))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.nth_nat Xs) J)))))))) (forall ((I2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (J tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (tptp.nth_VEBT_VEBT (tptp.list_u1324408373059187874T_VEBT Xs I2 X) J))) (let ((_let_2 (= I2 J))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_s6755466524823107622T_VEBT Xs))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.nth_VEBT_VEBT Xs J)))))))) (forall ((I2 tptp.nat) (Xs tptp.list_bool) (X tptp.bool) (J tptp.nat)) (let ((_let_1 (= I2 J))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_size_list_bool Xs))) (= (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool (tptp.list_update_bool Xs I2 X)) J)) (and (=> _let_1 (tptp.pp X)) (=> (not _let_1) (tptp.pp (tptp.aa_nat_bool (tptp.nth_bool Xs) J)))))))) (forall ((I2 tptp.nat) (Xs tptp.list_int) (J tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.nth_int (tptp.list_update_int Xs I2 X)) J))) (let ((_let_2 (= I2 J))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.size_size_list_int Xs))) (and (=> _let_2 (= _let_1 X)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_int (tptp.nth_int Xs) J)))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) X))))) (let ((_let_6 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_1 TreeList Summary)) X)) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2)))) _let_4))))))))))))))) (forall ((Y tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat X)) (tptp.some_nat Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_less (tptp.some_nat X)) (tptp.some_nat Y))))) (forall ((X tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.nth_VEBT_VEBT TreeList _let_3))) (let ((_let_5 (tptp.product_Pair_nat_nat Mi))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (not (= X Ma)) (= (tptp.vEBT_vebt_insert (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 Ma)) Deg TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Ma))) Deg (tptp.list_u1324408373059187874T_VEBT TreeList _let_3 (tptp.vEBT_vebt_insert _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_4) (tptp.vEBT_vebt_insert Summary _let_3) Summary))))))))))))) (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (tptp.nth_VEBT_VEBT TreeList _let_3))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (not (= X Ma)) (= (tptp.vEBT_vebt_insert (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Mi) Ma))) Deg (tptp.list_u1324408373059187874T_VEBT TreeList _let_3 (tptp.vEBT_vebt_insert _let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Mi) _let_2))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_4) (tptp.vEBT_vebt_insert Summary _let_3) Summary)))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary)) N2)) (=> (not (= Mi Ma)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) Ma)) (exists ((M2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (and (= (tptp.some_nat M2) (tptp.vEBT_vebt_mint Summary)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) (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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)))))))))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) tptp.one)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) (tptp.aa_num_num tptp.bit0 N2)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)) X)) Y)) (tptp.aa_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_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) tptp.one) _let_1) (forall ((M tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat _let_1 N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N2)) (= M N2))) (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.suc Nat) (tptp.aa_nat_nat tptp.suc Nat2)) (= Nat Nat2))) (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.suc X22) (tptp.aa_nat_nat tptp.suc Y22)) (= X22 Y22))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (= (tptp.vEBT_vebt_pred T X) (tptp.some_nat Sx)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set (tptp.vEBT_set_vebt T)) X) Sx))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (= (tptp.vEBT_vebt_succ T X) (tptp.some_nat Sx)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_succ_in_set (tptp.vEBT_set_vebt T)) X) Sx))))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)) (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)))))) (forall ((M tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 M) tptp.one))) (forall ((N2 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit0 N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.suc N2)))) (forall ((M tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2))))) (forall ((N2 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 N2)) (tptp.aa_nat_nat tptp.suc M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))) (forall ((M tptp.nat) (N2 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)) N2)) (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) N2)) K))) (forall ((M tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2))) (= (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 ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N2)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 I2)) I2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num tptp.one) N2) N2)) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) tptp.one) M)) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit0 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) tptp.one)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num tptp.one) N2))) (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex V))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B)) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) _let_1))))) (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real V))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) _let_1))))) (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) _let_1) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1)) (tptp.aa_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 ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex V)))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex B) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex _let_1 B)) (tptp.aa_complex_complex _let_1 C))))) (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real V)))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real _let_1 C))))) (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (tptp.ord_le2932123472753598470d_enat _let_1 _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger U))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (let ((_let_3 (tptp.ord_max_Code_integer _let_1 _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real U))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real V))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat U))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (let ((_let_3 (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat U))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat V))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int U))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int V))) (let ((_let_3 (tptp.aa_int_int (tptp.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.numera1916890842035813515d_enat X))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X))) (= (tptp.ord_max_Code_integer tptp.one_one_Code_integer _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera1916890842035813515d_enat X))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X))) (= (tptp.ord_max_Code_integer _let_1 tptp.one_one_Code_integer) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) J)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 J)) K))))) (forall ((K tptp.nat) (J tptp.nat) (I2 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)) I2) (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) I2)) K)))) (forall ((K tptp.nat) (J tptp.nat) (I2 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 I2) (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 I2) K)) J)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc N2)) tptp.one_one_nat) N2)) (forall ((K tptp.nat) (J tptp.nat) (I2 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 I2) (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 I2) K)) (tptp.aa_nat_nat tptp.suc J))))) (forall ((K tptp.nat) (J tptp.nat) (I2 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))) I2) (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) I2))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2))) (= (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 ((N2 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 N2) M)) M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N2) M))) (forall ((M tptp.nat) (N2 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) N2)) 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 N2) Q2)))) (forall ((M tptp.nat) (N2 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 N2) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 Q2))))) (forall ((M tptp.nat) (N2 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) N2)) 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 N2) Q2)))) (forall ((M tptp.nat) (N2 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 N2) Q2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 Q2))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P N)))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) I2)))))) (forall ((J tptp.nat) (K tptp.nat) (N2 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) N2)) K)))) (forall ((M tptp.nat) (N2 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 N2)) (=> (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 N2)) (tptp.aa_nat_nat _let_1 M)))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)))) (forall ((M tptp.nat) (K tptp.nat) (N2 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 N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))) (forall ((N2 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 N2) M)) N2) M)) (forall ((M tptp.nat) (N2 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) N2)) N2) M)) (forall ((M tptp.nat) (N2 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) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N2)) (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) (N2 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) N2)) M))) (forall ((M tptp.nat) (N2 tptp.nat) (L 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 (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 N2) L))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (= (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 N2) K)) (tptp.aa_nat_nat _let_1 N2))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 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.minus_minus_nat M) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (= (= (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 N2) K)) (= M N2)))))) (forall ((M tptp.nat) (N2 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) N2)) 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 N2) K)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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) N2)) (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 N2))))) (forall ((M tptp.nat) (N2 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) N2)) (tptp.aa_nat_nat tptp.suc M)))) (forall ((N2 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 N2) M)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat _let_1 N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))) (forall ((I2 tptp.nat) (J tptp.nat) (K 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.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 I2) K)) J)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) M))) (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) (N2 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 N2)) (= (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 N2) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))))) (forall ((J tptp.nat) (K tptp.nat) (I2 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)) I2)) (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 I2) K))))) (forall ((K tptp.nat) (J tptp.nat) (I2 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 I2) (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 I2) K)) J))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2))) (=> (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) (I2 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) I2)) 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)) I2)))) (forall ((I2 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 I2) J)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I2) K) (= J (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) I2))))) (forall ((M tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 tptp.one_one_nat)) N2)))) (forall ((K tptp.nat) (J tptp.nat) (I2 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)) I2)) (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 I2) K)))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I2)) (= (= (tptp.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 I2) 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)) N2)) (= (tptp.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 I2) J)) U)) M) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) 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 I2) 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)) N2)) (= 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) I2)) U)) N2))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) 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.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat I2) 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)) 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 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat I2) J)) U)) M)) N2))))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) 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 I2) 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)) N2))) (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) I2)) U)) N2)))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I2)) (= (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 I2) 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)) N2)) (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 I2) J)) U)) M)) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) 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 I2) 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)) N2)) (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) I2)) U)) N2))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat J) I2)) (= (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 I2) 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)) N2))) (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 I2) J)) U)) M)) N2))))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) 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 I2) 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)) N2))) (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) I2)) U)) N2)))))) (forall ((N2 tptp.nat)) (not (= N2 (tptp.aa_nat_nat tptp.suc N2)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (tptp.aa_nat_nat tptp.suc X) (tptp.aa_nat_nat tptp.suc Y)) (= X Y))) (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 ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool P N))) (exists ((M3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (not (tptp.pp (tptp.aa_nat_bool P M3))))))) (tptp.pp (tptp.aa_nat_bool P N2)))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (forall ((N tptp.nat)) (=> (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (tptp.pp (tptp.aa_nat_bool P M3)))) (tptp.pp (tptp.aa_nat_bool P N)))) (tptp.pp (tptp.aa_nat_bool P N2)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N2)))) (forall ((S2 tptp.nat) (T tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat S2) T)) (not (= S2 T)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (not (= M N2)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) B)))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool P X3)) (forall ((Y2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y2) X3))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (or (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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (forall ((M tptp.nat) (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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= M N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2))) (=> (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 ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N2))) (forall ((X tptp.char) (Y tptp.char)) (=> (not (= (tptp.size_size_char X) (tptp.size_size_char Y))) (not (= X Y)))) (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_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.aa_num_nat tptp.size_size_num X) (tptp.aa_num_nat tptp.size_size_num Y))) (not (= X 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.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) _let_1) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex Y) X)) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) X)) _let_1)))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.minus_minus_rat Y) X)) _let_1)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_int_fun_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 ((T tptp.vEBT_VEBT)) (= (tptp.vEBT_set_vebt T) (tptp.collect_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions T)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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) N2)) (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 N2))))))) (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.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) _let_2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) _let_2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Y) _let_2))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) _let_2) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.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.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)) X)) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_int_fun_nat_int tptp.power_power_int X) _let_2)) (tptp.aa_nat_int (tptp.aa_int_fun_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 ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2))) (=> (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))) (= N2 M))))) (forall ((I2 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 I2) J)) (=> (forall ((I3 tptp.nat)) (=> (= J (tptp.aa_nat_nat tptp.suc I3)) (tptp.pp (tptp.aa_nat_bool P I3)))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) J)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I3))) (tptp.pp (tptp.aa_nat_bool P I3))))) (tptp.pp (tptp.aa_nat_bool P I2)))))) (forall ((I2 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 I2) J)) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I3) (tptp.aa_nat_nat tptp.suc I3)))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool P I3))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J2) K2)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P J2) K2)) (tptp.pp (tptp.aa_nat_bool _let_1 K2)))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P I2) J)))))) (forall ((I2 tptp.nat) (J tptp.nat) (K 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 (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 I2)) K))))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2))) (=> (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 N2))))) (forall ((N2 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 N2)) 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 N2) M4)))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P I5)))) (and (tptp.pp (tptp.aa_nat_bool P N2)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) N2)) (tptp.pp (tptp.aa_nat_bool P I5))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.suc M))))) (forall ((M tptp.nat) (N2 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 N2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (= M N2))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P I5)))) (or (tptp.pp (tptp.aa_nat_bool P N2)) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) N2)) (tptp.pp (tptp.aa_nat_bool P I5))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N2)))))) (forall ((M tptp.nat) (N2 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 N2))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 N2))) (= M N2))))) (forall ((M tptp.nat) (N2 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) N2)) (=> (not (= _let_1 N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) N2)))))) (forall ((I2 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 I2)) K)) (not (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J2)) (not (= K (tptp.aa_nat_nat tptp.suc J2)))))))) (forall ((M tptp.nat) (N2 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)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((I2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) K)) (=> (not (= K (tptp.aa_nat_nat tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J2)) (not (= K (tptp.aa_nat_nat tptp.suc J2))))))))) (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (=> (= A2 (tptp.aa_nat_nat _let_1 A)) (= (tptp.aa_nat_nat tptp.suc A2) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc A)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.suc M)) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.suc M)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) (tptp.aa_nat_nat tptp.suc N2)))) (forall ((M tptp.nat) (N2 tptp.nat) (R tptp.fun_nat_fun_nat_bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (forall ((X3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X3) X3))) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat) (Z3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool R X3))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y4)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R Y4) Z3)) (tptp.pp (tptp.aa_nat_bool _let_1 Z3)))))) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R N) (tptp.aa_nat_nat tptp.suc N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R M) N2))))))) (forall ((M tptp.nat) (N2 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) N2)) (=> (tptp.pp (tptp.aa_nat_bool P M)) (=> (forall ((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 P N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N)))))) (tptp.pp (tptp.aa_nat_bool P N2)))))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (forall ((N 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)) N)) (tptp.pp (tptp.aa_nat_bool P M3)))) (tptp.pp (tptp.aa_nat_bool P N)))) (tptp.pp (tptp.aa_nat_bool P N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N2)) M)))) (forall ((N2 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 N2)) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (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 N2)) (= M _let_1)))))) (forall ((N2 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 N2)) M5)) (exists ((M2 tptp.nat)) (= M5 (tptp.aa_nat_nat tptp.suc M2))))) (forall ((M tptp.nat) (N2 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 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat tptp.suc N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (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 N2))) (= M _let_1)))))) (forall ((M tptp.nat) (N2 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)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (= M N2)))) (forall ((I2 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 I2) J)) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) K)))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))))) (forall ((I2 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 I2) J)) I2)))) (forall ((J tptp.nat) (I2 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) I2)) I2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K 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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2))) (=> (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 ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2))) (=> (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) (N2 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) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (forall ((F tptp.fun_nat_nat) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) J2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F I3)) (tptp.aa_nat_nat F J2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F I2)) (tptp.aa_nat_nat F J)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (not (= M N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= M N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= M N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (not (= M N2))))) (forall ((M tptp.nat) (K tptp.nat) (N2 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)) N2)) (not (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)))) (forall ((M tptp.nat) (K tptp.nat) (N2 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)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (K tptp.nat) (N2 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)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)))) (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 ((N tptp.nat)) (= L (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) K))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2))) (=> (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 ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2))) (=> (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) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (exists ((K3 tptp.nat)) (= N2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K3))))) (forall ((M tptp.nat) (N2 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) N2)) 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 N2) K)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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) N2)) (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 N2))))) (forall ((I2 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 I2) 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 I2) J)) U)) K))) (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 ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) L)))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) K))))) (forall ((I2 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 I2) J)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 I2)) (tptp.aa_nat_nat _let_1 J)))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) N2) N2)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) tptp.one_one_nat) N2)) (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) D))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real D) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real C) _let_2)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) _let_2))))) (forall ((F tptp.fun_nat_real) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (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 (tptp.aa_nat_nat tptp.suc N))))) (= (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 M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_rat) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (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 (tptp.aa_nat_nat tptp.suc N))))) (= (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 M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_num) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N)) (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N))))) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N2)) (tptp.aa_nat_num F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N)) (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N2)) (tptp.aa_nat_nat F M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N tptp.nat)) (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 (tptp.aa_nat_nat tptp.suc N))))) (= (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 M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))) (forall ((F tptp.fun_nat_real) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (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 (tptp.aa_nat_nat tptp.suc N))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N4)) (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 N4)))))) (forall ((F tptp.fun_nat_rat) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (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 (tptp.aa_nat_nat tptp.suc N))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N4)) (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 N4)))))) (forall ((F tptp.fun_nat_num) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N)) (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_nat_num F N2)) (tptp.aa_nat_num F N4)))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F N)) (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N4)) (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 N4)))))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (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 (tptp.aa_nat_nat tptp.suc N))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N4)) (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 N4)))))) (forall ((F tptp.fun_nat_set_int) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_set_int F N))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N4) (tptp.aa_nat_set_int F N2))))) (forall ((F tptp.fun_nat_rat) (N2 tptp.nat) (N4 tptp.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 F (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_rat F N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F N4)) (tptp.aa_nat_rat F N2)))))) (forall ((F tptp.fun_nat_num) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_num F N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N4)) (tptp.aa_nat_num F N2)))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat) (N4 tptp.nat)) (=> (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 F (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat F N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F N4)) (tptp.aa_nat_nat F N2)))))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (N4 tptp.nat)) (=> (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 F (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_int F N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F N4)) (tptp.aa_nat_int F N2)))))) (forall ((F tptp.fun_nat_set_int) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N) (tptp.aa_nat_set_int F (tptp.aa_nat_nat tptp.suc N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int F N2) (tptp.aa_nat_set_int F N4))))) (forall ((F tptp.fun_nat_rat) (N2 tptp.nat) (N4 tptp.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 F N)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc N))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (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 N4)))))) (forall ((F tptp.fun_nat_num) (N2 tptp.nat) (N4 tptp.nat)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N)) (tptp.aa_nat_num F (tptp.aa_nat_nat tptp.suc N))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F N2)) (tptp.aa_nat_num F N4)))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat) (N4 tptp.nat)) (=> (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 F N)) (tptp.aa_nat_nat F (tptp.aa_nat_nat tptp.suc N))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (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 N4)))))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (N4 tptp.nat)) (=> (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 F N)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc N))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N4)) (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 N4)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (not (forall ((Q3 tptp.nat)) (not (= N2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) Q3)))))))) (forall ((I2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) M))))) (forall ((I2 tptp.nat) (M tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) I2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (exists ((K3 tptp.nat)) (= N2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K3)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (exists ((K2 tptp.nat)) (= N2 (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) (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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat tptp.suc N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc N2)) M)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.suc M))) (= N2 M)))) (forall ((M tptp.nat) (N2 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)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((I2 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 I2) J)) (=> (tptp.pp (tptp.aa_nat_bool P J)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) J)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P N)))))) (tptp.pp (tptp.aa_nat_bool P I2)))))) (forall ((I2 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 I2) J)) (=> (tptp.pp (tptp.aa_nat_bool P I2)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) N)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) J)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N))))))) (tptp.pp (tptp.aa_nat_bool P J)))))) (forall ((M tptp.nat) (N2 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)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.suc M)) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.suc M)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2))))) (forall ((F tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N)) (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 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 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 ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.suc N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))) (= _let_138 tptp.suc) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.suc N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) N2))) (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz) Va Vb Vc))))) (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu Uv Uw)) X)))) (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw Ux Uy)))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_1 TreeList Summary))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi)))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Mi) X))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList _let_6))) (let ((_let_8 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X))) (= (tptp.vEBT_vebt_insert _let_2 X) (tptp.if_VEBT_VEBT (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_6) (tptp.size_s6755466524823107622T_VEBT TreeList))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_bool_bool (tptp.fdisj (tptp.aa_nat_bool _let_8 Mi)) (tptp.aa_nat_bool _let_8 Ma)))) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 X) Mi)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_5) Ma))) _let_1 (tptp.list_u1324408373059187874T_VEBT TreeList _let_6 (tptp.vEBT_vebt_insert _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_5) _let_3))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_7) (tptp.vEBT_vebt_insert Summary _let_6) Summary)) _let_2))))))))))) (forall ((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.plus_plus_rat B) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) A))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (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.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) B) A))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.vEBT_vebt_pred Summary _let_3))) (let ((_let_5 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList _let_3))) (let ((_let_8 (tptp.vEBT_vebt_mint _let_7))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_8) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_6)) _let_8)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 (tptp.some_nat _let_3))) (tptp.vEBT_vebt_pred _let_7 _let_6)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_4) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X) (tptp.some_nat Mi) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 _let_4)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList (tptp.the_nat _let_4))))))))))))))))))) (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.vEBT_vebt_pred Summary _let_3))) (let ((_let_5 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList _let_3))) (let ((_let_8 (tptp.vEBT_vebt_mint _let_7))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Ma)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_8) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_6)) _let_8)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 (tptp.some_nat _let_3))) (tptp.vEBT_vebt_pred _let_7 _let_6)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_4) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X) (tptp.some_nat Mi) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 _let_4)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList (tptp.the_nat _let_4)))))) tptp.none_nat))))))))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.vEBT_vebt_succ Summary _let_3))) (let ((_let_5 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList _let_3))) (let ((_let_8 (tptp.vEBT_vebt_maxt _let_7))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) X)) (= (tptp.vEBT_vebt_succ (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_8) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_less (tptp.some_nat _let_6)) _let_8)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 (tptp.some_nat _let_3))) (tptp.vEBT_vebt_succ _let_7 _let_6)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_4) tptp.none_nat) tptp.none_nat (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 _let_4)) (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList (tptp.the_nat _let_4)))))) tptp.none_nat))))))))))))) (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.vEBT_vebt_succ Summary _let_3))) (let ((_let_5 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2))))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList _let_3))) (let ((_let_8 (tptp.vEBT_vebt_maxt _let_7))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) Deg)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))) (= (tptp.vEBT_vebt_succ (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Deg TreeList Summary) X) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_8) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_less (tptp.some_nat _let_6)) _let_8)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 (tptp.some_nat _let_3))) (tptp.vEBT_vebt_succ _let_7 _let_6)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_4) tptp.none_nat) tptp.none_nat (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_5 _let_4)) (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList (tptp.the_nat _let_4))))))))))))))))))) (forall ((V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc V)))) (= (tptp.vEBT_vebt_insert (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList Summary) X) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) X)) _let_1 TreeList Summary)))) (= tptp.vEBT_VEBT_mul (tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)) (= tptp.vEBT_VEBT_add (tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2)) (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) N2))))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2)) (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) N2))))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) Z) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.some_nat X)) (tptp.some_nat Y)) (tptp.some_nat Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X) Y) Z) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat X)) (tptp.some_nat Y)) (tptp.some_nat Z)))) (forall ((R2 tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 R2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) R2)))) (forall ((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.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) tptp.one_one_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) tptp.one_one_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) tptp.one_one_int) A)) (forall ((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 ((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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) E)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat B) E)) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_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.times_times_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_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.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat B) C)) (tptp.aa_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.times_times_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_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.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat B) C)) (tptp.aa_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.times_times_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.times_times_rat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.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.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) C)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B) C)) A) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat B) A)) (tptp.aa_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.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int _let_1 C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) C) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_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)))) (= tptp.aTP_Lamm_af (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.one_one_complex)) (= tptp.aTP_Lamm_ag (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.one_one_real)) (= tptp.aTP_Lamm_ah (tptp.times_times_rat tptp.one_one_rat)) (= tptp.aTP_Lamm_ai (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat)) (= tptp.aTP_Lamm_aj (tptp.aa_int_fun_int_int tptp.times_times_int tptp.one_one_int)) (forall ((M tptp.real) (N2 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 N2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real M) N2))))))) (forall ((M tptp.rat) (N2 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 N2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.times_times_rat M) N2))))))) (forall ((M tptp.nat) (N2 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 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2))))))) (forall ((M tptp.int) (N2 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 N2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N2))))))) (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.plus_plus_rat A) tptp.one_one_rat)) (tptp.aa_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.plus_plus_rat A) tptp.one_one_rat)))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)))) (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real) (J tptp.real)) (let ((_let_1 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real N2) (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 I2) K)) N2)))) (=> _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 N2) K)) J))))))))) (forall ((I2 tptp.rat) (K tptp.rat) (N2 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 N2) (tptp.aa_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.plus_plus_rat I2) K)) N2)))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat N2) K)) J))))))))) (forall ((I2 tptp.nat) (K tptp.nat) (N2 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 N2) (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 I2) K)) N2)))) (=> _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 N2) K)) J))))))))) (forall ((I2 tptp.int) (K tptp.int) (N2 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 N2) (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 I2) K)) N2)))) (=> _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 N2) K)) J))))))))) (forall ((I2 tptp.real) (K tptp.real) (N2 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 I2) K)) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real N2) K))))) (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.plus_plus_rat I2) K)) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) (tptp.aa_rat_rat (tptp.minus_minus_rat N2) K))))) (forall ((I2 tptp.nat) (K tptp.nat) (N2 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 I2) K)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))))) (forall ((I2 tptp.int) (K tptp.int) (N2 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 I2) K)) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int N2) K))))) (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.plus_plus_rat B) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) A))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)) A))) (forall ((A tptp.int) (B tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) A))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.times_times_rat Y) Y)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) Y)) (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)))) (forall ((A tptp.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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) E)) C) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat B) E)) D)) (= C (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) E)) C) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat B) E)) D)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_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 ((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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_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 ((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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_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_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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_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 ((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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) E)) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_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 ((X tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) X)) tptp.one_one_complex) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) tptp.one_one_complex)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) tptp.one_one_complex)))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)) tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) X)) tptp.one_one_rat) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.minus_minus_rat X) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) tptp.one_one_int)))) (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (tptp.vEBT_vebt_succ Summary _let_4))) (let ((_let_6 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_3))))) (let ((_let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_8 (tptp.nth_VEBT_VEBT TreeList _let_4))) (let ((_let_9 (tptp.vEBT_vebt_maxt _let_8))) (let ((_let_10 (tptp.vEBT_vebt_succ (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_2 TreeList Summary) X))) (let ((_let_11 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Mi)))) (and (=> _let_11 (= _let_10 (tptp.some_nat Mi))) (=> (not _let_11) (= _let_10 (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_less (tptp.some_nat _let_7)) _let_9)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 (tptp.some_nat _let_4))) (tptp.vEBT_vebt_succ _let_8 _let_7)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat) tptp.none_nat (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 _let_5)) (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList (tptp.the_nat _let_5)))))) tptp.none_nat)))))))))))))))) (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (tptp.vEBT_vebt_pred Summary _let_4))) (let ((_let_6 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_3))))) (let ((_let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_8 (tptp.nth_VEBT_VEBT TreeList _let_4))) (let ((_let_9 (tptp.vEBT_vebt_mint _let_8))) (let ((_let_10 (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_2 TreeList Summary) X))) (let ((_let_11 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma) X)))) (and (=> _let_11 (= _let_10 (tptp.some_nat Ma))) (=> (not _let_11) (= _let_10 (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_7)) _let_9)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 (tptp.some_nat _let_4))) (tptp.vEBT_vebt_pred _let_8 _let_7)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi) X) (tptp.some_nat Mi) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 _let_5)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList (tptp.the_nat _let_5)))))) tptp.none_nat)))))))))))))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) _let_1)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)) _let_1)))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A)) _let_1)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)) _let_1)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) Y)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (tptp.vEBT_vebt_mint (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Ux Uy Uz)) (tptp.some_nat Mi))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (tptp.vEBT_vebt_maxt (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) Ux Uy Uz)) (tptp.some_nat Ma))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (= (tptp.vEBT_vebt_succ T X) tptp.none_nat) (= (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_ak T) X)) tptp.bot_bot_set_nat)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (= (= (tptp.vEBT_vebt_pred T X) tptp.none_nat) (= (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_al T) X)) tptp.bot_bot_set_nat)))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.ord_le72135733267957522d_enat B A) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B) A))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)) (= (tptp.ord_max_Code_integer A B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (= (tptp.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.aa_rat_rat (tptp.ord_max_rat A) B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_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 ((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 ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat _let_1) B) _let_1))) (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.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.ord_max_Code_integer A B))) (= (tptp.ord_max_Code_integer _let_1 B) _let_1))) (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.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A))) (let ((_let_2 (tptp.aa_Ext7969882492699152700d_enat _let_1 B))) (= (tptp.aa_Ext7969882492699152700d_enat _let_1 _let_2) _let_2)))) (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.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.ord_max_Code_integer A B))) (= (tptp.ord_max_Code_integer A _let_1) _let_1))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) A) A)) (forall ((A tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) A) A)) (forall ((A tptp.code_integer)) (= (tptp.ord_max_Code_integer A A) A)) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= (tptp.vEBT_vebt_mint T) tptp.none_nat) (= (tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))) (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (= (tptp.ord_le2932123472753598470d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B) C) A) (and (tptp.ord_le2932123472753598470d_enat B A) (tptp.ord_le2932123472753598470d_enat C A)))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.ord_max_Code_integer B C)) A)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) A))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.ord_max_rat B) C)) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A))))) (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num B) C)) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat B) C)) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int B) C)) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A))))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat A B) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (= (tptp.ord_max_Code_integer A B) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B) B))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B) B))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat B A) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B) A))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (= (tptp.ord_max_Code_integer A B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B) A))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B) A))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (= (tptp.ord_le72135733267957522d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y) Z) (and (tptp.ord_le72135733267957522d_enat X Z) (tptp.ord_le72135733267957522d_enat Y Z)))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.ord_max_Code_integer X Y)) Z)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) Z)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Y) Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y)) Z)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.ord_max_rat X) Y)) Z)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y)) Z)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Z)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) Z)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Z)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.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.extended_enat) (B tptp.extended_enat)) (=> (tptp.ord_le72135733267957522d_enat A B) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) B)) (= (tptp.ord_max_Code_integer A B) 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.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.aa_rat_rat (tptp.ord_max_rat A) B) B))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_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 ((S3 tptp.set_real)) (=> (exists ((X2 tptp.real)) (tptp.member_real X2 S3)) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Z4))))) (exists ((Y4 tptp.real)) (and (forall ((X2 tptp.real)) (=> (tptp.member_real X2 S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X2) Y4)))) (forall ((Z4 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Z4)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) Z4))))))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (exists ((N 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) N)))))) (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 ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B))) (let ((_let_2 (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A))) (= (tptp.aa_Ext7969882492699152700d_enat _let_1 (tptp.aa_Ext7969882492699152700d_enat _let_2 C)) (tptp.aa_Ext7969882492699152700d_enat _let_2 (tptp.aa_Ext7969882492699152700d_enat _let_1 C)))))) (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.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (tptp.ord_max_Code_integer B (tptp.ord_max_Code_integer A C)) (tptp.ord_max_Code_integer A (tptp.ord_max_Code_integer B C)))) (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 ((A tptp.extended_enat) (B tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B) (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B) A))) (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.code_integer) (B tptp.code_integer)) (= (tptp.ord_max_Code_integer A B) (tptp.ord_max_Code_integer B A))) (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.extended_enat) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat (tptp.aa_Ext7969882492699152700d_enat _let_1 B)) C) (tptp.aa_Ext7969882492699152700d_enat _let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B) C))))) (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.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.ord_max_Code_integer (tptp.ord_max_Code_integer A B) C) (tptp.ord_max_Code_integer A (tptp.ord_max_Code_integer B C)))) (forall ((C tptp.real)) (= (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_am C) (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (forall ((C tptp.rat)) (= (tptp.aTP_Lamm_an C) (tptp.times_times_rat C))) (forall ((C tptp.nat)) (= (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ao C) (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (forall ((C tptp.int)) (= (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ap C) (tptp.aa_int_fun_int_int tptp.times_times_int C))) (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) D)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) D)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat B) D)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)))) (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat C B) (tptp.ord_le2932123472753598470d_enat C (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B)))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.ord_max_Code_integer A B)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat A) B)))))) (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num 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.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat C A) (tptp.ord_le2932123472753598470d_enat C (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.ord_max_Code_integer 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.aa_rat_rat (tptp.ord_max_rat A) B)))))) (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 A)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) 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.extended_enat) (B tptp.extended_enat)) (= (tptp.ord_le2932123472753598470d_enat A B) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)) (= (tptp.ord_max_Code_integer A B) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B) B))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B) B))) (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (= (tptp.ord_le2932123472753598470d_enat B A) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B) A))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (= (tptp.ord_max_Code_integer A B) A))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= (tptp.aa_rat_rat (tptp.ord_max_rat A) B) A))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B) A))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B) A))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B) A))) (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (= (tptp.ord_le2932123472753598470d_enat Z (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y)) (or (tptp.ord_le2932123472753598470d_enat Z X) (tptp.ord_le2932123472753598470d_enat Z Y)))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger Z))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.ord_max_Code_integer X Y))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 X)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat X) Y))) (or (tptp.pp (tptp.aa_rat_bool _let_1 X)) (tptp.pp (tptp.aa_rat_bool _let_1 Y)))))) (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Z))) (= (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y))) (or (tptp.pp (tptp.aa_num_bool _let_1 X)) (tptp.pp (tptp.aa_num_bool _let_1 Y)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (tptp.pp (tptp.aa_nat_bool _let_1 Y)))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.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.extended_enat) (A tptp.extended_enat)) (tptp.ord_le2932123472753598470d_enat B (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat 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 B) (tptp.ord_max_Code_integer 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) (tptp.aa_rat_rat (tptp.ord_max_rat A) B)))) (forall ((B tptp.num) (A tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) (tptp.aa_num_num (tptp.aa_num_fun_num_num 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.extended_enat) (B tptp.extended_enat)) (tptp.ord_le2932123472753598470d_enat A (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat 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) (tptp.ord_max_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) (tptp.aa_rat_rat (tptp.ord_max_rat A) B)))) (forall ((A tptp.num) (B tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_num_num (tptp.aa_num_fun_num_num 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.extended_enat) (A tptp.extended_enat)) (= (tptp.ord_le2932123472753598470d_enat B A) (= A (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat 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 B) A)) (= A (tptp.ord_max_Code_integer 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.aa_rat_rat (tptp.ord_max_rat A) B)))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (= A (tptp.aa_num_num (tptp.aa_num_fun_num_num 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.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat B A) (=> (tptp.ord_le2932123472753598470d_enat C A) (tptp.ord_le2932123472753598470d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B) C) A)))) (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.ord_le3102999989581377725nteger B) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.ord_max_Code_integer B C)) A))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_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.aa_rat_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.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num 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.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B) C) A) (not (=> (tptp.ord_le2932123472753598470d_enat B A) (not (tptp.ord_le2932123472753598470d_enat C A)))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.ord_max_Code_integer B C)) A)) (not (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) A))))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.ord_max_rat B) C)) A)) (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.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num B) C)) A)) (not (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num 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.extended_enat) (B tptp.extended_enat)) (=> (= A (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B)) (tptp.ord_le2932123472753598470d_enat B A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A (tptp.ord_max_Code_integer A B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (tptp.aa_rat_rat (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.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (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.extended_enat) (A tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat B A) (= A (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat 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 B) A)) (= A (tptp.ord_max_Code_integer 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.aa_rat_rat (tptp.ord_max_rat A) B)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (= A (tptp.aa_num_num (tptp.aa_num_fun_num_num 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.extended_enat) (A tptp.extended_enat) (D tptp.extended_enat) (B tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat C A) (=> (tptp.ord_le2932123472753598470d_enat D B) (tptp.ord_le2932123472753598470d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat C) D) (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger C) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger D) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.ord_max_Code_integer C D)) (tptp.ord_max_Code_integer 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.aa_rat_rat (tptp.ord_max_rat C) D)) (tptp.aa_rat_rat (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.aa_num_fun_num_bool tptp.ord_less_eq_num C) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num D) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num C) D)) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) 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.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.ord_le72135733267957522d_enat C B) (tptp.ord_le72135733267957522d_enat C (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B)))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.ord_max_Code_integer 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.aa_rat_rat (tptp.ord_max_rat A) B)))))) (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num 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.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (=> (tptp.ord_le72135733267957522d_enat C A) (tptp.ord_le72135733267957522d_enat C (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.ord_max_Code_integer 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.aa_rat_rat (tptp.ord_max_rat A) B)))))) (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool _let_1 A)) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) 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.extended_enat) (A tptp.extended_enat)) (= (tptp.ord_le72135733267957522d_enat B A) (and (= A (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B)) (not (= 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 B) A)) (and (= A (tptp.ord_max_Code_integer A B)) (not (= A B))))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (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.aa_rat_rat (tptp.ord_max_rat A) B)) (not (= A B))))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (and (= A (tptp.aa_num_num (tptp.aa_num_fun_num_num 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.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (tptp.ord_le72135733267957522d_enat (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat B) C) A) (not (=> (tptp.ord_le72135733267957522d_enat B A) (not (tptp.ord_le72135733267957522d_enat C A)))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.ord_max_Code_integer B C)) A)) (not (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) A)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger C) A))))))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.aa_rat_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.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num B) C)) A)) (not (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num 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.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (= (tptp.ord_le72135733267957522d_enat Z (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y)) (or (tptp.ord_le72135733267957522d_enat Z X) (tptp.ord_le72135733267957522d_enat Z Y)))) (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.ord_max_Code_integer X Y))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 X)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real X) Y))) (or (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat X) Y))) (or (tptp.pp (tptp.aa_rat_bool _let_1 X)) (tptp.pp (tptp.aa_rat_bool _let_1 Y)))))) (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num Z))) (= (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y))) (or (tptp.pp (tptp.aa_num_bool _let_1 X)) (tptp.pp (tptp.aa_num_bool _let_1 Y)))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (tptp.pp (tptp.aa_nat_bool _let_1 Y)))))) (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int Z))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.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 ((F tptp.fun_Pr2477239776880934807at_nat) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (tptp.vEBT_V1502963449132264192at_nat F (tptp.some_P7363390416028606310at_nat A) (tptp.some_P7363390416028606310at_nat B)) (tptp.some_P7363390416028606310at_nat (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat F A) B)))) (forall ((F tptp.fun_num_fun_num_num) (A tptp.num) (B tptp.num)) (= (tptp.vEBT_V819420779217536731ft_num F (tptp.some_num A) (tptp.some_num B)) (tptp.some_num (tptp.aa_num_num (tptp.aa_num_fun_num_num F A) B)))) (forall ((F tptp.fun_nat_fun_nat_nat) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat F) (tptp.some_nat A)) (tptp.some_nat B)) (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F A) B)))) (forall ((Uu tptp.fun_Pr2477239776880934807at_nat) (Uv tptp.option4927543243414619207at_nat)) (= (tptp.vEBT_V1502963449132264192at_nat Uu tptp.none_P5556105721700978146at_nat Uv) tptp.none_P5556105721700978146at_nat)) (forall ((Uu tptp.fun_num_fun_num_num) (Uv tptp.option_num)) (= (tptp.vEBT_V819420779217536731ft_num Uu tptp.none_num Uv) tptp.none_num)) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uv tptp.option_nat)) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat Uu) tptp.none_nat) Uv) tptp.none_nat)) (forall ((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.times_times_rat X))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 Y)) (tptp.aa_rat_rat (tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat Y) B))) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_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 ((Uw tptp.fun_Pr2477239776880934807at_nat) (V tptp.product_prod_nat_nat)) (= (tptp.vEBT_V1502963449132264192at_nat Uw (tptp.some_P7363390416028606310at_nat V) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)) (forall ((Uw tptp.fun_num_fun_num_num) (V tptp.num)) (= (tptp.vEBT_V819420779217536731ft_num Uw (tptp.some_num V) tptp.none_num) tptp.none_num)) (forall ((Uw tptp.fun_nat_fun_nat_nat) (V tptp.nat)) (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat Uw) (tptp.some_nat V)) tptp.none_nat) tptp.none_nat)) (forall ((X tptp.fun_Pr2477239776880934807at_nat) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (tptp.vEBT_V1502963449132264192at_nat X Xa2 Xb) Y) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa2 (tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (tptp.some_P7363390416028606310at_nat A3)) (forall ((B2 tptp.product_prod_nat_nat)) (=> (= Xb (tptp.some_P7363390416028606310at_nat B2)) (not (= Y (tptp.some_P7363390416028606310at_nat (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat X A3) B2)))))))))))))) (forall ((X tptp.fun_num_fun_num_num) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (tptp.vEBT_V819420779217536731ft_num X Xa2 Xb) Y) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (tptp.some_num V2))) (=> (= Xb tptp.none_num) _let_1)) (not (forall ((A3 tptp.num)) (=> (= Xa2 (tptp.some_num A3)) (forall ((B2 tptp.num)) (=> (= Xb (tptp.some_num B2)) (not (= Y (tptp.some_num (tptp.aa_num_num (tptp.aa_num_fun_num_num X A3) B2)))))))))))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb) Y) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (tptp.some_nat V2))) (=> (= Xb tptp.none_nat) _let_1)) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (tptp.some_nat A3)) (forall ((B2 tptp.nat)) (=> (= Xb (tptp.some_nat B2)) (not (= Y (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X A3) B2)))))))))))))) (forall ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_succ_in_set Xs) X) Y)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Y) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) Xs)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X4)))))))) (forall ((Xs tptp.set_nat) (X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set Xs) X) Y)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Y) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) Xs)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) X)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Y)))))))) (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (tptp.vEBT_vebt_maxt (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu Uv Uw)) tptp.none_nat)) (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (tptp.vEBT_vebt_mint (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu Uv Uw)) tptp.none_nat)) (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uy Uz Va) Vb) tptp.none_nat)) (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (tptp.vEBT_vebt_succ (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Ux Uy Uz) Va) tptp.none_nat)) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_1) X))) (forall ((X tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) _let_1) X))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat)) (= (tptp.vEBT_VEBT_set_vebt (tptp.vEBT_vebt_buildup N2)) tptp.bot_bot_set_nat)) (forall ((X tptp.set_nat)) (= (tptp.ord_max_set_nat X tptp.bot_bot_set_nat) X)) (forall ((X tptp.set_int)) (= (tptp.ord_max_set_int X tptp.bot_bot_set_int) X)) (forall ((X tptp.set_real)) (= (tptp.ord_max_set_real X tptp.bot_bot_set_real) X)) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) tptp.bot_bot_nat) X)) (forall ((X tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) tptp.bot_bo4199563552545308370d_enat) X)) (forall ((X tptp.set_nat)) (= (tptp.ord_max_set_nat tptp.bot_bot_set_nat X) X)) (forall ((X tptp.set_int)) (= (tptp.ord_max_set_int tptp.bot_bot_set_int X) X)) (forall ((X tptp.set_real)) (= (tptp.ord_max_set_real tptp.bot_bot_set_real X) X)) (forall ((X tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.bot_bot_nat) X) X)) (forall ((X tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.bot_bo4199563552545308370d_enat) X) X)) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.ord_le2932123472753598470d_enat (tptp.numera1916890842035813515d_enat M) (tptp.numera1916890842035813515d_enat N2)) (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 N2))))) (forall ((A2 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2))) (forall ((A2 tptp.set_real)) (tptp.ord_less_eq_set_real tptp.bot_bot_set_real A2)) (forall ((A2 tptp.set_int)) (tptp.ord_less_eq_set_int tptp.bot_bot_set_int A2)) (forall ((A2 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat)) (= A2 tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_real)) (= (tptp.ord_less_eq_set_real A2 tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))) (forall ((A2 tptp.set_int)) (= (tptp.ord_less_eq_set_int A2 tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (= (tptp.minus_minus_set_real A2 B3) tptp.bot_bot_set_real) (tptp.ord_less_eq_set_real A2 B3))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (= (tptp.minus_minus_set_nat A2 B3) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= (tptp.minus_minus_set_int A2 B3) tptp.bot_bot_set_int) (tptp.ord_less_eq_set_int A2 B3))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.ord_le72135733267957522d_enat (tptp.numera1916890842035813515d_enat M) (tptp.numera1916890842035813515d_enat N2)) (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 N2))))) (forall ((M tptp.nat) (N2 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 N2))))) (forall ((M tptp.nat) (N2 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 N2)))))) (forall ((X tptp.set_int)) (tptp.ord_less_eq_set_int X X)) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) X))) (forall ((X tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) X))) (forall ((X tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) X))) (forall ((X tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) X))) (forall ((A tptp.set_int)) (tptp.ord_less_eq_set_int A A)) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) A))) (forall ((A tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.member_complex X3 B3))) (tptp.ord_le211207098394363844omplex A2 B3))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.member_real X3 B3))) (tptp.ord_less_eq_set_real A2 B3))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.member_set_nat X3 A2) (tptp.member_set_nat X3 B3))) (tptp.ord_le6893508408891458716et_nat A2 B3))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.member_nat X3))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.member_int X3 B3))) (tptp.ord_less_eq_set_int A2 B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (not (= A2 B3)) (tptp.ord_less_set_int A2 B3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.ord_less_eq_set_int B3 A2) (= A2 B3)))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.minus_minus_set_nat A2 B3))) (= (tptp.minus_minus_set_nat _let_1 B3) _let_1))) (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (= (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3)) (and (tptp.member_complex C A2) (not (tptp.member_complex C B3))))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (= (tptp.member_real C (tptp.minus_minus_set_real A2 B3)) (and (tptp.member_real C A2) (not (tptp.member_real C B3))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3)) (and (tptp.member_set_nat C A2) (not (tptp.member_set_nat C B3))))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.member_int C (tptp.minus_minus_set_int A2 B3)) (and (tptp.member_int C A2) (not (tptp.member_int C B3))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (= (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.member_complex C A2) (=> (not (tptp.member_complex C B3)) (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3))))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.member_real C A2) (=> (not (tptp.member_real C B3)) (tptp.member_real C (tptp.minus_minus_set_real A2 B3))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.member_set_nat C A2) (=> (not (tptp.member_set_nat C B3)) (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3))))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.member_int C A2) (=> (not (tptp.member_int C B3)) (tptp.member_int C (tptp.minus_minus_set_int A2 B3))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (=> (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))))))) (forall ((A2 tptp.set_int)) (= (tptp.minus_minus_set_int A2 tptp.bot_bot_set_int) A2)) (forall ((A2 tptp.set_real)) (= (tptp.minus_minus_set_real A2 tptp.bot_bot_set_real) A2)) (forall ((A2 tptp.set_nat)) (= (tptp.minus_minus_set_nat A2 tptp.bot_bot_set_nat) A2)) (forall ((A2 tptp.set_int)) (= (tptp.minus_minus_set_int tptp.bot_bot_set_int A2) tptp.bot_bot_set_int)) (forall ((A2 tptp.set_real)) (= (tptp.minus_minus_set_real tptp.bot_bot_set_real A2) tptp.bot_bot_set_real)) (forall ((A2 tptp.set_nat)) (= (tptp.minus_minus_set_nat tptp.bot_bot_set_nat A2) tptp.bot_bot_set_nat)) (forall ((A2 tptp.set_int)) (= (tptp.minus_minus_set_int A2 A2) tptp.bot_bot_set_int)) (forall ((A2 tptp.set_real)) (= (tptp.minus_minus_set_real A2 A2) tptp.bot_bot_set_real)) (forall ((A2 tptp.set_nat)) (= (tptp.minus_minus_set_nat A2 A2) tptp.bot_bot_set_nat)) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (tptp.minus_minus_set_real A2 B3) (tptp.collect_real (tptp.minus_6582619742941512235l_bool (tptp.aTP_Lamm_a A2) (tptp.aTP_Lamm_a B3))))) (forall ((A2 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.minus_1052850069191792384nt_int A2 B3) (tptp.collec213857154873943460nt_int (tptp.minus_7866439474815358650t_bool (tptp.aTP_Lamm_aa A2) (tptp.aTP_Lamm_aa B3))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (= (tptp.minus_811609699411566653omplex A2 B3) (tptp.collect_complex (tptp.minus_5423061390740260265x_bool (tptp.aTP_Lamm_ab A2) (tptp.aTP_Lamm_ab B3))))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.minus_2163939370556025621et_nat A2 B3) (tptp.collect_set_nat (tptp.minus_8322047804725131473t_bool (tptp.aTP_Lamm_ac A2) (tptp.aTP_Lamm_ac B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.minus_minus_set_int A2 B3) (tptp.collect_int (tptp.minus_7727386867957376939t_bool (tptp.aTP_Lamm_ae A2) (tptp.aTP_Lamm_ae B3))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.minus_minus_set_nat A2 B3) (tptp.collect_nat (tptp.minus_1628305797571225351t_bool (tptp.aTP_Lamm_ad A2) (tptp.aTP_Lamm_ad B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (tptp.minus_minus_set_real A2 B3) (tptp.collect_real (tptp.aa_set8565328311858951076l_bool (tptp.aTP_Lamm_aq A2) B3)))) (forall ((A2 tptp.set_Pr958786334691620121nt_int) (B3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.minus_1052850069191792384nt_int A2 B3) (tptp.collec213857154873943460nt_int (tptp.aa_set1381271197253378494t_bool (tptp.aTP_Lamm_ar A2) B3)))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (= (tptp.minus_811609699411566653omplex A2 B3) (tptp.collect_complex (tptp.aa_set3741564773079358752x_bool (tptp.aTP_Lamm_as A2) B3)))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.minus_2163939370556025621et_nat A2 B3) (tptp.collect_set_nat (tptp.aa_set9121396911425987952t_bool (tptp.aTP_Lamm_at A2) B3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.minus_minus_set_int A2 B3) (tptp.collect_int (tptp.aa_set7012339369581096484t_bool (tptp.aTP_Lamm_au A2) B3)))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.minus_minus_set_nat A2 B3) (tptp.collect_nat (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_av A2) B3)))) (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3)) (not (tptp.member_complex C B3)))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.member_real C (tptp.minus_minus_set_real A2 B3)) (not (tptp.member_real C B3)))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3)) (not (tptp.member_set_nat C B3)))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.member_int C (tptp.minus_minus_set_int A2 B3)) (not (tptp.member_int C B3)))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3)) (tptp.member_complex C A2))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.member_real C (tptp.minus_minus_set_real A2 B3)) (tptp.member_real C A2))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3)) (tptp.member_set_nat C A2))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.member_int C (tptp.minus_minus_set_int A2 B3)) (tptp.member_int C A2))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))) (tptp.pp (tptp.aa_set_nat_bool _let_1 A2))))) (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.member_complex C (tptp.minus_811609699411566653omplex A2 B3)) (not (=> (tptp.member_complex C A2) (tptp.member_complex C B3))))) (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.member_real C (tptp.minus_minus_set_real A2 B3)) (not (=> (tptp.member_real C A2) (tptp.member_real C B3))))) (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.member_set_nat C (tptp.minus_2163939370556025621et_nat A2 B3)) (not (=> (tptp.member_set_nat C A2) (tptp.member_set_nat C B3))))) (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.member_int C (tptp.minus_minus_set_int A2 B3)) (not (=> (tptp.member_int C A2) (tptp.member_int C B3))))) (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.minus_minus_set_nat A2 B3))) (not (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((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 ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.ord_less_set_complex A2 B3) (exists ((B2 tptp.complex)) (tptp.member_complex B2 (tptp.minus_811609699411566653omplex B3 A2))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (tptp.ord_less_set_real A2 B3) (exists ((B2 tptp.real)) (tptp.member_real B2 (tptp.minus_minus_set_real B3 A2))))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (tptp.ord_less_set_set_nat A2 B3) (exists ((B2 tptp.set_nat)) (tptp.member_set_nat B2 (tptp.minus_2163939370556025621et_nat B3 A2))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_set_int A2 B3) (exists ((B2 tptp.int)) (tptp.member_int B2 (tptp.minus_minus_set_int B3 A2))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat A2) B3)) (exists ((B2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B2) (tptp.minus_minus_set_nat B3 A2)))))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (= B A))))) (forall ((A tptp.num) (B tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (= B A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (= B A))))) (forall ((A tptp.int) (B tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (= B A))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool _let_3 X)))) (let ((_let_5 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y))) (let ((_let_6 (tptp.pp (tptp.aa_rat_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_rat_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_rat_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_rat_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Z))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool _let_3 X)))) (let ((_let_5 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y))) (let ((_let_6 (tptp.pp (tptp.aa_num_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_num_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_num_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_num_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Z))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool _let_3 X)))) (let ((_let_5 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y))) (let ((_let_6 (tptp.pp (tptp.aa_nat_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_nat_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_nat_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_nat_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool _let_1 Y)))) (let ((_let_3 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool _let_3 X)))) (let ((_let_5 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y))) (let ((_let_6 (tptp.pp (tptp.aa_int_bool _let_5 Z)))) (let ((_let_7 (tptp.pp (tptp.aa_int_bool _let_5 X)))) (let ((_let_8 (tptp.pp (tptp.aa_int_bool _let_3 Y)))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool _let_1 Z)))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= X Y) (and (tptp.ord_less_eq_set_int X Y) (tptp.ord_less_eq_set_int Y X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (= X Y) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (= (= X Y) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= X Y) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (= (= X Y) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (tptp.ord_less_eq_set_int B C) (tptp.ord_less_eq_set_int A C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) C))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (= B C) (tptp.ord_less_eq_set_int A C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y) (=> (tptp.ord_less_eq_set_int Y X) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= X Y)))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (tptp.ord_less_eq_set_int B C) (tptp.ord_less_eq_set_int A C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y) (=> (tptp.ord_less_eq_set_int Y Z) (tptp.ord_less_eq_set_int X Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((P tptp.fun_rat_fun_rat_bool) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A3) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B2)))) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P B2) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B2)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A) B))))) (forall ((P tptp.fun_num_fun_num_bool) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A3) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B2)))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P B2) A3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A) B))))) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A3) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B2) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B))))) (forall ((P tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A3) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B2)))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P B2) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= A B) (and (tptp.ord_less_eq_set_int B A) (tptp.ord_less_eq_set_int A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A B) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (= (= A B) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A B) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (= A B) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.ord_less_eq_set_int B A) (=> (tptp.ord_less_eq_set_int A B) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (= A B)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (= A B)))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int B A) (=> (tptp.ord_less_eq_set_int C B) (tptp.ord_less_eq_set_int C A)))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (tptp.ord_less_eq_set_int B A) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (= A B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= A B) (and (tptp.ord_less_eq_set_int A B) (tptp.ord_less_eq_set_int B A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A B) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (= (= A B) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A B) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (= (= A B) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_nat_num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_nat_num F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_nat_num F C)))))))) (forall ((A tptp.num) (F tptp.fun_int_num) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_int_num F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_int_num F X3)) (tptp.aa_int_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_int_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F C)))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F C)))))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F B)) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F B)) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F A)) C)))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (tptp.ord_less_eq_set_int X Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_rat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_num F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_rat_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_nat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_rat_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_int F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_rat_int F C))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_rat F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_num_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_num F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_num_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_nat F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) (tptp.aa_num_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_num_int) (B tptp.num) (C tptp.num)) (=> (= A (tptp.aa_num_int F B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_num_int F C))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B tptp.nat) (C tptp.nat)) (=> (= A (tptp.aa_nat_rat F B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_nat_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_nat_num) (B tptp.nat) (C tptp.nat)) (=> (= A (tptp.aa_nat_num F B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) (tptp.aa_nat_num F C))))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (= (tptp.aa_rat_rat F B) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (= (tptp.aa_rat_num F B) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (= (tptp.aa_rat_nat F B) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (= (tptp.aa_rat_int F B) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (= (tptp.aa_num_rat F B) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (= (tptp.aa_num_num F B) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (= (tptp.aa_num_nat F B) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (= (tptp.aa_num_int F B) C) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (= (tptp.aa_nat_rat F B) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (= (tptp.aa_nat_num F B) C) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F X3)) (tptp.aa_nat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num F A)) C)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int Y X) (= (tptp.ord_less_eq_set_int X Y) (= X Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= X Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= X Y)))) (forall ((X tptp.real)) (exists ((Y4 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X)))) (forall ((X tptp.rat)) (exists ((Y4 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X)))) (forall ((X tptp.int)) (exists ((Y4 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y4) X)))) (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) X_1)))) (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) X_1)))) (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) X_1)))) (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) X_1)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (exists ((Z3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Z3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (exists ((Z3 tptp.rat)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (= X Y)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (= B C) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (forall ((Y2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y2) X3)) (tptp.pp (tptp.aa_nat_bool P Y2)))) (tptp.pp (tptp.aa_nat_bool P X3)))) (tptp.pp (tptp.aa_nat_bool P A)))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (= X Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (= X Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (= X Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (= X Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (=> (not (= X Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) A)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) A)))) (forall ((A tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) A)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) A)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) A)))) (forall ((P tptp.fun_nat_bool)) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_12))) (exists ((N5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool P N5)) (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M6) N5)) (not (tptp.pp (tptp.aa_nat_bool P M6))))))))) (forall ((P tptp.fun_re1255401033344146673l_bool) (A tptp.real) (B tptp.real)) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A3) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B2)))) (=> (forall ((A3 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) A3))) (=> (forall ((A3 tptp.real) (B2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P B2) A3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B2)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A) B)))))) (forall ((P tptp.fun_rat_fun_rat_bool) (A tptp.rat) (B tptp.rat)) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A3) B2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B2)))) (=> (forall ((A3 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) A3))) (=> (forall ((A3 tptp.rat) (B2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P B2) A3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A3) B2)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool P A) B)))))) (forall ((P tptp.fun_num_fun_num_bool) (A tptp.num) (B tptp.num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A3) B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B2)))) (=> (forall ((A3 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) A3))) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P B2) A3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A3) B2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool P A) B)))))) (forall ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A3) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)))) (=> (forall ((A3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) A3))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B2) A3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B)))))) (forall ((P tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A3) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B2)))) (=> (forall ((A3 tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) A3))) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P B2) A3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A3) B2)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A) B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((X tptp.real) (Y tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)) (= X Y)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (not (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (= A B)))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (not (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (= A B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (not (= A B)))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (not (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (not (= A B)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (not (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (not (= A B)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (not (= A B)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.real) (Y tptp.real)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) Z)) (tptp.pp (tptp.aa_real_bool _let_1 Z)))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num X))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((A tptp.real) (F tptp.fun_real_real) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_real F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real F C))))))) (forall ((A tptp.rat) (F tptp.fun_real_rat) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_rat F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_real_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_real_num) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_num F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X3)) (tptp.aa_real_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) (tptp.aa_real_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_real_nat) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_nat F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X3)) (tptp.aa_real_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_real_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_real_int) (B tptp.real) (C tptp.real)) (=> (= A (tptp.aa_real_int F B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F X3)) (tptp.aa_real_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_real_int F C))))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_real F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_rat_real F C))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_rat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat F C))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_num F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) (tptp.aa_rat_num F C))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_nat F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) (tptp.aa_rat_nat F C))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B tptp.rat) (C tptp.rat)) (=> (= A (tptp.aa_rat_int F B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_rat_int F C))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (= (tptp.aa_real_real F B) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F A)) C)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (= (tptp.aa_real_rat F B) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F A)) C)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (= (tptp.aa_real_num F B) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X3)) (tptp.aa_real_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F A)) C)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (= (tptp.aa_real_nat F B) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X3)) (tptp.aa_real_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F A)) C)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (= (tptp.aa_real_int F B) C) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F X3)) (tptp.aa_real_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_real F B) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_rat F B) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_num F B) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_nat F B) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (= (tptp.aa_rat_int F B) C) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F A)) C)))))) (forall ((X tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) X)))) (forall ((X tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) X)))) (forall ((X tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) X)))) (forall ((X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) X)))) (forall ((X tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) X)))) (forall ((A tptp.real) (F tptp.fun_real_real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real F B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_num_real) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_nat_real) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F X3)) (tptp.aa_nat_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real F C)))))))) (forall ((A tptp.real) (F tptp.fun_int_real) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_int_real F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X3)) (tptp.aa_int_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_int_real F C)))))))) (forall ((A tptp.rat) (F tptp.fun_real_rat) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_real_rat F B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_real_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F C)))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F C)))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F B)) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F A)) C)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F B)) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F A)) C)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F B)) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F X3)) (tptp.aa_real_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_real_num F A)) C)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F B)) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X3)) (tptp.aa_real_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F A)) C)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F B)) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F X3)) (tptp.aa_real_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_real_int F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F A)) C)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((X tptp.real) (Y tptp.real) (P tptp.bool)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (tptp.pp P)))) (forall ((X tptp.rat) (Y tptp.rat) (P tptp.bool)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)) (tptp.pp P)))) (forall ((X tptp.num) (Y tptp.num) (P tptp.bool)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)) (tptp.pp P)))) (forall ((X tptp.nat) (Y tptp.nat) (P tptp.bool)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)) (tptp.pp P)))) (forall ((X tptp.int) (Y tptp.int) (P tptp.bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)) (tptp.pp P)))) (forall ((X tptp.real) (Y tptp.real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (= X Y) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (= X Y) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (= X Y) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (= X Y) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (= Y X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (= Y X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (= Y X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (= Y X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (= Y X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X))))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X))))) (forall ((A2 tptp.set_nat) (C2 tptp.set_nat) (D2 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) C2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat D2) B3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.minus_minus_set_nat A2 B3)) (tptp.minus_minus_set_nat C2 D2)))))) (forall ((A2 tptp.set_int) (C2 tptp.set_int) (D2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 C2) (=> (tptp.ord_less_eq_set_int D2 B3) (tptp.ord_less_eq_set_int (tptp.minus_minus_set_int A2 B3) (tptp.minus_minus_set_int C2 D2))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.minus_minus_set_nat A2 B3)) A2))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (tptp.ord_less_eq_set_int (tptp.minus_minus_set_int A2 B3) A2)) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) C2)) (= (tptp.minus_minus_set_nat B3 (tptp.minus_minus_set_nat C2 A2)) A2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.ord_less_eq_set_int B3 C2) (= (tptp.minus_minus_set_int B3 (tptp.minus_minus_set_int C2 A2)) A2)))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X tptp.complex)) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (tptp.member_complex X A2) (tptp.member_complex X B3)))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X tptp.real)) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (tptp.member_real X A2) (tptp.member_real X B3)))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (X tptp.set_nat)) (=> (tptp.ord_le6893508408891458716et_nat A2 B3) (=> (tptp.member_set_nat X A2) (tptp.member_set_nat X B3)))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (tptp.member_nat X))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X tptp.int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.member_int X A2) (tptp.member_int X B3)))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (tptp.member_complex C A2) (tptp.member_complex C B3)))) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (tptp.member_real C A2) (tptp.member_real C B3)))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (C tptp.set_nat)) (=> (tptp.ord_le6893508408891458716et_nat A2 B3) (=> (tptp.member_set_nat C A2) (tptp.member_set_nat C B3)))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (tptp.member_nat C))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.member_int C A2) (tptp.member_int C B3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_set_int A2 B3) (not (=> (tptp.ord_less_eq_set_int A2 B3) (tptp.ord_less_eq_set_int B3 A2))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (not (=> (tptp.ord_less_eq_set_int A2 B3) (not (tptp.ord_less_eq_set_int B3 A2)))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (= (tptp.ord_le211207098394363844omplex A2 B3) (forall ((X4 tptp.complex)) (=> (tptp.member_complex X4 A2) (tptp.member_complex X4 B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (tptp.ord_less_eq_set_real A2 B3) (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A2) (tptp.member_real X4 B3))))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.ord_le6893508408891458716et_nat A2 B3) (forall ((X4 tptp.set_nat)) (=> (tptp.member_set_nat X4 A2) (tptp.member_set_nat X4 B3))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (forall ((X4 tptp.nat)) (let ((_let_1 (tptp.member_nat X4))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int A2 B3) (forall ((X4 tptp.int)) (=> (tptp.member_int X4 A2) (tptp.member_int X4 B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (tptp.ord_less_eq_set_int A2 B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (tptp.ord_less_eq_set_int B3 A2))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_set_int A2 B3) (and (tptp.ord_less_eq_set_int A2 B3) (not (= A2 B3))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (= (tptp.ord_le211207098394363844omplex A2 B3) (forall ((T2 tptp.complex)) (=> (tptp.member_complex T2 A2) (tptp.member_complex T2 B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (tptp.ord_less_eq_set_real A2 B3) (forall ((T2 tptp.real)) (=> (tptp.member_real T2 A2) (tptp.member_real T2 B3))))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.ord_le6893508408891458716et_nat A2 B3) (forall ((T2 tptp.set_nat)) (=> (tptp.member_set_nat T2 A2) (tptp.member_set_nat T2 B3))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (forall ((T2 tptp.nat)) (let ((_let_1 (tptp.member_nat T2))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 A2)) (tptp.pp (tptp.aa_set_nat_bool _let_1 B3))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int A2 B3) (forall ((T2 tptp.int)) (=> (tptp.member_int T2 A2) (tptp.member_int T2 B3))))) (forall ((A2 tptp.set_int)) (tptp.ord_less_eq_set_int A2 A2)) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q X3)))) (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int P) (tptp.collec213857154873943460nt_int Q)))) (forall ((P tptp.fun_complex_bool) (Q tptp.fun_complex_bool)) (=> (forall ((X3 tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool P X3)) (tptp.pp (tptp.aa_complex_bool Q X3)))) (tptp.ord_le211207098394363844omplex (tptp.collect_complex P) (tptp.collect_complex Q)))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool P X3)) (tptp.pp (tptp.aa_set_nat_bool Q X3)))) (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat P) (tptp.collect_set_nat Q)))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool Q X3)))) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.collect_nat P)) (tptp.collect_nat Q))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool Q X3)))) (tptp.ord_less_eq_set_int (tptp.collect_int P) (tptp.collect_int Q)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.ord_less_eq_set_int B3 C2) (tptp.ord_less_eq_set_int A2 C2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= A2 B3) (and (tptp.ord_less_eq_set_int A2 B3) (tptp.ord_less_eq_set_int B3 A2)))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (= (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int P) (tptp.collec213857154873943460nt_int Q)) (forall ((X4 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X4)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q X4)))))) (forall ((P tptp.fun_complex_bool) (Q tptp.fun_complex_bool)) (= (tptp.ord_le211207098394363844omplex (tptp.collect_complex P) (tptp.collect_complex Q)) (forall ((X4 tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool P X4)) (tptp.pp (tptp.aa_complex_bool Q X4)))))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (= (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat P) (tptp.collect_set_nat Q)) (forall ((X4 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool P X4)) (tptp.pp (tptp.aa_set_nat_bool Q X4)))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.collect_nat P)) (tptp.collect_nat Q))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X4)) (tptp.pp (tptp.aa_nat_bool Q X4)))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (= (tptp.ord_less_eq_set_int (tptp.collect_int P) (tptp.collect_int Q)) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X4)) (tptp.pp (tptp.aa_int_bool Q X4)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_set_int A2 B3) (tptp.ord_less_eq_set_int A2 B3))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (tptp.ord_less_set_int A2 B3) (=> (tptp.ord_less_eq_set_int B3 C2) (tptp.ord_less_set_int A2 C2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_set_int A2 B3) (and (tptp.ord_less_eq_set_int A2 B3) (not (tptp.ord_less_eq_set_int B3 A2))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C2 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.ord_less_set_int B3 C2) (tptp.ord_less_set_int A2 C2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int A2 B3) (or (tptp.ord_less_set_int A2 B3) (= A2 B3)))) (= tptp.bot_bo1796632182523588997nt_int (tptp.collec213857154873943460nt_int tptp.aTP_Lamm_aw)) (= tptp.bot_bot_set_complex (tptp.collect_complex tptp.aTP_Lamm_ax)) (= tptp.bot_bot_set_set_nat (tptp.collect_set_nat tptp.aTP_Lamm_ay)) (= tptp.bot_bot_set_nat (tptp.collect_nat tptp.aTP_Lamm_az)) (= tptp.bot_bot_set_int (tptp.collect_int tptp.aTP_Lamm_ba)) (= tptp.bot_bot_set_real (tptp.collect_real tptp.aTP_Lamm_bb)) (forall ((A2 tptp.set_real) (P tptp.fun_real_bool)) (tptp.ord_less_eq_set_real (tptp.collect_real (tptp.aa_fun6476784834714468668l_bool (tptp.aTP_Lamm_bc A2) P)) A2)) (forall ((A2 tptp.set_Pr958786334691620121nt_int) (P tptp.fun_Pr803113274115125473t_bool)) (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_bd A2) P)) A2)) (forall ((A2 tptp.set_complex) (P tptp.fun_complex_bool)) (tptp.ord_le211207098394363844omplex (tptp.collect_complex (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_be A2) P)) A2)) (forall ((A2 tptp.set_set_nat) (P tptp.fun_set_nat_bool)) (tptp.ord_le6893508408891458716et_nat (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_bf A2) P)) A2)) (forall ((A2 tptp.set_nat) (P tptp.fun_nat_bool)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bg A2) P))) A2))) (forall ((A2 tptp.set_int) (P tptp.fun_int_bool)) (tptp.ord_less_eq_set_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bh A2) P)) A2)) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (= (tptp.ord_le211207098394363844omplex A2 B3) (tptp.ord_le4633831435867229666x_bool (tptp.aTP_Lamm_ab A2) (tptp.aTP_Lamm_ab B3)))) (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (tptp.ord_less_eq_set_real A2 B3) (tptp.ord_le5573776112191778788l_bool (tptp.aTP_Lamm_a A2) (tptp.aTP_Lamm_a B3)))) (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (tptp.ord_le6893508408891458716et_nat A2 B3) (tptp.ord_le1461730252015488778t_bool (tptp.aTP_Lamm_ac A2) (tptp.aTP_Lamm_ac B3)))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (tptp.ord_le8840051076831633728t_bool (tptp.aTP_Lamm_ad A2) (tptp.aTP_Lamm_ad B3)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int A2 B3) (tptp.ord_le5715760110363009508t_bool (tptp.aTP_Lamm_ae A2) (tptp.aTP_Lamm_ae B3)))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int Y X) (not (tptp.ord_less_set_int X Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))))) (forall ((Y tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((A tptp.real) (B tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))) (= A B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (tptp.ord_less_set_int A B)) (or (not (tptp.ord_less_eq_set_int A B)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (= A B)))) (forall ((X tptp.real) (Y tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (not (tptp.ord_less_set_int X Y)) (= (tptp.ord_less_eq_set_int X Y) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y) (= (not (tptp.ord_less_set_int X Y)) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (= X Y)))) (forall ((Z tptp.real) (Y tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X3)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z)))) (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) X3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X3)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)))) (forall ((Y tptp.real) (Z tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Z)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z)))) (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Z)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.ord_less_set_int X Y) (and (tptp.ord_less_eq_set_int X Y) (not (tptp.ord_less_eq_set_int Y X))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))))) (forall ((Y tptp.real) (X tptp.real)) (=> (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))) (forall ((Y tptp.num) (X tptp.num)) (=> (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))) (forall ((Y tptp.int) (X tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (= A B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.ord_less_eq_set_int A B) (or (tptp.ord_less_set_int A B) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (= A B)))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (= A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (= A B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (not (= A B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.ord_less_set_int A B) (and (tptp.ord_less_eq_set_int A B) (not (= A B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (not (= A B))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (not (= A B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (not (= A B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (not (= A B))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (tptp.ord_less_set_int B C) (tptp.ord_less_set_int A C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) C))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) C)) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_set_int A B) (=> (tptp.ord_less_eq_set_int B C) (tptp.ord_less_set_int A C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (tptp.pp (tptp.aa_num_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (tptp.ord_less_set_int A B) (and (tptp.ord_less_eq_set_int A B) (not (tptp.ord_less_eq_set_int B A))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) X)) (=> (forall ((W2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) W2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real W2) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) W2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z))))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) X)) (=> (forall ((W2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) W2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W2) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) W2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (forall ((W2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) W2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real W2) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real W2) Z))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (forall ((W2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) W2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W2) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W2) Z))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z))))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (= A B)))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.ord_less_eq_set_int B A) (or (tptp.ord_less_set_int B A) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (= A B)))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (= A B)))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (= A B)))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (= A B)))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (not (= A B))))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.ord_less_set_int B A) (and (tptp.ord_less_eq_set_int B A) (not (= A B))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (= A B))))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (= A B))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (= A B))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (= A B))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_eq_set_int B A) (=> (tptp.ord_less_set_int C B) (tptp.ord_less_set_int C A)))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num C))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (=> (tptp.pp (tptp.aa_num_bool _let_1 B)) (tptp.pp (tptp.aa_num_bool _let_1 A)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) A))))) (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (tptp.ord_less_set_int B A) (=> (tptp.ord_less_eq_set_int C B) (tptp.ord_less_set_int C A)))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) A))))) (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) A))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) A))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) A))))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))))) (forall ((B tptp.set_int) (A tptp.set_int)) (= (tptp.ord_less_set_int B A) (and (tptp.ord_less_eq_set_int B A) (not (tptp.ord_less_eq_set_int A B))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))))) (forall ((B tptp.num) (A tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.ord_less_set_int A B) (tptp.ord_less_eq_set_int A B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) A)))) (forall ((B tptp.set_int) (A tptp.set_int)) (=> (tptp.ord_less_set_int B A) (tptp.ord_less_eq_set_int B A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.ord_less_eq_set_int X Y) (or (tptp.ord_less_set_int X Y) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (not (= X Y))))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.ord_less_set_int X Y) (and (tptp.ord_less_eq_set_int X Y) (not (= X Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (not (= X Y))))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (not (= X Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (not (= X Y))))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (not (= X Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.ord_less_set_int X Y) (tptp.ord_less_eq_set_int X Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (tptp.ord_less_eq_set_int A B) (=> (not (= A B)) (tptp.ord_less_set_int A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (not (= A B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (tptp.ord_less_eq_set_int A B) (tptp.ord_less_set_int A B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Z))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y) (=> (tptp.ord_less_set_int Y Z) (tptp.ord_less_set_int X Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Z))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) Z)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Z))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) Z)) (tptp.pp (tptp.aa_real_bool _let_1 Z)))))) (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (tptp.ord_less_set_int X Y) (=> (tptp.ord_less_eq_set_int Y Z) (tptp.ord_less_set_int X Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) Z)) (tptp.pp (tptp.aa_rat_bool _let_1 Z)))))) (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num X))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) Z)) (tptp.pp (tptp.aa_num_bool _let_1 Z)))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) Z)) (tptp.pp (tptp.aa_nat_bool _let_1 Z)))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) Z)) (tptp.pp (tptp.aa_int_bool _let_1 Z)))))) (forall ((A tptp.real) (F tptp.fun_real_real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real F B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real F C))))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_rat_real F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_rat_real F C))))))) (forall ((A tptp.real) (F tptp.fun_num_real) (B tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_num_real F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_num_real F C))))))) (forall ((A tptp.real) (F tptp.fun_nat_real) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_nat_real F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F X3)) (tptp.aa_nat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_nat_real F C))))))) (forall ((A tptp.real) (F tptp.fun_int_real) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_int_real F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X3)) (tptp.aa_int_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_int_real F C))))))) (forall ((A tptp.rat) (F tptp.fun_real_rat) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_real_rat F B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_real_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_num_rat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_num_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_nat_rat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_nat_rat F B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_nat_rat F C))))))) (forall ((A tptp.rat) (F tptp.fun_int_rat) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_int_rat F B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) C)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_int_rat F C))))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_rat_num F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_rat_nat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_rat_int F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_num) (C tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_int) (C tptp.int)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int F A)) C)))))) (forall ((A tptp.real) (F tptp.fun_rat_real) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_rat_real F C)))))))) (forall ((A tptp.rat) (F tptp.fun_rat_rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_rat_num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_rat_num F X3)) (tptp.aa_rat_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_rat_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_rat_nat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_rat_nat F X3)) (tptp.aa_rat_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_rat_nat F C)))))))) (forall ((A tptp.int) (F tptp.fun_rat_int) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_rat_int F B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_rat_int F X3)) (tptp.aa_rat_int F Y4))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_rat_int F C)))))))) (forall ((A tptp.real) (F tptp.fun_num_real) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_num_real F C)))))))) (forall ((A tptp.rat) (F tptp.fun_num_rat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_num_rat F C)))))))) (forall ((A tptp.num) (F tptp.fun_num_num) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num A))) (=> (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num F X3)) (tptp.aa_num_num F Y4))))) (tptp.pp (tptp.aa_num_bool _let_1 (tptp.aa_num_num F C)))))))) (forall ((A tptp.nat) (F tptp.fun_num_nat) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat F X3)) (tptp.aa_num_nat F Y4))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_num_nat F C)))))))) (forall ((A tptp.int) (F tptp.fun_num_int) (B tptp.num) (C tptp.num)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_num_int F B))) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Y4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int F X3)) (tptp.aa_num_int F Y4))))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_num_int F C)))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F B)) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_rat_real F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F X3)) (tptp.aa_rat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_rat_real F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F X3)) (tptp.aa_num_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F B)) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F X3)) (tptp.aa_nat_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real F A)) C)))))) (forall ((A tptp.int) (B tptp.int) (F tptp.fun_int_real) (C tptp.real)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F B)) C)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X3)) (tptp.aa_int_real F Y4))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F A)) C)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F B)) C)) (=> (forall ((X3 tptp.real) (Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F A)) C)))))) (forall ((A tptp.rat) (B tptp.rat) (F tptp.fun_rat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat F B)) C)) (=> (forall ((X3 tptp.rat) (Y4 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F X3)) (tptp.aa_rat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat F A)) C)))))) (forall ((A tptp.num) (B tptp.num) (F tptp.fun_num_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat F B)) C)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F X3)) (tptp.aa_num_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat F A)) C)))))) (forall ((A tptp.nat) (B tptp.nat) (F tptp.fun_nat_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F B)) C)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F A)) C)))))) (forall ((A tptp.int) (B tptp.int) (F tptp.fun_int_rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F B)) C)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Y4)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat F Y4))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F A)) C)))))) (forall ((X tptp.real) (Y tptp.real)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))) (forall ((X tptp.rat) (Y tptp.rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) X)))) (forall ((X tptp.num) (Y tptp.num)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Y) X)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Y) X)))) (forall ((X tptp.int) (Y tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (= X Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y) (or (tptp.ord_less_set_int X Y) (= X Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X) Y)) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)) (= X Y)))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)) (= X Y)))) (forall ((A tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A))) (forall ((A tptp.set_real)) (tptp.ord_less_eq_set_real tptp.bot_bot_set_real A)) (forall ((A tptp.set_int)) (tptp.ord_less_eq_set_int tptp.bot_bot_set_int A)) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.bot_bot_nat) A))) (forall ((A tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat)) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.set_real)) (= (tptp.ord_less_eq_set_real A tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_int)) (= (tptp.ord_less_eq_set_int A tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.bot_bot_nat)) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat)) (= A tptp.bot_bot_set_nat))) (forall ((A tptp.set_real)) (=> (tptp.ord_less_eq_set_real A tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))) (forall ((A tptp.set_int)) (=> (tptp.ord_less_eq_set_int A tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.bot_bot_nat)) (= A tptp.bot_bot_nat))) (forall ((A tptp.set_nat)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat A) tptp.bot_bot_set_nat)))) (forall ((A tptp.set_int)) (not (tptp.ord_less_set_int A tptp.bot_bot_set_int))) (forall ((A tptp.set_real)) (not (tptp.ord_less_set_real A tptp.bot_bot_set_real))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.bot_bot_nat)))) (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat tptp.bot_bot_set_nat) A)))) (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (tptp.ord_less_set_int tptp.bot_bot_set_int A))) (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (tptp.ord_less_set_real tptp.bot_bot_set_real A))) (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.bot_bot_nat) A)))) (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat A) B))) (let ((_let_2 (tptp.ord_le2932123472753598470d_enat A B))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.ord_max_Code_integer A B))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) B)))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.set_int) (B tptp.set_int)) (let ((_let_1 (tptp.ord_max_set_int A B))) (let ((_let_2 (tptp.ord_less_eq_set_int A B))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.ord_max_rat A) B))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.num) (B tptp.num)) (let ((_let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num A) B))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B)))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat A) B))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int A) B))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 A)))))) (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat Y X) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y) X))) (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger Y) X)) (= (tptp.ord_max_Code_integer X Y) X))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int Y X) (= (tptp.ord_max_set_int X Y) X))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) X)) (= (tptp.aa_rat_rat (tptp.ord_max_rat X) Y) X))) (forall ((Y tptp.num) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Y) X)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y) X))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y) X))) (forall ((Y tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Y) X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y) X))) (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (tptp.ord_le2932123472753598470d_enat X Y) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X) Y) Y))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) Y)) (= (tptp.ord_max_Code_integer X Y) Y))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y) (= (tptp.ord_max_set_int X Y) Y))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (= (tptp.aa_rat_rat (tptp.ord_max_rat X) Y) Y))) (forall ((X tptp.num) (Y tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X) Y) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y) Y))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X) Y) Y))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) B) A)) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) B) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) B) A)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) B) A)) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) A) B)) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) A) B)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) A) B)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) A) B)) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat C))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) B) A)) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) B) A)) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) B) A)) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) B) A)) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.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.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B)) C)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C)) B))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) B))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) B))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 B)) C) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.times_times_rat B) C))))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) A) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat B) A)) 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.plus_plus_rat A))) (= (= (tptp.aa_rat_rat _let_1 B) (tptp.aa_rat_rat _let_1 C)) (= B C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (= (tptp.aa_nat_nat _let_1 B) (tptp.aa_nat_nat _let_1 C)) (= B C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (= (tptp.aa_int_int _let_1 B) (tptp.aa_int_int _let_1 C)) (= B C)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.plus_plus_rat B) A) (tptp.aa_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 ((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.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_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.plus_plus_rat A) C)) (tptp.aa_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_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.plus_plus_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.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.aa_com3342990543769683525omplex 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.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 ((X2 tptp.real)) (exists ((X_1 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) X_1)))) (forall ((X2 tptp.rat)) (exists ((X_1 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) X_1)))) (forall ((X2 tptp.real)) (exists ((Y4 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y4) X2)))) (forall ((X2 tptp.rat)) (exists ((Y4 tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y4) X2)))) (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.times_times_rat A))) (= (tptp.aa_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.times_times_rat B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.times_times_rat A))) (= (tptp.aa_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.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.times_times_rat A) B) (tptp.aa_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 ((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.times_times_rat B))) (let ((_let_2 (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 ((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.plus_plus_rat A))) (= (tptp.aa_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.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 ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I2 J) (= K L)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real I2) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (= K L)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat I2) K) (tptp.aa_rat_rat (tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (= K L)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (= K L)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L)))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K))) (=> (= A2 (tptp.aa_real_real _let_1 A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A2) B) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)))))) (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat K))) (=> (= A2 (tptp.aa_rat_rat _let_1 A)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat A2) B) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)))))) (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (=> (= A2 (tptp.aa_nat_nat _let_1 A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A2) B) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)))))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (=> (= A2 (tptp.aa_int_int _let_1 A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A2) B) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)))))) (forall ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K))) (=> (= B3 (tptp.aa_real_real _let_2 B)) (= (tptp.aa_real_real _let_1 B3) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 B))))))) (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat A))) (let ((_let_2 (tptp.plus_plus_rat K))) (=> (= B3 (tptp.aa_rat_rat _let_2 B)) (= (tptp.aa_rat_rat _let_1 B3) (tptp.aa_rat_rat _let_2 (tptp.aa_rat_rat _let_1 B))))))) (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (=> (= B3 (tptp.aa_nat_nat _let_2 B)) (= (tptp.aa_nat_nat _let_1 B3) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 B))))))) (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (=> (= B3 (tptp.aa_int_int _let_2 B)) (= (tptp.aa_int_int _let_1 B3) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 B))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat A))) (= (tptp.aa_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.plus_plus_rat B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 B)) C) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 B)) C) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (= (tptp.aa_real_real _let_1 B) (tptp.aa_real_real _let_1 C)) (= B C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat A))) (= (= (tptp.aa_rat_rat _let_1 B) (tptp.aa_rat_rat _let_1 C)) (= B C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (= (tptp.aa_int_int _let_1 B) (tptp.aa_int_int _let_1 C)) (= B C)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.plus_plus_rat B) A) (tptp.aa_rat_rat (tptp.plus_plus_rat C) A)) (= B C))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) A)) (= B C))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat A) B) (tptp.aa_rat_rat (tptp.plus_plus_rat B) A))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_2 C)) (tptp.aa_real_real _let_2 (tptp.aa_real_real _let_1 C)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat B))) (let ((_let_2 (tptp.plus_plus_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_2 C)) (tptp.aa_rat_rat _let_2 (tptp.aa_rat_rat _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_2 C)) (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat _let_1 C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 C)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A))) (=> (= (tptp.aa_real_real _let_1 B) (tptp.aa_real_real _let_1 C)) (= B C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat A))) (=> (= (tptp.aa_rat_rat _let_1 B) (tptp.aa_rat_rat _let_1 C)) (= B C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (=> (= (tptp.aa_nat_nat _let_1 B) (tptp.aa_nat_nat _let_1 C)) (= B C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (=> (= (tptp.aa_int_int _let_1 B) (tptp.aa_int_int _let_1 C)) (= B C)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) A)) (= B C))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.plus_plus_rat B) A) (tptp.aa_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 ((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 ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 C)) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B)) C)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat A))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 C)) B) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) C)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 C)) B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat _let_1 B)) C)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 C)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) D)) (= (= A B) (= C D)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)) (= (= A B) (= C D)))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I2 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 I2) 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.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.plus_plus_rat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I2 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 I2) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 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.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 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 I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I2 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 I2) 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.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.plus_plus_rat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat B) D)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) D)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (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.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.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)) (=> (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.plus_plus_rat A) C)) (tptp.aa_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)) (exists ((C4 tptp.nat)) (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C4))))) (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.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_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.plus_plus_rat A) C)) (tptp.aa_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 ((I2 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 I2) 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 I2) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I2 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 I2) 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.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.plus_plus_rat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I2 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 I2) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 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.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.plus_plus_rat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 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 I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I2 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 I2) J)) (= K L)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.plus_plus_rat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) D)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat B) D)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) D)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (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.aa_rat_rat (tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) D))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (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.aa_rat_rat (tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C))))) (forall ((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)) (let ((_let_1 (tptp.minus_minus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)))))) (forall ((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.aa_rat_rat (tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat B) D)))))) (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int D) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) D)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real C) D)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) D))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.minus_minus_rat C) D)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) D))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) D)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D))))) (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real D) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) D)))))) (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat D) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat B) D)))))) (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int D) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) D)))))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat tptp.one_one_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.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 ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex Z) W)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat Z) W)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.times_times_rat Y) W)))) (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex Z) W)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) W)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Y) Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Z) W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z)))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat Z) W)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat X) W)) (tptp.aa_rat_rat (tptp.times_times_rat Y) Z)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 B)) C) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C) B))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.times_times_rat C) B))))) (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K))) (=> (= A2 (tptp.aa_real_real _let_1 A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A2) B) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))))) (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat K))) (=> (= A2 (tptp.aa_rat_rat _let_1 A)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A2) B) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)))))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (=> (= A2 (tptp.aa_int_int _let_1 A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A2) B) (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) C) (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) B)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) C) (= A (tptp.aa_rat_rat (tptp.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.aa_rat_rat (tptp.minus_minus_rat C) B)) (= (tptp.aa_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.plus_plus_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 B)) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) C)) B))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.minus_minus_rat B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.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.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) C) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.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)) (let ((_let_1 (tptp.minus_minus_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat B) C)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 C)) B)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 C)) B)))) (forall ((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.plus_plus_rat C) B) A) (= C (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat C) B) A) (= C (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) B)))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) B) A) (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 B)) C) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat A))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat _let_1 B)) C) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.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 ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)) C) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) C) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B)) C) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) C) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))) (forall ((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.plus_plus_rat (tptp.aa_rat_rat (tptp.ord_max_rat X) Y)) Z) (tptp.aa_rat_rat (tptp.ord_max_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) Z)) (tptp.aa_rat_rat (tptp.plus_plus_rat Y) Z)))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) Z) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.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.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.ord_max_Code_integer X Y) Z) (tptp.ord_max_Code_integer (tptp.plus_p5714425477246183910nteger X Z) (tptp.plus_p5714425477246183910nteger Y Z)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real Y) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_real_real _let_1 Y)) (tptp.aa_real_real _let_1 Z))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.plus_plus_rat X))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat (tptp.ord_max_rat Y) Z)) (tptp.aa_rat_rat (tptp.ord_max_rat (tptp.aa_rat_rat _let_1 Y)) (tptp.aa_rat_rat _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat Y) Z)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat _let_1 Y)) (tptp.aa_nat_nat _let_1 Z))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int X))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.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.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger X (tptp.ord_max_Code_integer Y Z)) (tptp.ord_max_Code_integer (tptp.plus_p5714425477246183910nteger X Y) (tptp.plus_p5714425477246183910nteger X Z)))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger (tptp.ord_max_Code_integer X Y) Z) (tptp.ord_max_Code_integer (tptp.minus_8373710615458151222nteger X Z) (tptp.minus_8373710615458151222nteger 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.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.ord_max_rat X) Y)) Z) (tptp.aa_rat_rat (tptp.ord_max_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Z)) (tptp.aa_rat_rat (tptp.minus_minus_rat Y) Z)))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.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 ((I2 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 I2) 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 I2) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I2 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 I2) 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.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.plus_plus_rat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real J) L))))) (forall ((I2 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 I2) 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.plus_plus_rat I2) K)) (tptp.aa_rat_rat (tptp.plus_plus_rat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat J) L))))) (forall ((I2 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 I2) 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 I2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) L))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.plus_plus_rat A) C)) (tptp.aa_rat_rat (tptp.plus_plus_rat B) D)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) D)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) D)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) D)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.plus_plus_rat A) C)) (tptp.aa_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)) (= (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.aa_rat_rat (tptp.minus_minus_rat A) B)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.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.aa_rat_rat (tptp.minus_minus_rat C) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.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 ((A tptp.real) (B tptp.real) (C tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real C) B))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.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.aa_rat_rat (tptp.minus_minus_rat C) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.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_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) (tptp.aa_rat_rat (tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) (tptp.aa_rat_rat (tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) _let_1 TreeList Vc)) X)) (or (= X Mi) (= X Ma) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) _let_2)))) _let_4)))))))) (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.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 S2)) X)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList _let_3)) (tptp.aa_nat_nat (tptp.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 ((L tptp.num) (R2 tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (tptp.unique5026877609467782581ep_nat L (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Q2) R2)))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat L))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) R2)))) (and (=> _let_4 (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat R2) _let_3)))) (=> (not _let_4) (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat _let_1) R2))))))))) (forall ((L tptp.num) (R2 tptp.int) (Q2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R2)))) (let ((_let_3 (tptp.aa_num_int tptp.numeral_numeral_int L))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_3) R2)))) (and (=> _let_4 (= _let_2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int R2) _let_3)))) (=> (not _let_4) (= _let_2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_1) R2))))))))) (forall ((L tptp.num) (R2 tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (tptp.unique4921790084139445826nteger L (tptp.produc1086072967326762835nteger Q2 R2)))) (let ((_let_3 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger L))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_3) R2)))) (and (=> _let_4 (= _let_2 (tptp.produc1086072967326762835nteger (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger R2 _let_3)))) (=> (not _let_4) (= _let_2 (tptp.produc1086072967326762835nteger _let_1 R2))))))))) (forall ((N2 tptp.nat) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.vEBT_vebt_buildup N2)) X)))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (tptp.vEBT_vebt_pred X Xa2) Y) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A3 tptp.bool)) (let ((_let_1 (tptp.pp A3))) (=> (exists ((Uw2 tptp.bool)) (= X (tptp.vEBT_Leaf A3 Uw2))) (=> (= Xa2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (not (and (=> _let_1 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_1) (= Y tptp.none_nat)))))))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.pp A3))) (let ((_let_2 (tptp.pp B2))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (=> (exists ((Va2 tptp.nat)) (= Xa2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (not (and (=> _let_2 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (and (=> _let_1 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_1) (= Y tptp.none_nat))))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uy2 Uz2 Va3))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Vd2 Ve))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vh Vi))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.vEBT_vebt_pred Summary2 _let_4))) (let ((_let_6 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_3))))) (let ((_let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_8 (tptp.nth_VEBT_VEBT TreeList2 _let_4))) (let ((_let_9 (tptp.vEBT_vebt_mint _let_8))) (let ((_let_10 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2)))) (=> (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_2 TreeList2 Summary2)) (not (and (=> _let_10 (= Y (tptp.some_nat Ma2))) (=> (not _let_10) (= Y (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_7)) _let_9)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 (tptp.some_nat _let_4))) (tptp.vEBT_vebt_pred _let_8 _let_7)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) Xa2) (tptp.some_nat Mi2) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 _let_5)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList2 (tptp.the_nat _let_5)))))) tptp.none_nat))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (tptp.vEBT_vebt_succ X Xa2) Y) (=> (forall ((Uu2 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.pp B2))) (=> (= X (tptp.vEBT_Leaf Uu2 B2)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> _let_1 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_1) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uv2 tptp.bool) (Uw2 tptp.bool)) (= X (tptp.vEBT_Leaf Uv2 Uw2))) (=> (exists ((N tptp.nat)) (= Xa2 (tptp.aa_nat_nat tptp.suc N))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Ux2 Uy2 Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Vc2 Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vg Vh))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.vEBT_vebt_succ Summary2 _let_4))) (let ((_let_6 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_3))))) (let ((_let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_8 (tptp.nth_VEBT_VEBT TreeList2 _let_4))) (let ((_let_9 (tptp.vEBT_vebt_maxt _let_8))) (let ((_let_10 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2)))) (=> (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_2 TreeList2 Summary2)) (not (and (=> _let_10 (= Y (tptp.some_nat Mi2))) (=> (not _let_10) (= Y (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_9) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_less (tptp.some_nat _let_7)) _let_9)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 (tptp.some_nat _let_4))) (tptp.vEBT_vebt_succ _let_8 _let_7)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_5) tptp.none_nat) tptp.none_nat (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_6 _let_5)) (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList2 (tptp.the_nat _let_5)))))) tptp.none_nat)))))))))))))))))))))))))) (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 ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (tptp.vEBT_vebt_delete X Xa2) Y) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (=> (= X (tptp.vEBT_Leaf A3 B2)) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y (tptp.vEBT_Leaf tptp.fFalse B2)))))) (=> (forall ((A3 tptp.bool)) (=> (exists ((B2 tptp.bool)) (= X (tptp.vEBT_Leaf A3 B2))) (=> (= Xa2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (not (= Y (tptp.vEBT_Leaf A3 tptp.fFalse)))))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_1) (=> (exists ((N tptp.nat)) (= Xa2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (not (= Y _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg2 TreeList2 Summary2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry 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 TrLst Smry))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm 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.aa_nat_nat tptp.suc tptp.zero_zero_nat) Tr Sm))) (=> (= X _let_1) (not (= Y _let_1))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (tptp.the_nat (tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (let ((_let_7 (tptp.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_5) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList2 _let_5)))))) (let ((_let_8 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Xa2))) (let ((_let_9 (tptp.aa_nat_bool _let_8 Mi2))) (let ((_let_10 (tptp.if_nat _let_9))) (let ((_let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_10 _let_7) Xa2))) (let ((_let_12 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList2 _let_12) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (tptp.list_u1324408373059187874T_VEBT TreeList2 _let_12 _let_13))) (let ((_let_15 (tptp.if_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies _let_9) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat _let_7) Ma2))) (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies (tptp.aa_bool_bool tptp.fNot _let_9)) (tptp.aa_nat_bool _let_8 Ma2)))))) (let ((_let_16 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_10 _let_11) Mi2))) (let ((_let_17 (tptp.product_Pair_nat_nat _let_16))) (let ((_let_18 (tptp.vEBT_vebt_delete Summary2 _let_12))) (let ((_let_19 (tptp.vEBT_vebt_maxt _let_18))) (let ((_let_20 (tptp.the_nat _let_19))) (let ((_let_21 (and (= Xa2 Mi2) (= Xa2 Ma2)))) (let ((_let_22 (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (=> (= X _let_2) (not (and (=> _let_22 (= Y _let_2)) (=> (not _let_22) (and (=> _let_21 (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Summary2))) (=> (not _let_21) (= Y (tptp.if_VEBT_VEBT (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_12) (tptp.size_s6755466524823107622T_VEBT TreeList2)) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_13) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_17 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_15 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_19) tptp.none_nat)) _let_16) (tptp.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_6) _let_20)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_14 _let_20)))))) Ma2))) _let_1 _let_14 _let_18) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_17 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_15 (tptp.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_12) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_14 _let_12))))) Ma2))) _let_1 _let_14 Summary2)) _let_2)))))))))))))))))))))))))))))))))))))))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) N2) (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))) N2)))) (forall ((T tptp.vEBT_VEBT)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) tptp.zero_zero_nat)))) (forall ((T tptp.vEBT_VEBT)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_vebt_buildup N2)) X)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.bool) (B tptp.bool)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt (tptp.vEBT_Leaf A B)) tptp.zero_zero_nat)))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (=> (= N2 tptp.one_one_nat) (exists ((A3 tptp.bool) (B2 tptp.bool)) (= T (tptp.vEBT_Leaf A3 B2)))))) (forall ((T tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) tptp.one_one_nat)) (exists ((A3 tptp.bool) (B2 tptp.bool)) (= T (tptp.vEBT_Leaf A3 B2))))) (forall ((T tptp.vEBT_VEBT)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) tptp.one_one_nat)) (exists ((A4 tptp.bool) (B4 tptp.bool)) (= T (tptp.vEBT_Leaf A4 B4))))) (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 ((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.vEBT_invar_vebt (tptp.vEBT_vebt_buildup N2)) N2)))) (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 ((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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int 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 ((Tree tptp.vEBT_VEBT) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Tree) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member Tree) X)) (or (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member Tree) X)) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima Tree) X)))))) (forall ((X21 tptp.bool) (X222 tptp.bool) (Y21 tptp.bool) (Y222 tptp.bool)) (= (= (tptp.vEBT_Leaf X21 X222) (tptp.vEBT_Leaf Y21 Y222)) (and (= (tptp.pp X21) (tptp.pp Y21)) (= (tptp.pp X222) (tptp.pp Y222))))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))) (= N2 tptp.zero_zero_nat))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.times_times_rat A) C) (tptp.aa_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.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C))) (= (= (tptp.aa_complex_complex _let_1 A) (tptp.aa_complex_complex _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (= (= (tptp.aa_real_real _let_1 A) (tptp.aa_real_real _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.times_times_rat C))) (= (= (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (= (= (tptp.aa_nat_nat _let_1 A) (tptp.aa_nat_nat _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (= (tptp.aa_int_int _let_1 A) (tptp.aa_int_int _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat (tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))) (forall ((B tptp.complex) (A tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))) (forall ((B tptp.real) (A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))) (forall ((B tptp.nat) (A tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))) (forall ((B tptp.int) (A tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) A) tptp.zero_zero_rat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) A) tptp.zero_zero_int)) (forall ((A tptp.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.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) C) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) C) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex C))) (= (= (tptp.aa_complex_complex _let_1 A) (tptp.aa_complex_complex _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real C))) (= (= (tptp.aa_real_real _let_1 A) (tptp.aa_real_real _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat C))) (= (= (tptp.aa_rat_rat _let_1 A) (tptp.aa_rat_rat _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) tptp.zero_zero_int) A)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A tptp.zero_z3403309356797280102nteger) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (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 ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N2 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 tptp.zero_zero_nat) A))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N2))) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_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.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) B) (tptp.modulo364778990260209775nteger A B))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_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.modulo_modulo_int A) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger B A) B) (tptp.modulo364778990260209775nteger A B))) (forall ((M tptp.nat) (K tptp.nat) (N2 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 N2) K)) (or (= M N2) (= K tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (or (= M N2) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) B) (tptp.modulo364778990260209775nteger A B))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2) M))) (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 ((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.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 A) tptp.zero_zero_nat) A)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)) (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.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.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.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.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.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.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)) (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.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.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.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.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.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.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_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.aa_rat_rat (tptp.minus_minus_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.minus_minus_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) A)))) (forall ((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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) X)) (tptp.aa_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 ((C tptp.complex) (B tptp.complex)) (= (= C (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (forall ((C tptp.int) (B tptp.int)) (= (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))) (forall ((C tptp.complex) (A tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.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.aa_com3342990543769683525omplex 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.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))) (forall ((C tptp.int) (B tptp.int)) (= (= C (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))) (forall ((A tptp.complex) (C tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.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 ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B)) B) A))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) B) A))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.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 ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B)) A) B))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.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 ((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)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.times_times_rat C) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.times_times_rat B) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C) A)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat C) A)) (tptp.aa_rat_rat (tptp.times_times_rat B) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 A)) (tptp.aa_complex_complex _let_1 B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C))) (let ((_let_2 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat C))) (let ((_let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)))))))) (forall ((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)) (= (tptp.aa_complex_complex _let_117 tptp.one_one_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real _let_119 tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_rat_rat _let_116 tptp.one_one_rat) tptp.zero_zero_rat) (= (tptp.aa_int_int _let_118 tptp.one_one_int) tptp.zero_zero_int) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) A) tptp.one_one_rat))) (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) A) tptp.one_one_nat))) (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) A) tptp.one_one_int))) (forall ((A tptp.real)) (= (= tptp.zero_zero_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))) (forall ((B tptp.real) (A tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) A) tptp.one_one_rat))) (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_rat)) (forall ((N2 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 N2)) tptp.zero_zero_nat)) (forall ((N2 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 N2)) tptp.zero_zero_real)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int) (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_int)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.zero_zero_complex) (tptp.aa_nat_nat tptp.suc N2)) 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.aa_int_fun_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.aa_com8181001469867462503omplex tptp.power_power_complex tptp.zero_zero_complex) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) B) tptp.zero_zero_int)) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) B) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.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.aa_int_fun_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.aa_com8181001469867462503omplex tptp.power_power_complex A) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) A)) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A B) B) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A B) B) tptp.zero_z3403309356797280102nteger)) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C) A) B) (tptp.modulo364778990260209775nteger A B))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B)) A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B) A) B) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) B) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B)) B) (tptp.modulo364778990260209775nteger A B))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= N2 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) (tptp.aa_nat_nat tptp.suc N2)))) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera1916890842035813515d_enat X))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X))) (= (tptp.ord_max_Code_integer _let_1 tptp.zero_z3403309356797280102nteger) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.numera1916890842035813515d_enat X))) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X))) (= (tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat X))) (= (tptp.aa_rat_rat (tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))) (forall ((X tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))) (forall ((M tptp.nat) (N2 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) N2)) (and (= M _let_1) (= N2 _let_1))))) (forall ((M tptp.nat) (N2 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) N2) _let_1) (and (= M _let_1) (= N2 _let_1))))) (forall ((M tptp.nat) (N2 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) N2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real) (= (tptp.aa_rat_rat (tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int) (= (tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger tptp.one_one_Code_integer) tptp.one_one_Code_integer) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real) (= (tptp.aa_rat_rat (tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int) (= (tptp.ord_max_Code_integer tptp.one_one_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) (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 ((N2 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) N2) _let_1))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (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) N2)))))) (forall ((M tptp.nat) (N2 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) N2))) (and (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (forall ((M tptp.nat) (K tptp.nat) (N2 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 N2) 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) N2))))) (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) (N2 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) N2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (= N2 tptp.zero_zero_nat))))) (forall ((N2 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 N2) M))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.one_one_nat)) (= N2 tptp.zero_zero_nat))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)))) (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) N2)))))))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))) (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool _let_1 B)))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B)))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((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 ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) A)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) (tptp.aa_rat_rat (tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) A)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_rat_rat (tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) B)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) N2) 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) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2) 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) N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2) 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) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2) 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) N2))))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2) 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) N2))))) (forall ((M tptp.nat) (N2 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) N2))) (and (tptp.pp (tptp.aa_nat_bool _let_1 M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (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.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) N2))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (=> (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) N2)))))) (forall ((M tptp.nat) (K tptp.nat) (N2 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 N2) 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) N2))))) (forall ((N2 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) N2)) (= (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 N2) M)) N2) M))) (forall ((N2 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) N2)) (= (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) N2)) N2) M))) (forall ((N2 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 N2) K)) M))) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N2))) (forall ((K tptp.nat) (N2 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) N2)) M))) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N2))) (forall ((M tptp.nat) (N2 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 N2) K)))) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N2))) (forall ((M tptp.nat) (K tptp.nat) (N2 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) N2)))) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N2))) (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.aa_rat_rat (tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real 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.aa_rat_rat (tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real 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.aa_rat_rat (tptp.divide_divide_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real 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.aa_rat_rat (tptp.divide_divide_rat B) A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.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.aa_int_fun_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.aa_com8181001469867462503omplex tptp.power_power_complex A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((B tptp.real) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))))) (forall ((B tptp.rat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))))) (forall ((B tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))))) (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M))))))) (forall ((A tptp.real) (B tptp.real) (N2 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) N2)) (= (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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))))))) (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2)) (= (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) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2))) (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) (N2 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) 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.power_power_nat A) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2))) (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) (N2 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) N2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))))) _let_158 _let_157 _let_156 _let_158 _let_157 _let_156 (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 ((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.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))) (forall ((K tptp.num) (N2 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) N2))) _let_1) tptp.one_one_nat)))) _let_155 _let_154 _let_155 _let_154 (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.aa_int_fun_nat_int tptp.power_power_int X) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_int_fun_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.aa_int_fun_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 ((B tptp.real) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M))))))) (forall ((B tptp.rat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M))))))) (forall ((B tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M))))))) (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M))))))) (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.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.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (= _let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) M)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (= _let_1 tptp.one_one_nat)))) (forall ((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.aa_int_int (tptp.aa_int_fun_int_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.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) A)))) (forall ((M tptp.nat) (N2 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) N2)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N2))) (let ((_let_3 (= _let_1 N2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 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) N2)) (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) N2)) N2)))) (forall ((Uu tptp.bool) (Uv tptp.bool) (Uw tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Leaf Uu Uv)) Uw)))) (forall ((M tptp.nat) (D tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat D) Q3))))) (forall ((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 ((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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B) A) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.modulo364778990260209775nteger A B) A) (= (tptp.divide6298287555418463151nteger A B) tptp.zero_z3403309356797280102nteger))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool) (D3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uu2 Uv2) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2) Deg3))))))) (forall ((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.bot_bot_nat tptp.zero_zero_nat) (forall ((A tptp.bool) (B tptp.bool)) (= (tptp.vEBT_vebt_delete (tptp.vEBT_Leaf A B) tptp.zero_zero_nat) (tptp.vEBT_Leaf tptp.fFalse B))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B2) X3)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Uy2 (tptp.aa_nat_nat tptp.suc V2) TreeList2 S) X3)))))))) (= (tptp.vEBT_vebt_buildup tptp.zero_zero_nat) _let_153) (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.aa_int_int (tptp.aa_int_fun_int_int 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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))))) (forall ((N2 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 N2))) (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 N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))) (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_zero_int) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) (tptp.aa_num_int tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))) (forall ((N2 tptp.num) (Q2 tptp.num)) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)) (forall ((N2 tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)) (forall ((N2 tptp.num)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)) (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.vEBT_Node Uu tptp.zero_zero_nat Uv Uw)) Ux)))) (forall ((X tptp.produc1260151622200656695at_nat)) (=> (forall ((Uu2 tptp.fun_Pr2477239776880934807at_nat) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (tptp.produc7814092408141220007at_nat Uu2 (tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat Uv2))))) (=> (forall ((Uw2 tptp.fun_Pr2477239776880934807at_nat) (V2 tptp.product_prod_nat_nat)) (not (= X (tptp.produc7814092408141220007at_nat Uw2 (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat V2) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 tptp.fun_Pr2477239776880934807at_nat) (A3 tptp.product_prod_nat_nat) (B2 tptp.product_prod_nat_nat)) (not (= X (tptp.produc7814092408141220007at_nat F2 (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat A3) (tptp.some_P7363390416028606310at_nat B2)))))))))) (forall ((X tptp.produc7004362771917097900on_nat)) (=> (forall ((Uu2 tptp.fun_nat_fun_nat_nat) (Uv2 tptp.option_nat)) (not (= X (tptp.produc6699827698519632094on_nat Uu2 (tptp.produc5098337634421038937on_nat tptp.none_nat Uv2))))) (=> (forall ((Uw2 tptp.fun_nat_fun_nat_nat) (V2 tptp.nat)) (not (= X (tptp.produc6699827698519632094on_nat Uw2 (tptp.produc5098337634421038937on_nat (tptp.some_nat V2) tptp.none_nat))))) (not (forall ((F2 tptp.fun_nat_fun_nat_nat) (A3 tptp.nat) (B2 tptp.nat)) (not (= X (tptp.produc6699827698519632094on_nat F2 (tptp.produc5098337634421038937on_nat (tptp.some_nat A3) (tptp.some_nat B2)))))))))) (forall ((X tptp.produc2703417854250991842on_num)) (=> (forall ((Uu2 tptp.fun_num_fun_num_num) (Uv2 tptp.option_num)) (not (= X (tptp.produc6360833703471310868on_num Uu2 (tptp.produc8585076106096196333on_num tptp.none_num Uv2))))) (=> (forall ((Uw2 tptp.fun_num_fun_num_num) (V2 tptp.num)) (not (= X (tptp.produc6360833703471310868on_num Uw2 (tptp.produc8585076106096196333on_num (tptp.some_num V2) tptp.none_num))))) (not (forall ((F2 tptp.fun_num_fun_num_num) (A3 tptp.num) (B2 tptp.num)) (not (= X (tptp.produc6360833703471310868on_num F2 (tptp.produc8585076106096196333on_num (tptp.some_num A3) (tptp.some_num B2)))))))))) (forall ((X tptp.produc533602882674032673at_nat)) (=> (forall ((Uu2 tptp.fun_Pr248683899324676269t_bool) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (tptp.produc5961576194287291153at_nat Uu2 (tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat Uv2))))) (=> (forall ((Uw2 tptp.fun_Pr248683899324676269t_bool) (V2 tptp.product_prod_nat_nat)) (not (= X (tptp.produc5961576194287291153at_nat Uw2 (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat V2) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 tptp.fun_Pr248683899324676269t_bool) (X3 tptp.product_prod_nat_nat) (Y4 tptp.product_prod_nat_nat)) (not (= X (tptp.produc5961576194287291153at_nat F2 (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat X3) (tptp.some_P7363390416028606310at_nat Y4)))))))))) (forall ((X tptp.produc3700678068921409119on_nat)) (=> (forall ((Uu2 tptp.fun_nat_fun_nat_bool) (Uv2 tptp.option_nat)) (not (= X (tptp.produc2004789812759622991on_nat Uu2 (tptp.produc5098337634421038937on_nat tptp.none_nat Uv2))))) (=> (forall ((Uw2 tptp.fun_nat_fun_nat_bool) (V2 tptp.nat)) (not (= X (tptp.produc2004789812759622991on_nat Uw2 (tptp.produc5098337634421038937on_nat (tptp.some_nat V2) tptp.none_nat))))) (not (forall ((F2 tptp.fun_nat_fun_nat_bool) (X3 tptp.nat) (Y4 tptp.nat)) (not (= X (tptp.produc2004789812759622991on_nat F2 (tptp.produc5098337634421038937on_nat (tptp.some_nat X3) (tptp.some_nat Y4)))))))))) (forall ((X tptp.produc6167219322466932359on_num)) (=> (forall ((Uu2 tptp.fun_num_fun_num_bool) (Uv2 tptp.option_num)) (not (= X (tptp.produc8433281988922931063on_num Uu2 (tptp.produc8585076106096196333on_num tptp.none_num Uv2))))) (=> (forall ((Uw2 tptp.fun_num_fun_num_bool) (V2 tptp.num)) (not (= X (tptp.produc8433281988922931063on_num Uw2 (tptp.produc8585076106096196333on_num (tptp.some_num V2) tptp.none_num))))) (not (forall ((F2 tptp.fun_num_fun_num_bool) (X3 tptp.num) (Y4 tptp.num)) (not (= X (tptp.produc8433281988922931063on_num F2 (tptp.produc8585076106096196333on_num (tptp.some_num X3) (tptp.some_num Y4)))))))))) (forall ((N2 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) 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.modulo_modulo_nat M) N2)) N2)))) (forall ((A tptp.bool) (B tptp.bool)) (= (tptp.vEBT_vebt_delete (tptp.vEBT_Leaf A B) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.vEBT_Leaf A tptp.fFalse))) (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 ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (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.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) N2) tptp.zero_zero_rat))) (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.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat tptp.zero_zero_nat) N2) 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)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) N2) tptp.zero_zero_real))) (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.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int) N2) tptp.zero_zero_int))) (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.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.zero_zero_complex) N2) tptp.zero_zero_complex))) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B)) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B) C)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C)) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A C)) B) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) C))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger A B)) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger _let_1 A) (tptp.aa_Cod1783974652533396728nteger _let_1 B))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) 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.modulo_modulo_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A B)) C))) (forall ((A tptp.nat) (C tptp.nat) (A5 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 A5) 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 A5) B5)) C))))) (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A5) C)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B5) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A5) B5)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A5 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 A5) 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 (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A C)) (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) C))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A))) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B)) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) C))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C)) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C) B) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) C))) (forall ((A tptp.nat) (C tptp.nat) (A5 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 A5) 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 A5) B5)) C))))) (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A5) C)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B5) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_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.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A5) B5)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A5 C)) (=> (= (tptp.modulo364778990260209775nteger B C) (tptp.modulo364778990260209775nteger B5 C)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A5 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)) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger A B) C))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_1 B)) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) C))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C)) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger (tptp.modulo364778990260209775nteger A C) B) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) C))) (forall ((A tptp.int) (C tptp.int) (A5 tptp.int) (B tptp.int) (B5 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A5) C)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B5) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_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.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A5) B5)) C))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (A5 tptp.code_integer) (B tptp.code_integer) (B5 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger A5 C)) (=> (= (tptp.modulo364778990260209775nteger B C) (tptp.modulo364778990260209775nteger B5 C)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A5 B5) C))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) C))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) C) (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger A B) C))) (forall ((A tptp.nat) (B tptp.nat) (N2 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)) N2)) 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) N2)) B))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) N2)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (tptp.modulo364778990260209775nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.modulo364778990260209775nteger A B)) N2) B) (tptp.modulo364778990260209775nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2) B))) (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_vebt_member (tptp.vEBT_Leaf A B)) X)) (and (=> _let_2 (tptp.pp A)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B)) _let_1))))))) (forall ((M tptp.nat) (N2 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) N2))) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc M)) N2))) (forall ((M tptp.nat) (N2 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) N2)))) N2) (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))) N2))) (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)))) (= (tptp.vEBT_vebt_buildup _let_38) _let_153) (forall ((M tptp.nat) (N2 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) N2)) M))) (forall ((X tptp.nat) (A tptp.bool) (B tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A B))) (let ((_let_2 (tptp.vEBT_vebt_insert _let_1 X))) (let ((_let_3 (= X tptp.one_one_nat))) (let ((_let_4 (= X tptp.zero_zero_nat))) (and (=> _let_4 (= _let_2 (tptp.vEBT_Leaf tptp.fTrue B))) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.vEBT_Leaf A tptp.fTrue))) (=> (not _let_3) (= _let_2 _let_1)))))))))) (forall ((Uu tptp.bool) (Uv tptp.bool)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Leaf Uu Uv) tptp.zero_zero_nat) tptp.none_nat)) (tptp.pp (tptp.aa_real_bool _let_71 tptp.zero_zero_real)) (tptp.pp (tptp.aa_rat_bool _let_102 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_nat_bool _let_149 tptp.zero_zero_nat)) _let_134 (forall ((X tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) X))) (not (tptp.pp (tptp.aa_real_bool _let_72 tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_rat_bool _let_95 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_135 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_96 tptp.zero_zero_int))) (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 D1)) (=> (tptp.pp (tptp.aa_real_bool _let_1 D22)) (exists ((E2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real E2))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (tptp.pp (tptp.aa_real_bool _let_1 D1)) (tptp.pp (tptp.aa_real_bool _let_1 D22))))))))) (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 D1)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 D22)) (exists ((E2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat E2))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool _let_1 D1)) (tptp.pp (tptp.aa_rat_bool _let_1 D22))))))))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (not (= N2 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 (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (tptp.numera6690914467698888265omplex N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (tptp.aa_num_real tptp.numeral_numeral_real N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _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 N2)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int Q2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2))) _let_2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 M)) _let_2) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N2)) _let_2)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2) _let_1)))))) (forall ((M tptp.num) (N2 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 N2)) _let_1)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) _let_1)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one))) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2) _let_1)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) C)) (= A B)))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C)) (= A B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.times_times_rat A) C) (tptp.aa_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.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex _let_1 A) (tptp.aa_complex_complex _let_1 B)) (= A B))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.aa_real_real _let_1 A) (tptp.aa_real_real _let_1 B)) (= A B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.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.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B) tptp.zero_zero_complex))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.zero_zero_real))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (tptp.aa_rat_rat (tptp.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.complex) (B tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B tptp.zero_zero_complex))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (tptp.aa_rat_rat (tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat tptp.zero_zero_rat) A) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.zero_zero_int) A) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat A) tptp.zero_zero_rat) A)) (forall ((A tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.zero_zero_int) A)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex tptp.zero_zero_complex) A) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.zero_zero_real) A) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.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)) (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 ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux Uy)) Uz)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A B) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.real) (B tptp.real)) (= (= A B) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A B) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) tptp.zero_zero_rat))) (forall ((A tptp.int) (B tptp.int)) (= (= A B) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.rat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (tptp.aa_nat_rat (tptp.power_power_rat A) N2) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2) tptp.zero_zero_nat)))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2) tptp.zero_zero_real)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2) tptp.zero_zero_int)))) (forall ((A tptp.complex) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2) tptp.zero_zero_complex)))) (= (tptp.aa_num_nat tptp.size_size_num tptp.one) tptp.zero_zero_nat) (forall ((Uu tptp.bool)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull (tptp.vEBT_Leaf Uu tptp.fTrue))))) (forall ((Uv tptp.bool)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull (tptp.vEBT_Leaf tptp.fTrue Uv))))) (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_153)) (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (not (forall ((Va2 tptp.nat)) (not (= X (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2))))))))) (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc X22)))) (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) (X22 tptp.nat)) (=> (= Nat (tptp.aa_nat_nat tptp.suc X22)) (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) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N))))) (tptp.pp (tptp.aa_nat_bool P N2))))) (forall ((P tptp.fun_nat_fun_nat_bool) (M tptp.nat) (N2 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 ((Y4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.suc Y4)))) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P X3) Y4)) (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 Y4))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M) N2)))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N))) (tptp.pp (tptp.aa_nat_bool P N)))) (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 ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M2 tptp.nat)) (= N2 (tptp.aa_nat_nat tptp.suc M2))))) (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 ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2))) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (not (= N2 tptp.zero_zero_nat)))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P 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 (tptp.pp (tptp.aa_nat_bool P N))) (exists ((M3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N)) (not (tptp.pp (tptp.aa_nat_bool P M3)))))))) (tptp.pp (tptp.aa_nat_bool P N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) N2))) (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 ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (or (= K tptp.zero_zero_nat) (= M N2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (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 ((M tptp.nat) (N2 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M) tptp.zero_zero_nat) (= M N2)))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2))) (= (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 ((M tptp.nat) (N2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2) (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) N2)) N2)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C)) (= (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger _let_1 C)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger (tptp.divide6298287555418463151nteger A B) C)) (tptp.modulo364778990260209775nteger A B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.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.modulo_modulo_int A))) (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.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) C))) (tptp.aa_int_int _let_1 B))))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 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) N2))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P M))) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N2)) (=> (= 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 N2) I5)) J3)) (tptp.pp (tptp.aa_nat_bool P J3)))))))))) (forall ((N2 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) N2)) (=> (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) N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2)) (= A B))))))) (forall ((N2 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) N2)) (=> (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) N2) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)) (= A B))))))) (forall ((N2 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) N2)) (=> (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) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2)) (= A B))))))) (forall ((N2 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) N2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)) (= A B))))))) (forall ((A tptp.real) (N2 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) N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2)) (=> (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) N2)) (= A B))))))) (forall ((A tptp.rat) (N2 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) N2) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)) (=> (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) N2)) (= A B))))))) (forall ((A tptp.nat) (N2 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) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2)) (=> (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) N2)) (= A B))))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) N2) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)) (=> (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) N2)) (= A B))))))) (= tptp.aTP_Lamm_bi (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.zero_zero_complex)) (= tptp.aTP_Lamm_bj (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.zero_zero_real)) (= tptp.aTP_Lamm_bk (tptp.times_times_rat tptp.zero_zero_rat)) (= tptp.aTP_Lamm_bl (tptp.aa_nat_fun_nat_nat tptp.times_times_nat tptp.zero_zero_nat)) (= tptp.aTP_Lamm_bm (tptp.aa_int_fun_int_int tptp.times_times_int tptp.zero_zero_int)) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B2) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Info2 tptp.zero_zero_nat Ts S) X3)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node Info2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Ts S) X3)))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc V2)) TreeList2 Summary2) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 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 (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2) X3)))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B2) tptp.zero_zero_nat)))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool) (N tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg2 TreeList2 Summary2) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry 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 TrLst Smry) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm 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 tptp.zero_zero_nat) Tr Sm) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 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 (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2) X3)))))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool) (Uw2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uu2 Uv2) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2) Uz2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2) X3)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 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 V2) TreeList2 Vc2) X3)))) (not (forall ((V2 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 V2) TreeList2 Vd2) X3)))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B2) X3)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2) X3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2) X3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2) X3)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 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 (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2) X3)))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 tptp.bool) (B2 tptp.bool)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uu2 B2) tptp.zero_zero_nat)))) (=> (forall ((Uv2 tptp.bool) (Uw2 tptp.bool) (N tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uv2 Uw2) (tptp.aa_nat_nat tptp.suc N))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va3 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Ux2 Uy2 Uz2) Va3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Vc2 Vd2) Ve)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vg Vh) Vi)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 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 (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2) X3))))))))))) (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uu2 Uv2) tptp.zero_zero_nat)))) (=> (forall ((A3 tptp.bool) (Uw2 tptp.bool)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 Uw2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool) (Va2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uy2 Uz2 Va3) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Vd2 Ve) Vf)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (not (= X (tptp.produc738532404422230701BT_nat (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vh Vi) Vj)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (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 (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2) X3)))))))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) tptp.zero_zero_nat Va Vb)) X)) (or (= X Mi) (= X Ma)))) (forall ((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.aa_int_fun_int_int tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) 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_2) B)) (= _let_2 (tptp.aa_int_int _let_1 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.aa_num_Code_integer 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 ((Q2 tptp.num) (N2 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 N2))) _let_1))))) (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2))) _let_1))))) (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N2)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one) _let_1))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C)) (not (forall ((D3 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) D3)))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) (not (forall ((D3 tptp.code_integer)) (not (= B (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) D3)))))))) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B) C) (tptp.plus_p5714425477246183910nteger (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C)) (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) C)))) (forall ((M tptp.nat) (N2 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) N2))) M) tptp.one_one_nat))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat) (P2 tptp.nat) (M 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 N2) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) P2)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N) P2)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (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 N)) P2)))))) (tptp.pp (tptp.aa_nat_bool P M))))))) (forall ((M tptp.nat) (N2 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 N2))) N2))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Y) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y) X)) (exists ((Q3 tptp.nat)) (= X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) Q3))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N2 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 N2) Q2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (not (forall ((S tptp.nat)) (not (= N2 (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) S))))))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N2 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 N2) Q2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (not (forall ((S tptp.nat)) (not (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Q2) S))))))))) (forall ((A tptp.real) (B tptp.real) (N2 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) N2)) (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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2))))))) (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2)) (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) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2))))))) (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2)) (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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2))))))) (forall ((A tptp.int) (B tptp.int) (N2 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) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2))))))) (forall ((A tptp.bool) (B tptp.bool) (N2 tptp.nat)) (let ((_let_1 (tptp.vEBT_Leaf A B))) (= (tptp.vEBT_vebt_delete _let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N2))) _let_1))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (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) N2)) N2))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2) (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) N2)) N2)))) (forall ((B tptp.bool) (A tptp.bool)) (let ((_let_1 (tptp.vEBT_vebt_maxt (tptp.vEBT_Leaf A B)))) (let ((_let_2 (tptp.pp A))) (let ((_let_3 (tptp.pp B))) (and (=> _let_3 (= _let_1 (tptp.some_nat tptp.one_one_nat))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.none_nat))))))))) (forall ((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.bool) (B tptp.bool)) (let ((_let_1 (tptp.vEBT_vebt_mint (tptp.vEBT_Leaf A B)))) (let ((_let_2 (tptp.pp B))) (let ((_let_3 (tptp.pp A))) (and (=> _let_3 (= _let_1 (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (= _let_1 tptp.none_nat))))))))) (forall ((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.bool) (Uw tptp.bool)) (let ((_let_1 (tptp.vEBT_vebt_pred (tptp.vEBT_Leaf A Uw) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (tptp.pp A))) (and (=> _let_2 (= _let_1 (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.none_nat)))))) (forall ((B tptp.bool) (Uu tptp.bool)) (let ((_let_1 (tptp.vEBT_vebt_succ (tptp.vEBT_Leaf Uu B) tptp.zero_zero_nat))) (let ((_let_2 (tptp.pp B))) (and (=> _let_2 (= _let_1 (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (= _let_1 tptp.none_nat)))))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real N2)) tptp.zero_zero_real)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat)))) (forall ((N2 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 N2)) tptp.zero_zero_nat)))) (forall ((N2 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 N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_num_real tptp.numeral_numeral_real N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((N2 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 N2)))) (forall ((N2 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 N2)))) (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.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)) (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.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)) (=> (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.times_times_rat B) A)) tptp.zero_zero_rat))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) tptp.zero_zero_int))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real 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.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 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.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)) (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.times_times_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (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.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 (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.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) (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.times_times_rat A) C)) (tptp.aa_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 ((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.times_times_rat A) C)) (tptp.aa_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)) (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.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_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.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 ((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.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)) (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.times_times_rat A) B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)))))) (forall ((A tptp.real)) (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.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) (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.times_times_rat A) C)) (tptp.aa_rat_rat (tptp.times_times_rat B) D))))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) D)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D))))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) D)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D))))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) D)) (=> (tptp.pp (tptp.aa_real_bool _let_1 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.times_times_rat A) C)) (tptp.aa_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 ((N2 tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real N2)) tptp.zero_zero_real)))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat)))) (forall ((N2 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 N2)) tptp.zero_zero_nat)))) (forall ((N2 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 N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_num_real tptp.numeral_numeral_real N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((N2 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 N2)))) (forall ((N2 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 N2)))) (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.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.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.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.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.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.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.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.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) (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.times_times_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 A)) (tptp.aa_nat_nat _let_1 B))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))))))) (forall ((A tptp.real) (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.times_times_rat A) C)) (tptp.aa_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)) (=> (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.times_times_rat A) C)) (tptp.aa_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 ((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.times_times_rat A) C)) (tptp.aa_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 ((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.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 ((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.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 ((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.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 ((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.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 ((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.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 ((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.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 ((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.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 ((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.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)) (=> (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.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 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.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 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.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)) (=> (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.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)) (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.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)) (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.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)) (=> (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.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)))))) _let_152 _let_151 _let_150 _let_148 _let_152 _let_151 _let_150 _let_148 (not (tptp.pp (tptp.aa_real_bool _let_108 tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_rat_bool _let_107 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_147 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_106 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.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) (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.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.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.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))))) _let_145 _let_144 _let_143 _let_142 (not (tptp.pp (tptp.aa_real_bool _let_105 tptp.zero_zero_real))) (not (tptp.pp (tptp.aa_rat_bool _let_103 tptp.zero_zero_rat))) (not (tptp.pp (tptp.aa_nat_bool _let_146 tptp.zero_zero_nat))) (not (tptp.pp (tptp.aa_int_bool _let_104 tptp.zero_zero_int))) _let_145 _let_144 _let_143 _let_142 (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.aa_rat_rat (tptp.minus_minus_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real) (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.aa_rat_rat (tptp.divide_divide_rat B) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y))))))) (forall ((A tptp.real) (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.aa_rat_rat (tptp.divide_divide_rat A) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat))))))) (forall ((A tptp.real) (B tptp.real) (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.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))))) (forall ((A tptp.real) (B tptp.real)) (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.aa_rat_rat (tptp.divide_divide_rat A) B)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B))))))) (forall ((A tptp.real) (N2 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) N2)))))) (forall ((A tptp.rat) (N2 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) N2)))))) (forall ((A tptp.nat) (N2 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) N2)))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) N2)))))) (forall ((A tptp.real) (B tptp.real) (N2 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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2)))))) (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)))))) (forall ((A tptp.nat) (B tptp.nat) (N2 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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2)))))) (forall ((A tptp.int) (B tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) tptp.zero_zero_rat)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) tptp.zero_zero_int)))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B))) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 B))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) tptp.zero_zero_real))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) B))) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat))))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))) (and (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))) (not (= C tptp.zero_zero_real))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))) (not (= C tptp.zero_zero_rat))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) tptp.zero_zero_real)) (or (and (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) tptp.zero_zero_real))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) tptp.zero_zero_rat)) (or (and (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) tptp.zero_zero_rat))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((A tptp.real) (N2 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) N2)))))) (forall ((A tptp.rat) (N2 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) N2)))))) (forall ((A tptp.nat) (N2 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) N2)))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) N2)))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C) B)))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) B)))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (= (tptp.aa_rat_rat (tptp.times_times_rat A) C) B)))) (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C) A) (= B (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C) A) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) C) A) (= B (tptp.aa_rat_rat (tptp.times_times_rat A) C))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C) B) (= A (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat A) C) B) (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))))) (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat A) C)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) C) A)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_1) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) (and (=> (not _let_1) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (tptp.aa_rat_rat (tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C) A) (and (=> (not _let_1) (= B (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C) A) (and (=> (not _let_1) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (tptp.aa_rat_rat (tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex W) Z)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Z) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex W) Y)))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z)) (= (tptp.aa_rat_rat (tptp.times_times_rat X) Z) (tptp.aa_rat_rat (tptp.times_times_rat W) Y)))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))) (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.aa_int_fun_nat_int tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_3)) B)) (= (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 _let_3)) (tptp.aa_int_int _let_1 B)))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.modulo364778990260209775nteger A _let_2)) B)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger A _let_2)) (tptp.divide6298287555418463151nteger A B))))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P I5)))) (or (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I5)))))))) (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)) (exists ((M6 tptp.nat)) (= N2 (tptp.aa_nat_nat tptp.suc M6))))) (forall ((N2 tptp.nat) (P tptp.fun_nat_bool)) (= (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool P I5)))) (and (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) N2)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc I5)))))))) (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)) (exists ((M2 tptp.nat)) (= N2 (tptp.aa_nat_nat tptp.suc M2))))) (forall ((M tptp.nat) (N2 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 N2))) (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) N2))))))) (forall ((M tptp.nat) (N2 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) N2)) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))) (forall ((M tptp.nat) (N2 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) N2) _let_1) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))) (forall ((X22 tptp.product_prod_nat_nat)) (= (tptp.size_s170228958280169651at_nat (tptp.some_P7363390416028606310at_nat X22)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X22 tptp.nat)) (= (tptp.size_size_option_nat (tptp.some_nat X22)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X22 tptp.num)) (= (tptp.size_size_option_num (tptp.some_num X22)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) J)) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) K2) J))))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N2)) (forall ((I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I) K2)) (not (tptp.pp (tptp.aa_nat_bool P I))))) (tptp.pp (tptp.aa_nat_bool P K2))))))) (= (tptp.size_size_option_nat tptp.none_nat) _let_38) (= (tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) _let_38) (= (tptp.size_size_option_num tptp.none_num) _let_38) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (= M N2))))) (forall ((I2 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 I2) 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 I2)) (tptp.aa_nat_nat _let_1 J))))))) (forall ((I2 tptp.nat) (J tptp.nat) (K 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 (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 I2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat J) K)))))) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) I2)) (=> (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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))))) (forall ((N2 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 N2)) (=> (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) N2)) M)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) tptp.zero_zero_nat) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= N2 tptp.zero_zero_nat)))) (= tptp.one_one_nat _let_38) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1) A) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_int_int (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.divide6298287555418463151nteger A _let_1) A) (= (tptp.plus_p5714425477246183910nteger A (tptp.modulo364778990260209775nteger A _let_1)) tptp.zero_z3403309356797280102nteger)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (or (= N2 tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.vEBT_Node Info tptp.zero_zero_nat Ts2 S2))) (= (tptp.vEBT_vebt_insert _let_1 X) _let_1))) (forall ((B tptp.bool) (A tptp.bool) (Va tptp.nat)) (let ((_let_1 (tptp.vEBT_vebt_pred (tptp.vEBT_Leaf A B) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va))))) (let ((_let_2 (tptp.pp A))) (let ((_let_3 (tptp.pp B))) (and (=> _let_3 (= _let_1 (tptp.some_nat tptp.one_one_nat))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.none_nat))))))))) (forall ((M tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger X M))) (let ((_let_2 (tptp.modulo364778990260209775nteger X (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X)) (or (= _let_2 _let_1) (= _let_2 (tptp.plus_p5714425477246183910nteger _let_1 M)))))))) (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X))) (let ((_let_2 (tptp.aa_nat_nat _let_1 M))) (let ((_let_3 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) X)) (or (= _let_3 _let_2) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) M))))))))) (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int X))) (let ((_let_2 (tptp.aa_int_int _let_1 M))) (let ((_let_3 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) M)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) M)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (or (= _let_3 _let_2) (= _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_2) M))))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) _let_1)) (= (tptp.minus_8373710615458151222nteger _let_1 B) (tptp.modulo364778990260209775nteger A B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.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.aa_int_fun_int_int tptp.modulo_modulo_int A))) (let ((_let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) 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_2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) B) (tptp.aa_int_int _let_1 B)))))))) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) A)) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger A B)) (tptp.modulo364778990260209775nteger A B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B))) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger A B))) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) B)) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A B) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B)) (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)) A)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B) (tptp.modulo364778990260209775nteger A B)) A)) (forall ((A tptp.nat) (B tptp.nat)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B)) (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B) (tptp.modulo364778990260209775nteger A B)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B)) (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B) (tptp.modulo364778990260209775nteger A B)) C) (tptp.plus_p5714425477246183910nteger A C))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B))) (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) C))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger A B)) (tptp.modulo364778990260209775nteger A B)) C) (tptp.plus_p5714425477246183910nteger A C))) (forall ((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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C))) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (= (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B) C) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger B C)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.modulo364778990260209775nteger B C)) C))))) (forall ((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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger A B))) (tptp.modulo364778990260209775nteger A B))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_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)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger A B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger A B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_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))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger A B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) B)) (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) B)) (tptp.modulo364778990260209775nteger A B))) (forall ((M tptp.nat) (N2 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 N2))) (= (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) N2)) Q2))) (tptp.aa_nat_nat _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2) (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) N2)) N2)))) (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (=> (forall ((Uv2 tptp.bool)) (not (= X (tptp.vEBT_Leaf tptp.fTrue Uv2)))) (=> (forall ((Uu2 tptp.bool)) (not (= X (tptp.vEBT_Leaf Uu2 tptp.fTrue)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2)))))))))) (forall ((N2 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) N2)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) (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) N2)) N2)))))) (forall ((X tptp.vEBT_VEBT)) (=> (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X))) (=> (forall ((Uv2 tptp.bool)) (not (= X (tptp.vEBT_Leaf tptp.fTrue Uv2)))) (=> (forall ((Uu2 tptp.bool)) (not (= X (tptp.vEBT_Leaf Uu2 tptp.fTrue)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2))))))))) (forall ((Uv tptp.bool) (Uw tptp.bool) (N2 tptp.nat)) (= (tptp.vEBT_vebt_succ (tptp.vEBT_Leaf Uv Uw) (tptp.aa_nat_nat tptp.suc N2)) tptp.none_nat)) (forall ((X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X)) (=> (not (= X (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2)))))))) (forall ((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.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.times_times_rat A) C)) (tptp.aa_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.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.times_times_rat A) C)) (tptp.aa_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.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.times_times_rat A) C)) (tptp.aa_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.times_times_rat A) C)) (tptp.aa_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.times_times_rat A) C)) (tptp.aa_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.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.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.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.times_times_rat A) C)) (tptp.aa_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.times_times_rat A) C)) (tptp.aa_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.times_times_rat A) C)) (tptp.aa_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.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.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.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.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.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.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.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 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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) X)) (tptp.aa_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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) X)) (tptp.aa_rat_rat (tptp.times_times_rat Y) Y))) tptp.zero_zero_rat)) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) Y))) tptp.zero_zero_int)) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) tptp.zero_zero_real))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat))))) (forall ((A tptp.real) (C tptp.real) (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.aa_rat_rat (tptp.divide_divide_rat A) C)) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (and (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 W)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real W) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) W))))))))) (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat W) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) W))))))))) (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) W)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real W) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) W)))))))) (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) W)))))))) (forall ((Y tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) W)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real W) Z)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) W)))))))) (forall ((Y tptp.rat) (X tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) W)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat W) Z)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) W)))))))) (forall ((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.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.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.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.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 ((A tptp.real) (N2 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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2))) (=> (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) (N2 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) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2))) (=> (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) (N2 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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2))) (=> (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) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2))) (=> (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 ((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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) X)) (tptp.aa_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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) X)) (tptp.aa_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_72 _let_141)) (tptp.pp (tptp.aa_rat_bool _let_95 _let_140)) (tptp.pp (tptp.aa_nat_bool _let_135 _let_139)) (tptp.pp (tptp.aa_int_bool _let_96 _let_137)) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real C))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B)))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.times_times_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real C))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (=> (tptp.pp (tptp.aa_real_bool _let_2 C)) (=> (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B))))))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat C))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 C)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.times_times_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))))))))) (forall ((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.times_times_rat Z) Y)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) Z))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.times_times_rat Z) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) Z))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) B))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.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.aa_rat_rat (tptp.divide_divide_rat B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.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.aa_rat_rat (tptp.divide_divide_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.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.aa_rat_rat (tptp.divide_divide_rat B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.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.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) B))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)))))))))))) (forall ((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.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool _let_1 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) A)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) B))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))))))) (forall ((A tptp.real) (N2 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) N2)) tptp.one_one_real))))) (forall ((A tptp.rat) (N2 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) N2)) tptp.one_one_rat))))) (forall ((A tptp.nat) (N2 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) N2)) tptp.one_one_nat))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) N2)) tptp.one_one_int))))) (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A)) tptp.one_one_real)) (or (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))) (and (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool _let_1 B))) (= A tptp.zero_zero_real))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))) (and (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (= A tptp.zero_zero_rat))))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) A))) (or (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool _let_1 B))) (and (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A))))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat (tptp.divide_divide_rat B) A))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool _let_1 B))) (and (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) A))))))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Z)) Y) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) (tptp.aa_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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex Y) Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat X) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Z) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) (tptp.aa_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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y)) Z) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) Z) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) (tptp.aa_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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex W) Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex W) Y))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.times_times_rat W) Y))) (tptp.aa_rat_rat (tptp.times_times_rat Y) Z)))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) Z)) B)) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) (tptp.aa_rat_rat (tptp.times_times_rat B) Z))) Z))))))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (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) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (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) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc 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.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) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))))) (forall ((A tptp.real) (N2 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 N2))) (=> (= (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) (N2 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 N2))) (=> (= (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) (N2 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 N2))) (=> (= (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) (N2 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 N2))) (=> (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_2) (tptp.aa_nat_int (tptp.aa_int_fun_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 ((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 ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Z)) Y) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Z)) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z)) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) (tptp.aa_rat_rat (tptp.times_times_rat Y) Z))) Z)))) (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex Y) Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Z)) Y)) Z)))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Y) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) Y)) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat X) (tptp.aa_rat_rat (tptp.divide_divide_rat Y) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) Z)) Y)) Z)))) (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex W) Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex W) Y))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Y) Z)))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.times_times_rat W) Y))) (tptp.aa_rat_rat (tptp.times_times_rat Y) Z)))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) Z)) B)) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) Z)) B)) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat A) Z)) B)) Z))))))) (= _let_136 _let_38) (forall ((X22 tptp.num)) (= (tptp.aa_num_nat tptp.size_size_num (tptp.aa_num_num tptp.bit0 X22)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_size_num X22)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N2)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((K2 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) N2)) (forall ((I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I) K2)) (not (tptp.pp (tptp.aa_nat_bool P I))))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc K2)))))))) (forall ((N2 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) N2)) (=> (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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) M)))))) (forall ((N2 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) N2)) (=> (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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)))))) (forall ((N2 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 N2)) (=> (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) N2))))))) (forall ((N2 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)) N2)) (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 N2) K))))) (forall ((N2 tptp.nat) (I2 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 tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat tptp.suc I2))) N2)))) (forall ((I2 tptp.nat) (N2 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 I2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I2) N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((N2 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) N2)) (=> (tptp.pp (tptp.aa_nat_bool P 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 P N)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc N)))))) (tptp.pp (tptp.aa_nat_bool P N2)))))) (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.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.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.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.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.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 ((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 ((M tptp.nat) (N2 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) N2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (forall ((M tptp.nat) (N2 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) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat _let_1 M))))))) (forall ((Q2 tptp.nat) (M 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) 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)) N2)) (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 N2) Q2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))))) (forall ((N2 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) N2)) (=> (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) N2)) M))))) (forall ((M 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) M)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) M) (= N2 tptp.one_one_nat)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger B) (tptp.modulo364778990260209775nteger A _let_2))) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger A _let_2)) tptp.one_one_Code_integer) (tptp.divide6298287555418463151nteger A B)))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat _let_2 B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_3))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 _let_3))) tptp.one_one_int) (tptp.aa_int_int _let_1 B))))))))) (forall ((Info tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.vEBT_Node Info (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Ts2 S2))) (= (tptp.vEBT_vebt_insert _let_1 X) _let_1))) (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) tptp.zero_zero_nat Uy Uz)) X)))) (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (not (= X (tptp.vEBT_Leaf A3 B2)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2)))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (let ((_let_2 (not _let_1))) (=> (= (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X)) _let_1) (=> (=> (= X (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse)) _let_2) (=> (=> (exists ((Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf tptp.fTrue Uv2))) _let_1) (=> (=> (exists ((Uu2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 tptp.fTrue))) _let_1) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2))) _let_2) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2))) _let_1)))))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.pp A3))) (let ((_let_2 (tptp.pp B2))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (not (and (=> _let_2 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (and (=> _let_1 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_1) (= Y tptp.none_nat)))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2))) (not (= Y (tptp.some_nat Ma2)))))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_mint X) Y) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.pp B2))) (let ((_let_2 (tptp.pp A3))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (not (and (=> _let_2 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (and (=> _let_1 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_1) (= Y tptp.none_nat)))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2))) (not (= Y (tptp.some_nat Mi2)))))))))) (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.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.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.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.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.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.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.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.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 ((Z3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) 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 Z3) 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 ((Z3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Z3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) 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.times_times_rat Z3) 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)) (let ((_let_1 (tptp.divide_divide_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) tptp.zero_zero_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.times_times_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))))) (forall ((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.times_times_rat Z) Y)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)))))) (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) Z))))) (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.times_times_rat Z) Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) Z))))) (forall ((C tptp.real) (A tptp.real) (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.aa_rat_rat (tptp.divide_divide_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.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.aa_rat_rat (tptp.divide_divide_rat B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.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.aa_rat_rat (tptp.divide_divide_rat B) C))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.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.aa_rat_rat (tptp.divide_divide_rat B) C)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.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)) (let ((_let_1 (tptp.divide_divide_rat C))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) C)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.times_times_rat A) B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B)))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_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.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat)))))))))))) (forall ((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.times_times_rat A) C))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) A)) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_2))) (=> (not _let_3) (and (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_2) B))) (=> (not _let_1) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))) (forall ((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.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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat U) X)) (tptp.aa_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 ((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.aa_rat_rat (tptp.divide_divide_rat B) A)) tptp.one_one_rat)) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (= A tptp.zero_zero_rat)))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.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.aa_rat_rat (tptp.divide_divide_rat B) A))) (or (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A)))))) (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool _let_2 C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 _let_1))))))))))))) (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool _let_2 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 _let_1))))))))))))) (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) tptp.zero_zero_real)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.times_times_rat W) Y))) (tptp.aa_rat_rat (tptp.times_times_rat Y) Z))) tptp.zero_zero_rat)))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))) (=> (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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (=> (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.times_times_rat A) _let_1)) _let_1)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))) (=> (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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (=> (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 ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real W) Z))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real W) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) Z))) tptp.zero_zero_real)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y)) (tptp.aa_rat_rat (tptp.divide_divide_rat W) Z))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat X) Z)) (tptp.aa_rat_rat (tptp.times_times_rat W) Y))) (tptp.aa_rat_rat (tptp.times_times_rat Y) Z))) tptp.zero_zero_rat)))))) (forall ((A tptp.real) (N2 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 N2))) A))))) (forall ((A tptp.rat) (N2 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 N2))) A))))) (forall ((A tptp.nat) (N2 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 N2))) A))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N2))) A))))) (forall ((A tptp.real) (N2 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 N2))) tptp.one_one_real))))) (forall ((A tptp.rat) (N2 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 N2))) tptp.one_one_rat))))) (forall ((A 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) 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 N2))) tptp.one_one_nat))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_nat_nat tptp.suc N2))) tptp.one_one_int))))) (= (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 _let_75 _let_2) tptp.zero_zero_real) (= (tptp.aa_nat_int _let_74 _let_2) tptp.zero_zero_int) (= (tptp.aa_nat_complex _let_73 _let_2) tptp.zero_zero_complex) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real _let_1 N3)) (tptp.aa_nat_real _let_1 N2)))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat _let_1 N3)) (tptp.aa_nat_rat _let_1 N2)))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 N3)) (tptp.aa_nat_nat _let_1 N2)))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int _let_1 N3)) (tptp.aa_nat_int _let_1 N2)))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real _let_1 N3)) (tptp.aa_nat_real _let_1 N2)))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.power_power_rat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat _let_1 N3)) (tptp.aa_nat_rat _let_1 N2)))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 N3)) (tptp.aa_nat_nat _let_1 N2)))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int _let_1 N3)) (tptp.aa_nat_int _let_1 N2)))))))) (forall ((A tptp.real) (N2 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) N2)) (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) N2)))))) (forall ((A tptp.rat) (N2 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) N2)) (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) N2)))))) (forall ((A tptp.nat) (N2 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) N2)) (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) N2)))))) (forall ((A tptp.int) (N2 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) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))))) (= _let_2 _let_39) (forall ((A tptp.real) (N2 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) N2)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))))))) (forall ((A tptp.rat) (N2 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) N2)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))))))) (forall ((A tptp.nat) (N2 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) N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat A) N2))))))) (forall ((A tptp.int) (N2 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) N2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))))))) (tptp.pp (tptp.aa_nat_bool _let_135 _let_2)) (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex 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 N2) M)) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 N2))))))) (forall ((A tptp.real) (N2 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 N2) M)) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (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 N2))))))) (forall ((A tptp.rat) (N2 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 N2) M)) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 N2))))))) (forall ((A tptp.nat) (N2 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 N2) M)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (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 N2))))))) (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2) M)) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (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 N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (let ((_let_2 (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (= N2 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) N2)) N2)))))))) (forall ((N2 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) N2)) (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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))))))) (forall ((N2 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) N2)) (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 N2) (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) N2)) N2)))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 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) N2))) (and (=> _let_1 (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J3) N2)) (=> (= 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 N2) I5)) J3)) (tptp.pp (tptp.aa_nat_bool P I5)))))))))) (forall ((Q2 tptp.nat) (M 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) 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 N2) 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)) N2))))) (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)) (= N2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((N2 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) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc M)) N2) (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 N2) tptp.one_one_nat))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2)) _let_1) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (= (tptp.pp Y) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2))) _let_1) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node Uy2 (tptp.aa_nat_nat tptp.suc V2) TreeList2 S))) (= (tptp.pp Y) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node Uy2 (tptp.aa_nat_nat tptp.suc V2) TreeList2 S))) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((S tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node Uy2 (tptp.aa_nat_nat tptp.suc V2) TreeList2 S))) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 N2)) (=> (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)) N2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2))) (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 N2) (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)) N2)))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) tptp.zero_zero_nat TrLst2 Smry2))) (= (tptp.vEBT_vebt_delete _let_1 X) _let_1))) (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb Vc)) X)))) (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve2 tptp.nat)) (= (tptp.vEBT_vebt_succ (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) tptp.zero_zero_nat Vc Vd) Ve2) tptp.none_nat)) (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) tptp.zero_zero_nat Vd Ve2) Vf2) tptp.none_nat)) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2)) _let_1) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) _let_1) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2))) _let_1) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (= (tptp.pp Y) (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vc2))) (= (tptp.pp Y) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vd2))) (= (tptp.pp Y) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2))) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (not (= X (tptp.vEBT_Leaf Uu2 Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vd2))) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))))) (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_3) B))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)))))))))))) (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)))))))))))) (forall ((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.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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat U) X)) (tptp.aa_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 ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((U tptp.real) (V tptp.real) (R2 tptp.real) (S2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real U) V)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R2) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real U) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real V) U))) S2))) V)))))) (forall ((U tptp.rat) (V tptp.rat) (R2 tptp.rat) (S2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat U) V)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) R2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat R2) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.plus_plus_rat U) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat R2) (tptp.aa_rat_rat (tptp.minus_minus_rat V) U))) S2))) V)))))) (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.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_int_fun_nat_int tptp.power_power_int X) _let_2) (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A tptp.real)) (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.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.zero_zero_int)))) (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat _let_1 N2) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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) N2)) tptp.zero_zero_int)) (not (= (tptp.aa_nat_int _let_1 N2) tptp.zero_zero_int))))) (forall ((M tptp.nat) (N2 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) N2)) tptp.zero_zero_nat)) (not (= (tptp.aa_nat_nat _let_1 M) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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) N2)) tptp.zero_zero_int)) (not (= (tptp.aa_nat_int _let_1 M) tptp.zero_zero_int))))) (forall ((N2 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 N2) 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 N2) M)) tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2) 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 N2) M)) tptp.zero_zero_int))))) (forall ((A tptp.nat) (N2 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 N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) 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) N2)))) (=> (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 N2) M))))))))))) (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) 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) N2)))) (=> (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 N2) M))))))))))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (or (= N2 tptp.zero_zero_nat) (= N2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (or (= N2 tptp.zero_zero_nat) (= N2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (forall ((P tptp.fun_nat_bool) (N2 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 ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (tptp.pp (tptp.aa_nat_bool P (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.pp (tptp.aa_nat_bool P N2)))))) (forall ((M tptp.nat) (P2 tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex 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.aa_com3342990543769683525omplex 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.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.aa_int_fun_nat_int 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 ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex 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) N2)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (tptp.aa_nat_complex _let_1 N2))))) (forall ((N2 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) N2)) (= (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 N2) tptp.one_one_nat))) A) (tptp.aa_nat_real _let_1 N2))))) (forall ((N2 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) N2)) (= (tptp.aa_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 N2) tptp.one_one_nat))) A) (tptp.aa_nat_rat _let_1 N2))))) (forall ((N2 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) N2)) (= (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 N2) tptp.one_one_nat))) A) (tptp.aa_nat_nat _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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) N2)) (= (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 N2) tptp.one_one_nat))) A) (tptp.aa_nat_int _let_1 N2))))) (forall ((P tptp.fun_nat_bool) (M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (or (and (= N2 tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (exists ((Q4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat _let_1 Q4)) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc Q4)))) (tptp.pp (tptp.aa_nat_bool P Q4)))))))) (forall ((N2 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) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2) (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) N2)) N2)))))) (forall ((A tptp.nat) (N2 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 N2))) (= (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 N2) M)))) _let_2))))) (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int 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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)))) _let_2))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 N2))) (= (tptp.modulo364778990260209775nteger (tptp.divide6298287555418463151nteger A _let_2) (tptp.aa_nat_Code_integer _let_1 M)) (tptp.divide6298287555418463151nteger (tptp.modulo364778990260209775nteger A (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M))) _let_2))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi) Ma)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Tr2 Sm2))) (= (tptp.vEBT_vebt_delete _let_1 X) _let_1))) (forall ((V tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (= (tptp.vEBT_vebt_succ (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vg2 Vh2) Vi2) tptp.none_nat)) (forall ((V tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (= (tptp.vEBT_vebt_pred (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vh2 Vi2) Vj2) tptp.none_nat)) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat X) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.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.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.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_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.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.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.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.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_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.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.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1))) tptp.zero_zero_int))))) (forall ((A tptp.real) (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 (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))) N2))))) (forall ((A tptp.rat) (N2 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))) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_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))) N2))))) (forall ((P tptp.fun_nat_bool) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat)) (=> (forall ((N 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 tptp.zero_zero_nat) N)) (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))) N)))))) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P N)) (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))) N)))))) (tptp.pp (tptp.aa_nat_bool P N2)))))) (forall ((N2 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 N2)) (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 N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((N2 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)) N2)) (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 N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((M tptp.nat) (N2 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) N2)) (= (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 N2)) (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 N2) M)))) _let_2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) _let_2)) (tptp.aa_nat_int _let_1 N2)) (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.modulo_modulo_int A) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))) _let_2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) _let_2) (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.modulo364778990260209775nteger A (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))) _let_2)))))) (forall ((A tptp.real) (N2 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))) N2))))) (tptp.pp (tptp.aa_real_bool _let_1 A))))) (forall ((A tptp.rat) (N2 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))) N2))))) (tptp.pp (tptp.aa_rat_bool _let_1 A))))) (forall ((A tptp.int) (N2 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.aa_int_fun_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))) N2))))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.real) (N2 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))) N2)))) tptp.zero_zero_real)))) (forall ((A tptp.rat) (N2 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))) N2)))) tptp.zero_zero_rat)))) (forall ((A tptp.int) (N2 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.aa_int_fun_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))) N2)))) tptp.zero_zero_int)))) (forall ((X tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X) N2)) (tptp.aa_nat_nat _let_1 M))))))))) (forall ((X tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)))) (=> (tptp.pp (tptp.aa_nat_bool _let_2 N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X) N2)) (tptp.aa_nat_nat _let_1 N2))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_4 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2)) _let_1) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (= (tptp.pp Y) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_4 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2))) (= (tptp.pp Y) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (tptp.vEBT_Leaf A3 B2)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_4 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)) TreeList2 Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc V2)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_2) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat (tptp.aa_nat_nat tptp.suc V2) TreeList2 Vd2))) (not (and (=> _let_3 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_1)))) _let_3)))))))))))) (forall ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real U) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real U) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))))))))) (forall ((U tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (tptp.aa_nat_rat (tptp.power_power_rat U) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) (tptp.aa_rat_rat (tptp.times_times_rat X) Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 X)) (=> (tptp.pp (tptp.aa_rat_bool _let_2 Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat U) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) Y)) (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)))))))))) (forall ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt A1) A22)) (or (and (exists ((A4 tptp.bool) (B4 tptp.bool)) (= A1 (tptp.vEBT_Leaf A4 B4))) (= A22 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat A22 TreeList3 Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X4) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) N5)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N5)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) N5)) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) X_12)))) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList3))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_12)))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N5))) (and (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat A22 TreeList3 Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X4) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) _let_1)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) _let_1)) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) X_12)))) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList3))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_12))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi3) Ma3)) A22 TreeList3 Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X4) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) N5)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat _let_2 N5)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) N5)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I5)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) I5))))) (=> _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 TreeList3))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_12))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat 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 ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (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) I5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma3) N5)))) (forall ((X4 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X4) N5) I5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X4) N5)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi3) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Ma3))))))))))))) (exists ((TreeList3 tptp.list_VEBT_VEBT) (N5 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat tptp.suc N5))) (and (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi3) Ma3)) A22 TreeList3 Summary3)) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList3))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X4) N5)))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary3) _let_3)) (= (tptp.size_s6755466524823107622T_VEBT TreeList3) (tptp.aa_nat_nat _let_2 _let_3)) (= A22 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N5) _let_3)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I5)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary3) I5))))) (=> _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 TreeList3))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_12))))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat 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 ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I5) (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) I5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma3) N5)))) (forall ((X4 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X4) N5) I5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList3 I5)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X4) N5)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi3) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) 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) (B2 tptp.bool)) (= A1 (tptp.vEBT_Leaf A3 B2))) (not (= A22 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X2) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) 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 N) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) X_13)))) (not (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X2) X_13)))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat)) (=> (= A1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X2) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) 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 N)) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M2)) (=> (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) X_13)))) (not (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X2) X_13)))))))))))))))) (=> (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X2) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M2)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat _let_2 M2)) (=> (= M2 N) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M2)) (=> (forall ((I 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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M2))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) I))))) (=> (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X2) X_13))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi2) Ma2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) (tptp.aa_nat_nat _let_2 Deg2))) (not (=> (not _let_1) (forall ((I 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.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) N) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma2) N)))) (forall ((X2 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X2) N) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X2) N)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) X2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X2) Ma2)))))))))))))))))))))))) (not (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (M2 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (= A1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Deg2 TreeList2 Summary2)) (=> (= A22 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt X2) N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt Summary2) M2)) (=> (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat _let_2 M2)) (=> (= M2 (tptp.aa_nat_nat tptp.suc N)) (=> (= Deg2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N) M2)) (=> (forall ((I 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.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) M2))) (= (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2) I))))) (=> (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (not (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X2) X_13))))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Mi2) Ma2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) (tptp.aa_nat_nat _let_2 Deg2))) (not (=> (not _let_1) (forall ((I 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.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) N) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Ma2) N)))) (forall ((X2 tptp.nat)) (=> (and (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high X2) N) I) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT TreeList2 I)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low X2) N)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) X2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X2) Ma2))))))))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (tptp.vEBT_vebt_insert X Xa2) Y) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (not (and (=> _let_3 (= Y (tptp.vEBT_Leaf tptp.fTrue B2))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.vEBT_Leaf A3 tptp.fTrue))) (=> (not _let_2) (= Y _let_1))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 tptp.zero_zero_nat Ts S))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Ts S))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc V2)))) (=> (= X (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Summary2)) (not (= Y (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa2) Xa2)) _let_1 TreeList2 Summary2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Mi2) Xa2))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList2 _let_6))) (let ((_let_8 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Xa2))) (=> (= X _let_2) (not (= Y (tptp.if_VEBT_VEBT (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_6) (tptp.size_s6755466524823107622T_VEBT TreeList2))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_bool_bool (tptp.fdisj (tptp.aa_nat_bool _let_8 Mi2)) (tptp.aa_nat_bool _let_8 Ma2)))) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Xa2) Mi2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_5) Ma2))) _let_1 (tptp.list_u1324408373059187874T_VEBT TreeList2 _let_6 (tptp.vEBT_vebt_insert _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_5) _let_3))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_7) (tptp.vEBT_vebt_insert Summary2 _let_6) Summary2)) _let_2)))))))))))))))))))) (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A2) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) 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 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A2) N2)) (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 B3) N2)) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B3) N2)))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.vEBT_VEBT_set_vebt T)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) tptp.one_one_nat)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.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 ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_succ X Xa2) Y) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 B2))) (let ((_let_2 (tptp.pp B2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> _let_2 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (= Y tptp.none_nat))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel (tptp.produc738532404422230701BT_nat _let_1 tptp.zero_zero_nat))))))))) (=> (forall ((Uv2 tptp.bool) (Uw2 tptp.bool)) (=> (= X (tptp.vEBT_Leaf Uv2 Uw2)) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf Uv2 Uw2) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Ux2 Uy2 Uz2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Vc2 Vd2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vg Vh))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (tptp.vEBT_vebt_succ Summary2 _let_5))) (let ((_let_7 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))))) (let ((_let_8 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_9 (tptp.nth_VEBT_VEBT TreeList2 _let_5))) (let ((_let_10 (tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (and (=> _let_11 (= Y (tptp.some_nat Mi2))) (=> (not _let_11) (= Y (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_5) (tptp.size_s6755466524823107622T_VEBT TreeList2)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_10) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_less (tptp.some_nat _let_8)) _let_10)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_7 (tptp.some_nat _let_5))) (tptp.vEBT_vebt_succ _let_9 _let_8)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_6) tptp.none_nat) tptp.none_nat (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_7 _let_6)) (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList2 (tptp.the_nat _let_6)))))) tptp.none_nat)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2)))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_pred X Xa2) Y) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_1 tptp.zero_zero_nat)))))))) (=> (forall ((A3 tptp.bool) (Uw2 tptp.bool)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (tptp.vEBT_Leaf A3 Uw2))) (let ((_let_3 (tptp.pp A3))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> _let_3 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_3) (= Y tptp.none_nat))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_2 _let_1)))))))))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (=> (= X (tptp.vEBT_Leaf A3 B2)) (forall ((Va2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.pp A3))) (let ((_let_3 (tptp.pp B2))) (=> (= Xa2 _let_1) (=> (and (=> _let_3 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= Y tptp.none_nat))))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat (tptp.vEBT_Leaf A3 B2) _let_1))))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uy2 Uz2 Va3))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Vd2 Ve))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vh Vi))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (tptp.vEBT_vebt_pred Summary2 _let_5))) (let ((_let_7 (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_mul (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))))) (let ((_let_8 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_9 (tptp.nth_VEBT_VEBT TreeList2 _let_5))) (let ((_let_10 (tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (=> (and (=> _let_11 (= Y (tptp.some_nat Ma2))) (=> (not _let_11) (= Y (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_5) (tptp.size_s6755466524823107622T_VEBT TreeList2)) (tptp.if_option_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_10) tptp.none_nat))) (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.vEBT_VEBT_greater (tptp.some_nat _let_8)) _let_10)) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_7 (tptp.some_nat _let_5))) (tptp.vEBT_vebt_pred _let_9 _let_8)) (tptp.if_option_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_6) tptp.none_nat) (tptp.if_option_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Mi2) Xa2) (tptp.some_nat Mi2) tptp.none_nat) (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat tptp.vEBT_VEBT_add (tptp.aa_opt1882420858203594238on_nat _let_7 _let_6)) (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT TreeList2 (tptp.the_nat _let_6)))))) tptp.none_nat)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))))))))))))))))))) (forall ((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.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 ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (tptp.vEBT_vebt_delete X Xa2) Y) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y (tptp.vEBT_Leaf tptp.fFalse B2)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel (tptp.produc738532404422230701BT_nat _let_1 tptp.zero_zero_nat)))))))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (= Y (tptp.vEBT_Leaf A3 tptp.fFalse)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel (tptp.produc738532404422230701BT_nat _let_2 _let_1))))))))) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (=> (= X (tptp.vEBT_Leaf A3 B2)) (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N)))) (let ((_let_2 (tptp.vEBT_Leaf A3 B2))) (=> (= Xa2 _let_1) (=> (= Y _let_2) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel (tptp.produc738532404422230701BT_nat _let_2 _let_1)))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Deg2 TreeList2 Summary2))) (=> (= X _let_1) (=> (= Y _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry 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 TrLst Smry))) (=> (= X _let_1) (=> (= Y _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm 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.aa_nat_nat tptp.suc tptp.zero_zero_nat) Tr Sm))) (=> (= X _let_1) (=> (= Y _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (tptp.the_nat (tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_3) _let_4))) (let ((_let_7 (tptp.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_5) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_mint (tptp.nth_VEBT_VEBT TreeList2 _let_5)))))) (let ((_let_8 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Xa2))) (let ((_let_9 (tptp.aa_nat_bool _let_8 Mi2))) (let ((_let_10 (tptp.if_nat _let_9))) (let ((_let_11 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_10 _let_7) Xa2))) (let ((_let_12 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (tptp.vEBT_vebt_delete (tptp.nth_VEBT_VEBT TreeList2 _let_12) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (tptp.list_u1324408373059187874T_VEBT TreeList2 _let_12 _let_13))) (let ((_let_15 (tptp.if_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies _let_9) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat _let_7) Ma2))) (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies (tptp.aa_bool_bool tptp.fNot _let_9)) (tptp.aa_nat_bool _let_8 Ma2)))))) (let ((_let_16 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_10 _let_11) Mi2))) (let ((_let_17 (tptp.product_Pair_nat_nat _let_16))) (let ((_let_18 (tptp.vEBT_vebt_delete Summary2 _let_12))) (let ((_let_19 (tptp.vEBT_vebt_maxt _let_18))) (let ((_let_20 (tptp.the_nat _let_19))) (let ((_let_21 (and (= Xa2 Mi2) (= Xa2 Ma2)))) (let ((_let_22 (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (=> (= X _let_2) (=> (and (=> _let_22 (= Y _let_2)) (=> (not _let_22) (and (=> _let_21 (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Summary2))) (=> (not _let_21) (= Y (tptp.if_VEBT_VEBT (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_12) (tptp.size_s6755466524823107622T_VEBT TreeList2)) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_13) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_17 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_15 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat _let_19) tptp.none_nat)) _let_16) (tptp.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_6) _let_20)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_14 _let_20)))))) Ma2))) _let_1 _let_14 _let_18) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat _let_17 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_15 (tptp.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_12) _let_6)) (tptp.the_nat (tptp.vEBT_vebt_maxt (tptp.nth_VEBT_VEBT _let_14 _let_12))))) Ma2))) _let_1 _let_14 Summary2)) _let_2)))))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2)))))))))))))))))))))))))))))))))))))) (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 ((A2 tptp.nat) (N2 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) N2)) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A2) N2)))) (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (tptp.aa_num_num tptp.bit0 X22) (tptp.aa_num_num tptp.bit0 Y22)) (= X22 Y22))) (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 ((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 ((N2 tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat N2 tptp.zero_z5237406670263579293d_enat) N2)) (forall ((N2 tptp.extended_enat)) (= (tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat N2) tptp.zero_z5237406670263579293d_enat)) (forall ((X tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)))) (= X tptp.zero_zero_real))) (forall ((V tptp.num) (W tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 V))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_num_int tptp.numeral_numeral_int W))))) (forall ((K tptp.int)) (= (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 ((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 ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A2) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N2)) (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) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B3) N2)) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B3) N2)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A))) (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.zero_zero_int) C)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_2 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) C))) (tptp.aa_int_int _let_1 B))))))) (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.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 ((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 ((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 ((K tptp.int) (I2 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 I2) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I2)))))) (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 ((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 ((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 ((K tptp.int) (P tptp.fun_int_fun_int_bool) (N2 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 N2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int N2) K))) (forall ((I5 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)) (= N2 (tptp.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) I5)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I5) J3))))))) (forall ((K tptp.int) (P tptp.fun_int_fun_int_bool) (N2 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 N2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int N2) K))) (forall ((I5 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)) (= N2 (tptp.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) I5)) J3))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I5) J3))))))) (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 ((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 ((A tptp.int) (A5 tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A5)) (=> (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 A5) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R2) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) Q2))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R2) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) R2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) Q2))))) (forall ((I2 tptp.int) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int I2) 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) I2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) K))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I2)))))) (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 ((A tptp.int) (A5 tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A5)) (=> (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 A5) B)))))) (forall ((P tptp.fun_int_bool) (N2 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 N2) 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 ((I5 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)) (= N2 (tptp.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) I5)) J3))) (tptp.pp (tptp.aa_int_bool P I5))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (forall ((I5 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)) (= N2 (tptp.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) I5)) J3))) (tptp.pp (tptp.aa_int_bool P I5)))))))) (forall ((A2 tptp.int) (N2 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) N2)) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A2) N2)))) (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.aa_int_int (tptp.aa_int_fun_int_int 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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) A)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 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.aa_int_int (tptp.aa_int_fun_int_int 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 ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat (tptp.times_7803423173614009249d_enat M N2)) (and (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat M) (tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat N2)))) (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (tptp.plus_p3455044024723400733d_enat M N2) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((N2 tptp.extended_enat)) (= (tptp.ord_le2932123472753598470d_enat N2 tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.extended_enat)) (tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat N2)) (forall ((N2 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) N2)) (tptp.pp (tptp.aa_nat_bool P M6)))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((N2 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) N2)) (tptp.pp (tptp.aa_nat_bool P M6)))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 B))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) tptp.one_one_int)) A))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 B))) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A))))) (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) A))))) (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) A))))) (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) A))))) (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))) (forall ((A tptp.set_int)) (tptp.ord_less_eq_set_int A A)) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) A))) (forall ((A tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) A))) (forall ((A tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) A)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) A)))) (forall ((A tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) A)))) (forall ((A tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) A)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) A)))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R3) (tptp.aa_nat_nat tptp.suc N2)) A))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (exists ((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 X) N)) Y)))))) (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 ((N2 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) N2)) (=> (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) N2) A) (forall ((Y2 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y2)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y2) N2) A)) (= Y2 X3)))))))) (forall ((N2 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) N2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (exists ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R3) N2) A)))))) (forall ((B5 tptp.real) (A5 tptp.real)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B5) A5))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A5) B5)))) (forall ((B5 tptp.rat) (A5 tptp.rat)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B5) A5))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A5) B5)))) (forall ((B5 tptp.num) (A5 tptp.num)) (= (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B5) A5))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A5) B5)))) (forall ((B5 tptp.nat) (A5 tptp.nat)) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B5) A5))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A5) B5)))) (forall ((B5 tptp.int) (A5 tptp.int)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B5) A5))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A5) B5)))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) tptp.zero_zero_complex) A)) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.zero_zero_real) A)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.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 ((X22 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit0 X22)))) (forall ((X2 tptp.extended_enat) (Xa tptp.extended_enat)) (let ((_let_1 (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat X2) Xa))) (let ((_let_2 (tptp.ord_le2932123472753598470d_enat X2 Xa))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X2)))))) (forall ((X2 tptp.code_integer) (Xa tptp.code_integer)) (let ((_let_1 (tptp.ord_max_Code_integer X2 Xa))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X2) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X2)))))) (forall ((X2 tptp.set_int) (Xa tptp.set_int)) (let ((_let_1 (tptp.ord_max_set_int X2 Xa))) (let ((_let_2 (tptp.ord_less_eq_set_int X2 Xa))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X2)))))) (forall ((X2 tptp.rat) (Xa tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.ord_max_rat X2) Xa))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X2) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X2)))))) (forall ((X2 tptp.num) (Xa tptp.num)) (let ((_let_1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.ord_max_num X2) Xa))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X2) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X2)))))) (forall ((X2 tptp.nat) (Xa tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X2) Xa))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X2) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X2)))))) (forall ((X2 tptp.int) (Xa tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int X2) Xa))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X2) Xa)))) (and (=> _let_2 (= _let_1 Xa)) (=> (not _let_2) (= _let_1 X2)))))) (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A2) B3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A2) N2) tptp.zero_zero_nat) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat B3) N2) 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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B3) N2)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se2793503036327961859nteger (tptp.aa_nat_nat tptp.suc N2) A) (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_se2793503036327961859nteger N2 (tptp.divide6298287555418463151nteger A _let_1))))))) (forall ((N2 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 N2)) 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.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 N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))))) (forall ((N2 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 N2)) 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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se8260200283734997820nteger (tptp.aa_nat_nat tptp.suc N2) A) (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_se8260200283734997820nteger N2 (tptp.divide6298287555418463151nteger A _let_1))))))) (forall ((N2 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 N2)) 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.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 N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))))) (forall ((N2 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 N2)) 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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (tptp.vEBT_vebt_insert X Xa2) Y) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (and (=> _let_3 (= Y (tptp.vEBT_Leaf tptp.fTrue B2))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.vEBT_Leaf A3 tptp.fTrue))) (=> (not _let_2) (= Y _let_1))))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 tptp.zero_zero_nat Ts S))) (=> (= X _let_1) (=> (= Y _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Info2 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Ts S))) (=> (= X _let_1) (=> (= Y _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc V2)))) (let ((_let_2 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Summary2))) (=> (= X _let_2) (=> (= Y (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa2) Xa2)) _let_1 TreeList2 Summary2)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Mi2) Xa2))) (let ((_let_6 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (tptp.nth_VEBT_VEBT TreeList2 _let_6))) (let ((_let_8 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Xa2))) (=> (= X _let_2) (=> (= Y (tptp.if_VEBT_VEBT (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_6) (tptp.size_s6755466524823107622T_VEBT TreeList2))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_bool_bool (tptp.fdisj (tptp.aa_nat_bool _let_8 Mi2)) (tptp.aa_nat_bool _let_8 Ma2)))) (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat _let_4 Xa2) Mi2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat _let_5) Ma2))) _let_1 (tptp.list_u1324408373059187874T_VEBT TreeList2 _let_6 (tptp.vEBT_vebt_insert _let_7 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low _let_5) _let_3))) (tptp.if_VEBT_VEBT (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull _let_7) (tptp.vEBT_vebt_insert Summary2 _let_6) Summary2)) _let_2)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2)))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_6 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (let ((_let_7 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (=> (= X _let_7) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_7 Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2)) (tptp.pp Y)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= (tptp.pp Y) (and (=> _let_3 (tptp.pp A3)) (=> (not _let_3) (and (=> _let_2 (tptp.pp B2)) _let_2)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) tptp.zero_zero_nat Uy2 Uz2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat V2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) Vb2 Vc2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_6 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_7 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (=> (= X _let_2) (=> (= (tptp.pp Y) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3)))) _let_5)))))))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node Uy2 _let_1 TreeList2 S))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node Uy2 _let_1 TreeList2 S))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (not (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member X) Xa2)) (tptp.pp Y)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= (tptp.pp Y) (and (=> _let_3 (tptp.pp A3)) (=> (not _let_3) (and (=> _let_2 (tptp.pp B2)) _let_2)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Uu2 tptp.zero_zero_nat Uv2 Uw2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.vEBT_Node Uy2 _let_1 TreeList2 S))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (= X _let_2) (=> (= (tptp.pp Y) (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5719532721284313246member (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3)))) _let_5)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member X) Xa2)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (tptp.vEBT_Leaf A3 B2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (not (and (=> _let_2 (tptp.pp A3)) (=> (not _let_2) (and (=> _let_1 (tptp.pp B2)) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Ma2) Xa2))))) (let ((_let_6 (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa2) Mi2))))) (let ((_let_7 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Summary2))) (=> (= X _let_7) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel (tptp.produc738532404422230701BT_nat _let_7 Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2))) (=> (= X _let_1) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (=> (= X _let_1) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Vc2))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Vd2))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))))))))) (forall ((Q2 tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)) (forall ((Q2 tptp.extended_enat)) (= (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)) (forall ((N2 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 N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N2 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 N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N2 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 N2) 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 ((N2 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 N2) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) tptp.one_one_int))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z) tptp.one_one_int))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z)))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) K)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L) K)))) (forall ((K tptp.int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) L)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L) K)))) (forall ((I2 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 I2) K)) (=> (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I3) K)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) (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 ((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.modulo_modulo_int K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L)) L))))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int L))) (=> (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_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 tptp.zero_zero_int) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L)) L)))) (forall ((I2 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 I2) 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 I2)) (tptp.aa_int_int _let_1 J))))))) _let_134 (forall ((P tptp.fun_int_bool) (N2 tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int N2) K))) (and (=> (= K tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool P N2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (forall ((I5 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)) (= N2 (tptp.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) I5)) 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 ((I5 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)) (= N2 (tptp.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) I5)) J3))) (tptp.pp (tptp.aa_int_bool P J3)))))))) (forall ((B5 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B5) Q5)) 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 Q5))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int 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.aa_int_int (tptp.aa_int_fun_int_int 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 ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R2) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) R2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B) R2))))) (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (=> (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R2) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B) R2))))) (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B5 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B5) Q5)) R4))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R2) _let_2) (=> (tptp.pp (tptp.aa_int_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R4) B5)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) 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) Q5))))))))))) (forall ((I2 tptp.int) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int I2) K) I2) (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) I2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) K))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I2)))))) (forall ((B tptp.int) (Q2 tptp.int) (R2 tptp.int) (B5 tptp.int) (Q5 tptp.int) (R4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B5) Q5)) R4))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) Q2)) R2) _let_1) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R2) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) 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 Q5) Q2)))))))))) (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 Q5)) R4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 Q2)) R2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R4)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R4) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R2) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q5) Q2)))))))) (forall ((M tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int M) K)) M)))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L)) tptp.zero_zero_int)))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L))))) (forall ((B tptp.int) (Q5 tptp.int) (R4 tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int B))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int B))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Q5)) R4)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 Q2)) R2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R2) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R2)) (=> (tptp.pp (tptp.aa_int_bool _let_1 R4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Q2) Q5))))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L) _let_1))))) (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 ((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 ((M tptp.int) (N2 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) N2) tptp.one_one_int) (and (= M tptp.one_one_int) (= N2 tptp.one_one_int))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z) tptp.zero_zero_int)))) (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int W))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z) tptp.one_one_int))) (or (tptp.pp (tptp.aa_int_bool _let_1 Z)) (= W Z))))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) Z))))) (forall ((K tptp.int) (I2 tptp.int) (P tptp.fun_int_bool)) (=> (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 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) I3)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) (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 ((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 ((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 ((M tptp.int) (D tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q4 tptp.int)) (= M (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int D) Q4))))) (forall ((M tptp.int) (D tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int D) Q3))))) (forall ((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 ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (tptp.times_7803423173614009249d_enat M N2) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z1) Z22)) W) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z1) W)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z22) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int W))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Z1) Z22)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 Z1)) (tptp.aa_int_int _let_1 Z22))))) (forall ((K tptp.int) (I2 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) I2)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I3)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) (forall ((K tptp.int) (N2 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 N2) K)))) (forall ((N2 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 N2) K)) K))) (forall ((A tptp.int) (X tptp.int)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X)) (= A X) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) A)))) (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int W))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z1) Z22)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 Z1)) (tptp.aa_int_int _let_1 Z22))))) (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z1) Z22)) W) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z1) W)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z22) W)))) (forall ((I2 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 I2) K)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I3) K)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) (forall ((P tptp.fun_int_bool) (K tptp.int) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K)) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) I3)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)))))) (=> (forall ((I3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I3) K)) (=> (tptp.pp (tptp.aa_int_bool P I3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int I3) tptp.one_one_int)))))) (tptp.pp (tptp.aa_int_bool P I2)))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (=> (= X _let_1) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Vc2))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_3) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (let ((_let_5 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Vd2))) (=> (= X _let_5) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_5 Xa2)) (not (and (=> _let_4 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_2)))) _let_4)))))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima X) Xa2)) (tptp.pp Y)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat tptp.zero_zero_nat Ux2 Uy2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) tptp.zero_zero_nat Va3 Vb2))) (=> (= X _let_1) (=> (= (tptp.pp Y) (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) _let_1 TreeList2 Vc2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (= X _let_2) (=> (= (tptp.pp Y) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3)))) _let_5))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc V2))) (let ((_let_2 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 TreeList2 Vd2))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_4) (tptp.size_s6755466524823107622T_VEBT TreeList2))))) (=> (= X _let_2) (=> (= (tptp.pp Y) (and (=> _let_5 (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_membermima (tptp.nth_VEBT_VEBT TreeList2 _let_4)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.vEBT_VEBT_low Xa2) _let_3)))) _let_5)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel (tptp.produc738532404422230701BT_nat _let_2 Xa2))))))))))))))))))) (forall ((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.set_or633870826150836451st_rat A B) tptp.bot_bot_set_rat))) (forall ((B tptp.num) (A tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) A)) (= (tptp.set_or7049704709247886629st_num A B) tptp.bot_bot_set_num))) (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.set_or1269000886237332187st_nat A B) tptp.bot_bot_set_nat))) (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.set_or1266510415728281911st_int A B) tptp.bot_bot_set_int))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (= (tptp.set_or1222579329274155063t_real A B) tptp.bot_bot_set_real))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or370866239135849197et_int A B) (tptp.set_or370866239135849197et_int C D)) (or (not (tptp.ord_less_eq_set_int A B)) (and (tptp.ord_less_eq_set_int C A) (tptp.ord_less_eq_set_int B D))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_or633870826150836451st_rat A B) (tptp.set_or633870826150836451st_rat C D)) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) D)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_or7049704709247886629st_num A B) (tptp.set_or7049704709247886629st_num C D)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) D)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_or1269000886237332187st_nat A B)) (tptp.set_or1269000886237332187st_nat C D))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat B) D)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (tptp.ord_less_eq_set_int (tptp.set_or1266510415728281911st_int A B) (tptp.set_or1266510415728281911st_int C D)) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) D)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (tptp.ord_less_eq_set_real (tptp.set_or1222579329274155063t_real A B) (tptp.set_or1222579329274155063t_real C D)) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) D)))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (tptp.set_or370866239135849197et_int A B) tptp.bot_bot_set_set_int) (not (tptp.ord_less_eq_set_int A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.set_or633870826150836451st_rat A B) tptp.bot_bot_set_rat) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (= (= (tptp.set_or7049704709247886629st_num A B) tptp.bot_bot_set_num) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (tptp.set_or1269000886237332187st_nat A B) tptp.bot_bot_set_nat) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.set_or1266510415728281911st_int A B) tptp.bot_bot_set_int) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((A tptp.real) (B tptp.real)) (= (= (tptp.set_or1222579329274155063t_real A B) tptp.bot_bot_set_real) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))))) (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_set_int (tptp.set_or370866239135849197et_int A B)) (not (tptp.ord_less_eq_set_int A B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (tptp.set_or633870826150836451st_rat A B)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))))) (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (tptp.set_or7049704709247886629st_num A B)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (tptp.set_or1269000886237332187st_nat A B)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (tptp.set_or1266510415728281911st_int A B)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))))) (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (tptp.set_or1222579329274155063t_real A B)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))))) (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 ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) D)))))))))) (forall ((D tptp.int) (P tptp.fun_int_bool) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((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 ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) D)))))))))) (forall ((L tptp.set_int) (H tptp.set_int) (L2 tptp.set_int) (H2 tptp.set_int)) (= (= (tptp.set_or370866239135849197et_int L H) (tptp.set_or370866239135849197et_int L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.ord_less_eq_set_int L H)) (not (tptp.ord_less_eq_set_int L2 H2)))))) (forall ((L tptp.rat) (H tptp.rat) (L2 tptp.rat) (H2 tptp.rat)) (= (= (tptp.set_or633870826150836451st_rat L H) (tptp.set_or633870826150836451st_rat L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) H))) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L2) H2))))))) (forall ((L tptp.num) (H tptp.num) (L2 tptp.num) (H2 tptp.num)) (= (= (tptp.set_or7049704709247886629st_num L H) (tptp.set_or7049704709247886629st_num L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) H))) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L2) H2))))))) (forall ((L tptp.nat) (H tptp.nat) (L2 tptp.nat) (H2 tptp.nat)) (= (= (tptp.set_or1269000886237332187st_nat L H) (tptp.set_or1269000886237332187st_nat L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) H))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L2) H2))))))) (forall ((L tptp.int) (H tptp.int) (L2 tptp.int) (H2 tptp.int)) (= (= (tptp.set_or1266510415728281911st_int L H) (tptp.set_or1266510415728281911st_int L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) H))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L2) H2))))))) (forall ((L tptp.real) (H tptp.real) (L2 tptp.real) (H2 tptp.real)) (= (= (tptp.set_or1222579329274155063t_real L H) (tptp.set_or1222579329274155063t_real L2 H2)) (or (and (= L L2) (= H H2)) (and (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L) H))) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L2) H2))))))) (forall ((I2 tptp.set_nat) (L tptp.set_nat) (U tptp.set_nat)) (= (tptp.member_set_nat I2 (tptp.set_or4548717258645045905et_nat L U)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat L) I2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat I2) U))))) (forall ((I2 tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (tptp.member_set_int I2 (tptp.set_or370866239135849197et_int L U)) (and (tptp.ord_less_eq_set_int L I2) (tptp.ord_less_eq_set_int I2 U)))) (forall ((I2 tptp.rat) (L tptp.rat) (U tptp.rat)) (= (tptp.member_rat I2 (tptp.set_or633870826150836451st_rat L U)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) I2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) U))))) (forall ((I2 tptp.num) (L tptp.num) (U tptp.num)) (= (tptp.member_num I2 (tptp.set_or7049704709247886629st_num L U)) (and (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) I2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num I2) U))))) (forall ((I2 tptp.nat) (L tptp.nat) (U tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) (tptp.set_or1269000886237332187st_nat L U))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) U))))) (forall ((I2 tptp.int) (L tptp.int) (U tptp.int)) (= (tptp.member_int I2 (tptp.set_or1266510415728281911st_int L U)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) I2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) U))))) (forall ((I2 tptp.real) (L tptp.real) (U tptp.real)) (= (tptp.member_real I2 (tptp.set_or1222579329274155063t_real L U)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L) I2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I2) U))))) (forall ((D2 tptp.int) (A2 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (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) Xa))))))) (=> (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) D2)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (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) Xa))))))) (=> (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) D2)))))) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X2) D2))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (or (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (or (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1)))))))))) (forall ((D2 tptp.int) (A2 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (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) Xa))))))) (=> (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) D2)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (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) Xa))))))) (=> (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) D2)))))) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X2) D2))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (and (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (and (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1)))))))))) (forall ((D2 tptp.int) (B3 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa))))))) (=> (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) D2)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa))))))) (=> (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) D2)))))) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X2) D2))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (or (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (or (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1)))))))))) (forall ((D2 tptp.int) (B3 tptp.set_int) (P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa))))))) (=> (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) D2)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa))))))) (=> (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) D2)))))) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X2) D2))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (and (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (and (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1)))))))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q6 tptp.fun_real_bool)) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X3)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P3 X3)))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X3)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q6 X3)))))) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (= (and (tptp.pp (tptp.aa_real_bool P X2)) (tptp.pp (tptp.aa_real_bool Q X2))) (and (tptp.pp (tptp.aa_real_bool P3 X2)) (tptp.pp (tptp.aa_real_bool Q6 X2)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q6 tptp.fun_rat_bool)) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X3)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P3 X3)))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X3)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q6 X3)))))) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (= (and (tptp.pp (tptp.aa_rat_bool P X2)) (tptp.pp (tptp.aa_rat_bool Q X2))) (and (tptp.pp (tptp.aa_rat_bool P3 X2)) (tptp.pp (tptp.aa_rat_bool Q6 X2)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q6 tptp.fun_num_bool)) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X3)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P3 X3)))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X3)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q6 X3)))))) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X2)) (= (and (tptp.pp (tptp.aa_num_bool P X2)) (tptp.pp (tptp.aa_num_bool Q X2))) (and (tptp.pp (tptp.aa_num_bool P3 X2)) (tptp.pp (tptp.aa_num_bool Q6 X2)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q6 tptp.fun_nat_bool)) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X3)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P3 X3)))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X3)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q6 X3)))))) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (= (and (tptp.pp (tptp.aa_nat_bool P X2)) (tptp.pp (tptp.aa_nat_bool Q X2))) (and (tptp.pp (tptp.aa_nat_bool P3 X2)) (tptp.pp (tptp.aa_nat_bool Q6 X2)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q6 tptp.fun_int_bool)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P3 X3)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q6 X3)))))) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (= (and (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (and (tptp.pp (tptp.aa_int_bool P3 X2)) (tptp.pp (tptp.aa_int_bool Q6 X2)))))))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q6 tptp.fun_real_bool)) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X3)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P3 X3)))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z4) X3)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q6 X3)))))) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (= (or (tptp.pp (tptp.aa_real_bool P X2)) (tptp.pp (tptp.aa_real_bool Q X2))) (or (tptp.pp (tptp.aa_real_bool P3 X2)) (tptp.pp (tptp.aa_real_bool Q6 X2)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q6 tptp.fun_rat_bool)) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X3)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P3 X3)))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z4) X3)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q6 X3)))))) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (= (or (tptp.pp (tptp.aa_rat_bool P X2)) (tptp.pp (tptp.aa_rat_bool Q X2))) (or (tptp.pp (tptp.aa_rat_bool P3 X2)) (tptp.pp (tptp.aa_rat_bool Q6 X2)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q6 tptp.fun_num_bool)) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X3)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P3 X3)))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z4) X3)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q6 X3)))))) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X2)) (= (or (tptp.pp (tptp.aa_num_bool P X2)) (tptp.pp (tptp.aa_num_bool Q X2))) (or (tptp.pp (tptp.aa_num_bool P3 X2)) (tptp.pp (tptp.aa_num_bool Q6 X2)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q6 tptp.fun_nat_bool)) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X3)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P3 X3)))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z4) X3)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q6 X3)))))) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (= (or (tptp.pp (tptp.aa_nat_bool P X2)) (tptp.pp (tptp.aa_nat_bool Q X2))) (or (tptp.pp (tptp.aa_nat_bool P3 X2)) (tptp.pp (tptp.aa_nat_bool Q6 X2)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q6 tptp.fun_int_bool)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P3 X3)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q6 X3)))))) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (= (or (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (or (tptp.pp (tptp.aa_int_bool P3 X2)) (tptp.pp (tptp.aa_int_bool Q6 X2)))))))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (not (= X2 T)))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) T))))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) T))))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X2) T))))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) T))))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) T))))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T) X2)))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T) X2)))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num T) X2)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat T) X2)))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int T) X2)))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q6 tptp.fun_real_bool)) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Z4)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P3 X3)))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Z4)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q6 X3)))))) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) Z3)) (= (and (tptp.pp (tptp.aa_real_bool P X2)) (tptp.pp (tptp.aa_real_bool Q X2))) (and (tptp.pp (tptp.aa_real_bool P3 X2)) (tptp.pp (tptp.aa_real_bool Q6 X2)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q6 tptp.fun_rat_bool)) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z4)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P3 X3)))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z4)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q6 X3)))))) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) Z3)) (= (and (tptp.pp (tptp.aa_rat_bool P X2)) (tptp.pp (tptp.aa_rat_bool Q X2))) (and (tptp.pp (tptp.aa_rat_bool P3 X2)) (tptp.pp (tptp.aa_rat_bool Q6 X2)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q6 tptp.fun_num_bool)) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Z4)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P3 X3)))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Z4)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q6 X3)))))) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X2) Z3)) (= (and (tptp.pp (tptp.aa_num_bool P X2)) (tptp.pp (tptp.aa_num_bool Q X2))) (and (tptp.pp (tptp.aa_num_bool P3 X2)) (tptp.pp (tptp.aa_num_bool Q6 X2)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q6 tptp.fun_nat_bool)) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z4)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P3 X3)))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z4)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q6 X3)))))) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Z3)) (= (and (tptp.pp (tptp.aa_nat_bool P X2)) (tptp.pp (tptp.aa_nat_bool Q X2))) (and (tptp.pp (tptp.aa_nat_bool P3 X2)) (tptp.pp (tptp.aa_nat_bool Q6 X2)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q6 tptp.fun_int_bool)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P3 X3)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q6 X3)))))) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) Z3)) (= (and (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (and (tptp.pp (tptp.aa_int_bool P3 X2)) (tptp.pp (tptp.aa_int_bool Q6 X2)))))))))) (forall ((P tptp.fun_real_bool) (P3 tptp.fun_real_bool) (Q tptp.fun_real_bool) (Q6 tptp.fun_real_bool)) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Z4)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P3 X3)))))) (=> (exists ((Z4 tptp.real)) (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Z4)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q6 X3)))))) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) Z3)) (= (or (tptp.pp (tptp.aa_real_bool P X2)) (tptp.pp (tptp.aa_real_bool Q X2))) (or (tptp.pp (tptp.aa_real_bool P3 X2)) (tptp.pp (tptp.aa_real_bool Q6 X2)))))))))) (forall ((P tptp.fun_rat_bool) (P3 tptp.fun_rat_bool) (Q tptp.fun_rat_bool) (Q6 tptp.fun_rat_bool)) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z4)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P3 X3)))))) (=> (exists ((Z4 tptp.rat)) (forall ((X3 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Z4)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q6 X3)))))) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) Z3)) (= (or (tptp.pp (tptp.aa_rat_bool P X2)) (tptp.pp (tptp.aa_rat_bool Q X2))) (or (tptp.pp (tptp.aa_rat_bool P3 X2)) (tptp.pp (tptp.aa_rat_bool Q6 X2)))))))))) (forall ((P tptp.fun_num_bool) (P3 tptp.fun_num_bool) (Q tptp.fun_num_bool) (Q6 tptp.fun_num_bool)) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Z4)) (= (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P3 X3)))))) (=> (exists ((Z4 tptp.num)) (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Z4)) (= (tptp.pp (tptp.aa_num_bool Q X3)) (tptp.pp (tptp.aa_num_bool Q6 X3)))))) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X2) Z3)) (= (or (tptp.pp (tptp.aa_num_bool P X2)) (tptp.pp (tptp.aa_num_bool Q X2))) (or (tptp.pp (tptp.aa_num_bool P3 X2)) (tptp.pp (tptp.aa_num_bool Q6 X2)))))))))) (forall ((P tptp.fun_nat_bool) (P3 tptp.fun_nat_bool) (Q tptp.fun_nat_bool) (Q6 tptp.fun_nat_bool)) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z4)) (= (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool P3 X3)))))) (=> (exists ((Z4 tptp.nat)) (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Z4)) (= (tptp.pp (tptp.aa_nat_bool Q X3)) (tptp.pp (tptp.aa_nat_bool Q6 X3)))))) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Z3)) (= (or (tptp.pp (tptp.aa_nat_bool P X2)) (tptp.pp (tptp.aa_nat_bool Q X2))) (or (tptp.pp (tptp.aa_nat_bool P3 X2)) (tptp.pp (tptp.aa_nat_bool Q6 X2)))))))))) (forall ((P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (Q tptp.fun_int_bool) (Q6 tptp.fun_int_bool)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P3 X3)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q6 X3)))))) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) Z3)) (= (or (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (or (tptp.pp (tptp.aa_int_bool P3 X2)) (tptp.pp (tptp.aa_int_bool Q6 X2)))))))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) Z3)) (not (= X2 T)))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Z3)) (tptp.pp (tptp.aa_real_bool _let_1 T))))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Z3)) (tptp.pp (tptp.aa_rat_bool _let_1 T))))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_num X2))) (=> (tptp.pp (tptp.aa_num_bool _let_1 Z3)) (tptp.pp (tptp.aa_num_bool _let_1 T))))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 Z3)) (tptp.pp (tptp.aa_nat_bool _let_1 T))))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int X2))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z3)) (tptp.pp (tptp.aa_int_bool _let_1 T))))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) Z3)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T) X2))))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) Z3)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat T) X2))))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X2) Z3)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num T) X2))))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Z3)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat T) X2))))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) Z3)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int T) X2))))))) (forall ((P tptp.fun_nat_bool) (X tptp.nat) (M7 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) M7)))) (not (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P M2)) (not (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P X2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X2) M2))))))))))) (forall ((X tptp.produc8114805097830739791at_num)) (not (forall ((F2 tptp.fun_nat_fun_num_num) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.num)) (not (= X (tptp.produc460779904311030791at_num F2 (tptp.produc1195630363706982562at_num A3 (tptp.product_Pair_nat_num B2 Acc)))))))) (forall ((X tptp.produc9217583074051984497at_nat)) (not (forall ((F2 tptp.fun_nat_fun_nat_nat) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.nat)) (not (= X (tptp.produc2818902965508115497at_nat F2 (tptp.produc487386426758144856at_nat A3 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat B2) Acc)))))))) (forall ((D tptp.int) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D)))))) (= (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12))) (exists ((X4 tptp.int)) (and (tptp.member_int X4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D)) (tptp.pp (tptp.aa_int_bool P X4)))))))) (forall ((D2 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int T) tptp.one_one_int) B3) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (= X2 T) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X2) D2) T))))))) (forall ((D2 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (tptp.member_int T B3) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (= X2 T)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X2) D2) T)))))))) (forall ((D2 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) 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 X2) D2)) T))))))) (forall ((D2 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (tptp.member_int T B3) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X2) D2)))))))))) (forall ((D2 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) D2)) (=> (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int T) tptp.one_one_int) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (= X2 T) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X2) D2) T))))))) (forall ((D2 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) D2)) (=> (tptp.member_int T A2) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (= X2 T)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X2) D2) T)))))))) (forall ((D2 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) D2)) (=> (tptp.member_int T A2) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) 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 X2) D2)) T)))))))) (forall ((D2 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) D2)) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X2) D2))))))))) (forall ((D2 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X2) 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 X2) D2)) T))))))) (forall ((D2 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int T) tptp.one_one_int) B3) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X2) D2)))))))))) (forall ((D2 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) D2)) (=> (tptp.member_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int T) tptp.one_one_int) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X2) 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 X2) D2)) T)))))))) (forall ((D2 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) D2)) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X2) D2))))))))) (forall ((D2 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) D2)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P3 X3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (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) Xa))))))) (=> (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) D2)))))) (=> (forall ((X3 tptp.int) (K2 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 K2) D2)))))) (= (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12))) (or (exists ((X4 tptp.int)) (and (tptp.member_int X4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (tptp.pp (tptp.aa_int_bool P3 X4)))) (exists ((X4 tptp.int)) (and (tptp.member_int X4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (exists ((Xa4 tptp.int)) (and (tptp.member_int Xa4 A2) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xa4) X4)))))))))))))) (forall ((D2 tptp.int) (P tptp.fun_int_bool) (P3 tptp.fun_int_bool) (B3 tptp.set_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D2)) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P3 X3)))))) (=> (forall ((X3 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (tptp.member_int Xa (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb2 tptp.int)) (=> (tptp.member_int Xb2 B3) (not (= X3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb2) Xa))))))) (=> (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) D2)))))) (=> (forall ((X3 tptp.int) (K2 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 K2) D2)))))) (= (exists ((X_12 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_12))) (or (exists ((X4 tptp.int)) (and (tptp.member_int X4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (tptp.pp (tptp.aa_int_bool P3 X4)))) (exists ((X4 tptp.int)) (and (tptp.member_int X4 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (exists ((Xa4 tptp.int)) (and (tptp.member_int Xa4 B3) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xa4) X4)))))))))))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X2) T))))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X2) T))))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X2)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X2) T))))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X2) T))))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X2) T))))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T) X2)))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T) X2)))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Z3) X2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num T) X2)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat T) X2)))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T) X2)))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) Z3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X2) T)))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) Z3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X2) T)))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X2) Z3)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X2) T)))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Z3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X2) T)))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) Z3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X2) T)))))) (forall ((T tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) Z3)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T) X2))))))) (forall ((T tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) Z3)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat T) X2))))))) (forall ((T tptp.num)) (exists ((Z3 tptp.num)) (forall ((X2 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X2) Z3)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num T) X2))))))) (forall ((T tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Z3)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat T) X2))))))) (forall ((T tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) Z3)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int T) X2))))))) (forall ((P tptp.fun_real_bool) (D2 tptp.real) (Q tptp.fun_real_bool)) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K2) D2)))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K2) D2)))))) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D2)))) (= (or (tptp.pp (tptp.aa_real_bool P X2)) (tptp.pp (tptp.aa_real_bool Q X2))) (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) (D2 tptp.rat) (Q tptp.fun_rat_bool)) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.times_times_rat K2) D2)))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q (tptp.aa_rat_rat (tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.times_times_rat K2) D2)))))) (forall ((X2 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat X2) (tptp.aa_rat_rat (tptp.times_times_rat K4) D2)))) (= (or (tptp.pp (tptp.aa_rat_bool P X2)) (tptp.pp (tptp.aa_rat_bool Q X2))) (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) (D2 tptp.int) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D2)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D2)))))) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D2)))) (= (or (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (or (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1))))))))) (forall ((P tptp.fun_real_bool) (D2 tptp.real) (Q tptp.fun_real_bool)) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool P X3)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K2) D2)))))) (=> (forall ((X3 tptp.real) (K2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool Q X3)) (tptp.pp (tptp.aa_real_bool Q (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K2) D2)))))) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D2)))) (= (and (tptp.pp (tptp.aa_real_bool P X2)) (tptp.pp (tptp.aa_real_bool Q X2))) (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) (D2 tptp.rat) (Q tptp.fun_rat_bool)) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool P X3)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.times_times_rat K2) D2)))))) (=> (forall ((X3 tptp.rat) (K2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool Q X3)) (tptp.pp (tptp.aa_rat_bool Q (tptp.aa_rat_rat (tptp.minus_minus_rat X3) (tptp.aa_rat_rat (tptp.times_times_rat K2) D2)))))) (forall ((X2 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat X2) (tptp.aa_rat_rat (tptp.times_times_rat K4) D2)))) (= (and (tptp.pp (tptp.aa_rat_bool P X2)) (tptp.pp (tptp.aa_rat_bool Q X2))) (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) (D2 tptp.int) (Q tptp.fun_int_bool)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D2)))))) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool Q X3)) (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D2)))))) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D2)))) (= (and (tptp.pp (tptp.aa_int_bool P X2)) (tptp.pp (tptp.aa_int_bool Q X2))) (and (tptp.pp (tptp.aa_int_bool P _let_1)) (tptp.pp (tptp.aa_int_bool Q _let_1))))))))) (forall ((X tptp.int) (X5 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 X5)))) (let ((_let_4 (tptp.pp P))) (=> (= X X5) (=> (=> _let_3 (= _let_4 _let_1)) (= (and (tptp.pp (tptp.aa_int_bool _let_2 X)) _let_4) (and _let_3 _let_1))))))))) (forall ((X tptp.int) (X5 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 X5)))) (let ((_let_4 (tptp.pp P))) (=> (= X X5) (=> (=> _let_3 (= _let_4 _let_1)) (= (=> (tptp.pp (tptp.aa_int_bool _let_2 X)) _let_4) (=> _let_3 _let_1))))))))) (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (tptp.ord_less_set_set_int (tptp.set_or370866239135849197et_int A B) (tptp.set_or370866239135849197et_int C D)) (and (or (not (tptp.ord_less_eq_set_int A B)) (and (tptp.ord_less_eq_set_int C A) (tptp.ord_less_eq_set_int B D) (or (tptp.ord_less_set_int C A) (tptp.ord_less_set_int B D)))) (tptp.ord_less_eq_set_int C 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 C))) (= (tptp.ord_less_set_rat (tptp.set_or633870826150836451st_rat A B) (tptp.set_or633870826150836451st_rat C D)) (and (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B))) (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) D)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) D))))) (tptp.pp (tptp.aa_rat_bool _let_1 D)))))) (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num C))) (= (tptp.ord_less_set_num (tptp.set_or7049704709247886629st_num A B) (tptp.set_or7049704709247886629st_num C D)) (and (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) B))) (and (tptp.pp (tptp.aa_num_bool _let_1 A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num B) D)) (or (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num C) A)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num B) D))))) (tptp.pp (tptp.aa_num_bool _let_1 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 C))) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat (tptp.set_or1269000886237332187st_nat A B)) (tptp.set_or1269000886237332187st_nat C D))) (and (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) B))) (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) D)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) D))))) (tptp.pp (tptp.aa_nat_bool _let_1 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 C))) (= (tptp.ord_less_set_int (tptp.set_or1266510415728281911st_int A B) (tptp.set_or1266510415728281911st_int C D)) (and (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B))) (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) D)) (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int C) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int B) D))))) (tptp.pp (tptp.aa_int_bool _let_1 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 C))) (= (tptp.ord_less_set_real (tptp.set_or1222579329274155063t_real A B) (tptp.set_or1222579329274155063t_real C D)) (and (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B))) (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) D)) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) D))))) (tptp.pp (tptp.aa_real_bool _let_1 D)))))) (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) (K2 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 K2) D)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z4) X3)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P3 X3)))))) (=> (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P3 X_13))) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1)))))))) (forall ((D tptp.int) (P1 tptp.fun_int_bool) (P tptp.fun_int_bool)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) D)) (=> (forall ((X3 tptp.int) (K2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool P1 X3)) (tptp.pp (tptp.aa_int_bool P1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) D)))))) (=> (exists ((Z4 tptp.int)) (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Z4)) (= (tptp.pp (tptp.aa_int_bool P X3)) (tptp.pp (tptp.aa_int_bool P1 X3)))))) (=> (exists ((X_13 tptp.int)) (tptp.pp (tptp.aa_int_bool P1 X_13))) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1345352211410354436nteger (tptp.aa_nat_nat tptp.suc N2) A) (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_se1345352211410354436nteger N2 (tptp.divide6298287555418463151nteger A _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int (tptp.aa_nat_nat tptp.suc N2)) 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.modulo_modulo_int A) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))))) (forall ((N2 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 N2)) 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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))))) (forall ((A tptp.real) (B tptp.real) (P tptp.fun_re1255401033344146673l_bool)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((A3 tptp.real) (B2 tptp.real) (C3 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool P A3))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P B2) C3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A3) B2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B2) C3)) (tptp.pp (tptp.aa_real_bool _let_1 C3)))))))) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((D5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D5)) (forall ((A3 tptp.real) (B2 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A3) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B2) A3)) D5))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A3) B2))))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool P A) B)))))) (forall ((Z tptp.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.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 ((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.times_times_rat X) Z)) (tptp.aa_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 ((Q2 tptp.nat) (R2 tptp.nat)) (= (tptp.pp (tptp.aa_Pro2232559814647311250t_bool tptp.unique6322359934112328802ux_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Q2) R2))) (= R2 tptp.zero_zero_nat))) (forall ((Q2 tptp.int) (R2 tptp.int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool tptp.unique6319869463603278526ux_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R2))) (= R2 tptp.zero_zero_int))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N2) 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 ((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.times_times_rat X) Z)) (tptp.aa_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 ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int) B) (tptp.aa_int7462565939943104719nt_int _let_2 R2))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)) (tptp.aa_int7462565939943104719nt_int _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int _let_1 R2)) tptp.one_one_int))))))))) (forall ((N2 tptp.nat) (Xs tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (tptp.size_size_list_num Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_num Xs)) _let_1))) (= (tptp.nth_Pr6456567536196504476um_num (tptp.product_num_num Xs Ys) N2) (tptp.product_Pair_num_num (tptp.aa_nat_num (tptp.nth_num Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_num (tptp.nth_num Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_num)) (let ((_let_1 (tptp.size_size_list_num Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_nat Xs)) _let_1))) (= (tptp.nth_Pr8326237132889035090at_num (tptp.product_nat_num Xs Ys) N2) (tptp.product_Pair_nat_num (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_num (tptp.nth_num Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_nat)) (let ((_let_1 (tptp.size_size_list_nat Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_nat Xs)) _let_1))) (= (tptp.nth_Pr7617993195940197384at_nat (tptp.product_nat_nat Xs Ys) N2) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1))) (tptp.aa_nat_nat (tptp.nth_nat Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.size_s6755466524823107622T_VEBT Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_nat Xs)) _let_1))) (= (tptp.nth_Pr744662078594809490T_VEBT (tptp.produc7156399406898700509T_VEBT Xs Ys) N2) (tptp.produc599794634098209291T_VEBT (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.nth_VEBT_VEBT Ys (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_nat Xs)) _let_1))) (= (tptp.nth_Pr396318242284072693t_bool (tptp.product_nat_bool Xs Ys) N2) (tptp.produc3913204875133826030t_bool (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_bool (tptp.nth_bool Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_Code_integer) (Ys tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s3445333598471063425nteger Xs)) _let_1))) (= (tptp.nth_Pr136253548056570280r_bool (tptp.produc2469108709554126195r_bool Xs Ys) N2) (tptp.produc5135875973608410785r_bool (tptp.aa_nat_Code_integer (tptp.nth_Code_integer Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_bool (tptp.nth_bool Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_int)) (let ((_let_1 (tptp.size_size_list_int Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_nat Xs)) _let_1))) (= (tptp.nth_Pr3440142176431000676at_int (tptp.product_nat_int Xs Ys) N2) (tptp.product_Pair_nat_int (tptp.aa_nat_nat (tptp.nth_nat Xs) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_int (tptp.nth_int Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (tptp.size_size_list_nat Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) _let_1))) (= (tptp.nth_Pr1791586995822124652BT_nat (tptp.produc7295137177222721919BT_nat Xs Ys) N2) (tptp.produc738532404422230701BT_nat (tptp.nth_VEBT_VEBT Xs (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_nat (tptp.nth_nat Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (tptp.size_s6755466524823107622T_VEBT Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) _let_1))) (= (tptp.nth_Pr4953567300277697838T_VEBT (tptp.produc4743750530478302277T_VEBT Xs Ys) N2) (tptp.produc537772716801021591T_VEBT (tptp.nth_VEBT_VEBT Xs (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.nth_VEBT_VEBT Ys (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_bool)) (let ((_let_1 (tptp.size_size_list_bool Ys))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) _let_1))) (= (tptp.nth_Pr1289831921885633937T_bool (tptp.produc5466675335756156456T_bool Xs Ys) N2) (tptp.produc3035007008238225530T_bool (tptp.nth_VEBT_VEBT Xs (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)) (tptp.aa_nat_bool (tptp.nth_bool Ys) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((Z tptp.nat) (X tptp.nat) (A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z) X)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_min_in_set A2) Z)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set A2) X) X_1))))))) (forall ((X tptp.nat) (Z tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (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.vEBT_VEBT_max_in_set A2) Z)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (= A2 B3) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_succ_in_set A2) X) X_1)))))))) (forall ((T tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_invar_vebt T) N2)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.vEBT_VEBT_set_vebt T))))) (forall ((Xs tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_succ_in_set Xs) A) X_1)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat Xs)) (not (exists ((X2 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X2) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) X2)))))))) (forall ((Xs tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.vEBT_is_pred_in_set Xs) A) X_1)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat Xs)) (not (exists ((X2 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X2) Xs)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) A)))))))) (forall ((X1 tptp.code_integer) (X22 tptp.bool) (Y1 tptp.code_integer) (Y22 tptp.bool)) (= (= (tptp.produc5135875973608410785r_bool X1 X22) (tptp.produc5135875973608410785r_bool Y1 Y22)) (and (= X1 Y1) (= (tptp.pp X22) (tptp.pp Y22))))) (forall ((X1 tptp.num) (X22 tptp.num) (Y1 tptp.num) (Y22 tptp.num)) (= (= (tptp.product_Pair_num_num X1 X22) (tptp.product_Pair_num_num Y1 Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.nat) (X22 tptp.num) (Y1 tptp.nat) (Y22 tptp.num)) (= (= (tptp.product_Pair_nat_num X1 X22) (tptp.product_Pair_nat_num Y1 Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.nat) (X22 tptp.nat) (Y1 tptp.nat) (Y22 tptp.nat)) (= (= (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X1) X22) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X22) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))) (forall ((A tptp.code_integer) (B tptp.bool) (A5 tptp.code_integer) (B5 tptp.bool)) (= (= (tptp.produc5135875973608410785r_bool A B) (tptp.produc5135875973608410785r_bool A5 B5)) (and (= A A5) (= (tptp.pp B) (tptp.pp B5))))) (forall ((A tptp.num) (B tptp.num) (A5 tptp.num) (B5 tptp.num)) (= (= (tptp.product_Pair_num_num A B) (tptp.product_Pair_num_num A5 B5)) (and (= A A5) (= B B5)))) (forall ((A tptp.nat) (B tptp.num) (A5 tptp.nat) (B5 tptp.num)) (= (= (tptp.product_Pair_nat_num A B) (tptp.product_Pair_nat_num A5 B5)) (and (= A A5) (= B B5)))) (forall ((A tptp.nat) (B tptp.nat) (A5 tptp.nat) (B5 tptp.nat)) (= (= (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A5) B5)) (and (= A A5) (= B B5)))) (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B5 tptp.int)) (= (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A5) B5)) (and (= A A5) (= B B5)))) (forall ((Xs tptp.list_VEBT_VEBT)) (tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT2 Xs))) (forall ((Xs tptp.list_nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.set_nat2 Xs)))) (forall ((Xs tptp.list_int)) (tptp.finite_finite_int (tptp.set_int2 Xs))) (forall ((Xs tptp.list_complex)) (tptp.finite3207457112153483333omplex (tptp.set_complex2 Xs))) (forall ((A tptp.rat) (B tptp.rat)) (= (not (tptp.finite_finite_rat (tptp.set_or633870826150836451st_rat A B))) (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)) (= (not (tptp.finite_finite_real (tptp.set_or1222579329274155063t_real A B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (tptp.size_s7466405169056248089T_VEBT (tptp.produc4743750530478302277T_VEBT Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) (tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_bool)) (= (tptp.size_s1343096544515248124T_bool (tptp.produc5466675335756156456T_bool Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) (tptp.size_size_list_bool Ys)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (tptp.size_s3661962791536183091BT_int (tptp.produc7292646706713671643BT_int Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_s6755466524823107622T_VEBT Xs)) (tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_VEBT_VEBT)) (= (tptp.size_s7211631430880329078T_VEBT (tptp.produc2282853104913622818T_VEBT Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) (tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_bool)) (= (tptp.size_s6988337448923680857l_bool (tptp.product_bool_bool Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) (tptp.size_size_list_bool Ys)))) (forall ((Xs tptp.list_bool) (Ys tptp.list_int)) (= (tptp.size_s753689718144262038ol_int (tptp.product_bool_int Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_bool Xs)) (tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_VEBT_VEBT)) (= (tptp.size_s6639371672096860321T_VEBT (tptp.produc662631939642741121T_VEBT Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) (tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_bool)) (= (tptp.size_s323260168234592132t_bool (tptp.product_int_bool Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) (tptp.size_size_list_bool Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (= (tptp.size_s5157815400016825771nt_int (tptp.product_int_int Xs Ys)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.size_size_list_int Xs)) (tptp.size_size_list_int Ys)))) (forall ((N3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (exists ((M6 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) N3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X4) M6))))))) (forall ((N3 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) N3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) N2)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)))) (forall ((N3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (exists ((M6 tptp.nat)) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) N3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) M6))))))) (forall ((A2 tptp.set_VEBT_VEBT)) (=> (tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (tptp.set_VEBT_VEBT2 Xs2) A2)))) (forall ((A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (exists ((Xs2 tptp.list_nat)) (= (tptp.set_nat2 Xs2) A2)))) (forall ((A2 tptp.set_int)) (=> (tptp.finite_finite_int A2) (exists ((Xs2 tptp.list_int)) (= (tptp.set_int2 Xs2) A2)))) (forall ((A2 tptp.set_complex)) (=> (tptp.finite3207457112153483333omplex A2) (exists ((Xs2 tptp.list_complex)) (= (tptp.set_complex2 Xs2) A2)))) (forall ((P tptp.fun_nat_bool) (I2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_bn P) I2))))) (forall ((F tptp.fun_nat_nat) (U tptp.nat)) (=> (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 F N)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_bo F) U)))))) (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_bp A2) N2))))) (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (tptp.finite3207457112153483333omplex A2) (tptp.finite8712137658972009173omplex (tptp.collect_list_complex (tptp.aa_nat8039161444313734436x_bool (tptp.aTP_Lamm_bq A2) N2))))) (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (tptp.finite5795047828879050333T_VEBT A2) (tptp.finite3004134309566078307T_VEBT (tptp.collec5608196760682091941T_VEBT (tptp.aa_nat1297483763028037422T_bool (tptp.aTP_Lamm_br A2) N2))))) (forall ((A2 tptp.set_bool) (N2 tptp.nat)) (=> (tptp.finite_finite_bool A2) (tptp.finite7866827932528546246t_bool (tptp.collect_list_bool (tptp.aa_nat4862889769322786699l_bool (tptp.aTP_Lamm_bs A2) N2))))) (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (tptp.finite_finite_int A2) (tptp.finite3922522038869484883st_int (tptp.collect_list_int (tptp.aa_nat1619170893822700070t_bool (tptp.aTP_Lamm_bt A2) N2))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (not (tptp.finite_finite_rat (tptp.set_or633870826150836451st_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) B)) (not (tptp.finite_finite_real (tptp.set_or1222579329274155063t_real A B))))) (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.finite8100373058378681591st_nat (tptp.collect_list_nat (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_bu A2) N2))))) (forall ((A2 tptp.set_complex) (N2 tptp.nat)) (=> (tptp.finite3207457112153483333omplex A2) (tptp.finite8712137658972009173omplex (tptp.collect_list_complex (tptp.aa_nat8039161444313734436x_bool (tptp.aTP_Lamm_bv A2) N2))))) (forall ((A2 tptp.set_VEBT_VEBT) (N2 tptp.nat)) (=> (tptp.finite5795047828879050333T_VEBT A2) (tptp.finite3004134309566078307T_VEBT (tptp.collec5608196760682091941T_VEBT (tptp.aa_nat1297483763028037422T_bool (tptp.aTP_Lamm_bw A2) N2))))) (forall ((A2 tptp.set_bool) (N2 tptp.nat)) (=> (tptp.finite_finite_bool A2) (tptp.finite7866827932528546246t_bool (tptp.collect_list_bool (tptp.aa_nat4862889769322786699l_bool (tptp.aTP_Lamm_bx A2) N2))))) (forall ((A2 tptp.set_int) (N2 tptp.nat)) (=> (tptp.finite_finite_int A2) (tptp.finite3922522038869484883st_int (tptp.collect_list_int (tptp.aa_nat1619170893822700070t_bool (tptp.aTP_Lamm_by A2) N2))))) (forall ((L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q2) L)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) tptp.zero_zero_int)))))) (forall ((Y tptp.produc7417142470700560111r_bool)) (not (forall ((A3 tptp.code_integer) (B2 tptp.bool)) (not (= Y (tptp.produc5135875973608410785r_bool A3 B2)))))) (forall ((Y tptp.product_prod_num_num)) (not (forall ((A3 tptp.num) (B2 tptp.num)) (not (= Y (tptp.product_Pair_num_num A3 B2)))))) (forall ((Y tptp.product_prod_nat_num)) (not (forall ((A3 tptp.nat) (B2 tptp.num)) (not (= Y (tptp.product_Pair_nat_num A3 B2)))))) (forall ((Y tptp.product_prod_nat_nat)) (not (forall ((A3 tptp.nat) (B2 tptp.nat)) (not (= Y (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A3) B2)))))) (forall ((Y tptp.product_prod_int_int)) (not (forall ((A3 tptp.int) (B2 tptp.int)) (not (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B2)))))) (forall ((P2 tptp.produc7417142470700560111r_bool)) (exists ((X3 tptp.code_integer) (Y4 tptp.bool)) (= P2 (tptp.produc5135875973608410785r_bool X3 Y4)))) (forall ((P2 tptp.product_prod_num_num)) (exists ((X3 tptp.num) (Y4 tptp.num)) (= P2 (tptp.product_Pair_num_num X3 Y4)))) (forall ((P2 tptp.product_prod_nat_num)) (exists ((X3 tptp.nat) (Y4 tptp.num)) (= P2 (tptp.product_Pair_nat_num X3 Y4)))) (forall ((P2 tptp.product_prod_nat_nat)) (exists ((X3 tptp.nat) (Y4 tptp.nat)) (= P2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y4)))) (forall ((P2 tptp.product_prod_int_int)) (exists ((X3 tptp.int) (Y4 tptp.int)) (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y4)))) (forall ((P tptp.fun_Pr8281063099935739201l_bool) (P2 tptp.produc7417142470700560111r_bool)) (=> (forall ((A3 tptp.code_integer) (B2 tptp.bool)) (tptp.pp (tptp.aa_Pro6456355659118895914l_bool P (tptp.produc5135875973608410785r_bool A3 B2)))) (tptp.pp (tptp.aa_Pro6456355659118895914l_bool P P2)))) (forall ((P tptp.fun_Pr6287530515171585797m_bool) (P2 tptp.product_prod_num_num)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P (tptp.product_Pair_num_num A3 B2)))) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P P2)))) (forall ((P tptp.fun_Pr1727971692872576719m_bool) (P2 tptp.product_prod_nat_num)) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (tptp.pp (tptp.aa_Pro5426739851356932296m_bool P (tptp.product_Pair_nat_num A3 B2)))) (tptp.pp (tptp.aa_Pro5426739851356932296m_bool P P2)))) (forall ((P tptp.fun_Pr7757163693017731481t_bool) (P2 tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A3) B2)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P P2)))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (P2 tptp.product_prod_int_int)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B2)))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P P2)))) (forall ((A tptp.code_integer) (B tptp.bool) (A5 tptp.code_integer) (B5 tptp.bool)) (=> (= (tptp.produc5135875973608410785r_bool A B) (tptp.produc5135875973608410785r_bool A5 B5)) (not (=> (= A A5) (= (tptp.pp B) (not (tptp.pp B5))))))) (forall ((A tptp.num) (B tptp.num) (A5 tptp.num) (B5 tptp.num)) (=> (= (tptp.product_Pair_num_num A B) (tptp.product_Pair_num_num A5 B5)) (not (=> (= A A5) (not (= B B5)))))) (forall ((A tptp.nat) (B tptp.num) (A5 tptp.nat) (B5 tptp.num)) (=> (= (tptp.product_Pair_nat_num A B) (tptp.product_Pair_nat_num A5 B5)) (not (=> (= A A5) (not (= B B5)))))) (forall ((A tptp.nat) (B tptp.nat) (A5 tptp.nat) (B5 tptp.nat)) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A5) B5)) (not (=> (= A A5) (not (= B B5)))))) (forall ((A tptp.int) (B tptp.int) (A5 tptp.int) (B5 tptp.int)) (=> (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A5) B5)) (not (=> (= A A5) (not (= B B5)))))) (forall ((N3 tptp.set_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N3) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)))) (forall ((K tptp.int) (L tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int L))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int)))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) L)))) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R2))) (and (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) Q2)) R2)) (=> _let_3 (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) R2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int R2) L)))) (=> (not _let_3) (and (=> _let_2 (and (tptp.pp (tptp.aa_int_bool _let_1 R2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int R2) tptp.zero_zero_int)))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))) (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A B) (tptp.aa_int7462565939943104719nt_int _let_3 R2))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)) (tptp.aa_int7462565939943104719nt_int _let_3 (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_1 R2))))))))))) (forall ((K tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_bz K))))) (forall ((K tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_ca K))))) (forall ((A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aTP_Lamm_cb A2))))) (forall ((A2 tptp.set_complex)) (=> (tptp.finite3207457112153483333omplex A2) (tptp.finite6551019134538273531omplex (tptp.collect_set_complex (tptp.aTP_Lamm_cc A2))))) (forall ((A2 tptp.set_int)) (=> (tptp.finite_finite_int A2) (tptp.finite6197958912794628473et_int (tptp.collect_set_int (tptp.aTP_Lamm_cd A2))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (tptp.finite_finite_real (tptp.collect_real (tptp.aTP_Lamm_ce N2))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool tptp.aTP_Lamm_cf N2))))) (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (tptp.finite_finite_int B3) (= (tptp.finite_finite_int (tptp.minus_minus_set_int A2 B3)) (tptp.finite_finite_int A2)))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex)) (=> (tptp.finite3207457112153483333omplex B3) (= (tptp.finite3207457112153483333omplex (tptp.minus_811609699411566653omplex A2 B3)) (tptp.finite3207457112153483333omplex A2)))) (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.minus_minus_set_nat A2 B3))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.finite_finite_int A2) (tptp.finite_finite_int (tptp.minus_minus_set_int A2 B3)))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.finite3207457112153483333omplex A2) (tptp.finite3207457112153483333omplex (tptp.minus_811609699411566653omplex A2 B3)))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.minus_minus_set_nat A2 B3))))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (= (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_cg P) Q))) (and (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int P)) (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int Q))))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (= (tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ch P) Q))) (and (tptp.finite1152437895449049373et_nat (tptp.collect_set_nat P)) (tptp.finite1152437895449049373et_nat (tptp.collect_set_nat Q))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_ci P) Q)))) (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat Q)))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (= (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_cj P) Q))) (and (tptp.finite_finite_int (tptp.collect_int P)) (tptp.finite_finite_int (tptp.collect_int Q))))) (forall ((P tptp.fun_complex_bool) (Q tptp.fun_complex_bool)) (= (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_ck P) Q))) (and (tptp.finite3207457112153483333omplex (tptp.collect_complex P)) (tptp.finite3207457112153483333omplex (tptp.collect_complex Q))))) (forall ((P tptp.fun_Pr803113274115125473t_bool) (Q tptp.fun_Pr803113274115125473t_bool)) (=> (or (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int P)) (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int Q))) (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_cl P) Q))))) (forall ((P tptp.fun_set_nat_bool) (Q tptp.fun_set_nat_bool)) (=> (or (tptp.finite1152437895449049373et_nat (tptp.collect_set_nat P)) (tptp.finite1152437895449049373et_nat (tptp.collect_set_nat Q))) (tptp.finite1152437895449049373et_nat (tptp.collect_set_nat (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_cm P) Q))))) (forall ((P tptp.fun_nat_bool) (Q tptp.fun_nat_bool)) (=> (or (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat Q)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_cn P) Q)))))) (forall ((P tptp.fun_int_bool) (Q tptp.fun_int_bool)) (=> (or (tptp.finite_finite_int (tptp.collect_int P)) (tptp.finite_finite_int (tptp.collect_int Q))) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_co P) Q))))) (forall ((P tptp.fun_complex_bool) (Q tptp.fun_complex_bool)) (=> (or (tptp.finite3207457112153483333omplex (tptp.collect_complex P)) (tptp.finite3207457112153483333omplex (tptp.collect_complex Q))) (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_cp P) Q))))) (forall ((A tptp.int) (B tptp.int)) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_cq 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_cr 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_cs 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_ct A) B)))) (forall ((M7 tptp.set_list_VEBT_VEBT)) (=> (tptp.finite3004134309566078307T_VEBT M7) (exists ((N tptp.nat)) (forall ((X2 tptp.list_VEBT_VEBT)) (=> (tptp.member2936631157270082147T_VEBT X2 M7) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_s6755466524823107622T_VEBT X2)) N))))))) (forall ((M7 tptp.set_list_bool)) (=> (tptp.finite7866827932528546246t_bool M7) (exists ((N tptp.nat)) (forall ((X2 tptp.list_bool)) (=> (tptp.member_list_bool X2 M7) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_bool X2)) N))))))) (forall ((M7 tptp.set_list_int)) (=> (tptp.finite3922522038869484883st_int M7) (exists ((N tptp.nat)) (forall ((X2 tptp.list_int)) (=> (tptp.member_list_int X2 M7) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.size_size_list_int X2)) N))))))) (forall ((P tptp.fun_Pr803113274115125473t_bool)) (=> (not (tptp.finite2998713641127702882nt_int (tptp.collec213857154873943460nt_int P))) (exists ((X_1 tptp.product_prod_int_int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X_1))))) (forall ((P tptp.fun_set_nat_bool)) (=> (not (tptp.finite1152437895449049373et_nat (tptp.collect_set_nat P))) (exists ((X_1 tptp.set_nat)) (tptp.pp (tptp.aa_set_nat_bool P X_1))))) (forall ((P tptp.fun_nat_bool)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P)))) (exists ((X_1 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_1))))) (forall ((P tptp.fun_int_bool)) (=> (not (tptp.finite_finite_int (tptp.collect_int P))) (exists ((X_1 tptp.int)) (tptp.pp (tptp.aa_int_bool P X_1))))) (forall ((P tptp.fun_complex_bool)) (=> (not (tptp.finite3207457112153483333omplex (tptp.collect_complex P))) (exists ((X_1 tptp.complex)) (tptp.pp (tptp.aa_complex_bool P X_1))))) (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (R tptp.fun_re9121486324101951821t_bool)) (=> (not (tptp.finite_finite_real A2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_real_fun_nat_bool R X3) Xa)))))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (not (tptp.finite_finite_real (tptp.collect_real (tptp.aa_nat_fun_real_bool (tptp.aa_fun3382945097342017788l_bool (tptp.aTP_Lamm_cu A2) R) X3)))))))))) (forall ((A2 tptp.set_real) (B3 tptp.set_int) (R tptp.fun_re8661203372455305201t_bool)) (=> (not (tptp.finite_finite_real A2)) (=> (tptp.finite_finite_int B3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (exists ((Xa tptp.int)) (and (tptp.member_int Xa B3) (tptp.pp (tptp.aa_int_bool (tptp.aa_real_fun_int_bool R X3) Xa)))))) (exists ((X3 tptp.int)) (and (tptp.member_int X3 B3) (not (tptp.finite_finite_real (tptp.collect_real (tptp.aa_int_fun_real_bool (tptp.aa_fun1536421850685375484l_bool (tptp.aTP_Lamm_cv A2) R) X3)))))))))) (forall ((A2 tptp.set_real) (B3 tptp.set_complex) (R tptp.fun_re3010880487650781423x_bool)) (=> (not (tptp.finite_finite_real A2)) (=> (tptp.finite3207457112153483333omplex B3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (exists ((Xa tptp.complex)) (and (tptp.member_complex Xa B3) (tptp.pp (tptp.aa_complex_bool (tptp.aa_rea5887071448072802392x_bool R X3) Xa)))))) (exists ((X3 tptp.complex)) (and (tptp.member_complex X3 B3) (not (tptp.finite_finite_real (tptp.collect_real (tptp.aa_com8943241093633526360l_bool (tptp.aa_fun8455611678790336124l_bool (tptp.aTP_Lamm_cw A2) R) X3)))))))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (R tptp.fun_nat_fun_nat_bool)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X3) Xa)))))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3051233943552222972t_bool (tptp.aTP_Lamm_cx A2) R) X3))))))))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_int) (R tptp.fun_nat_fun_int_bool)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2))) (=> (tptp.finite_finite_int B3) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (exists ((Xa tptp.int)) (and (tptp.member_int Xa B3) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool R X3) Xa)))))) (exists ((X3 tptp.int)) (and (tptp.member_int X3 B3) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun8184653438340336124t_bool (tptp.aTP_Lamm_cy A2) R) X3))))))))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_complex) (R tptp.fun_na5941084329111710283x_bool)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2))) (=> (tptp.finite3207457112153483333omplex B3) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (exists ((Xa tptp.complex)) (and (tptp.member_complex Xa B3) (tptp.pp (tptp.aa_complex_bool (tptp.aa_nat5545486172511849908x_bool R X3) Xa)))))) (exists ((X3 tptp.complex)) (and (tptp.member_complex X3 B3) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_com5335841084339320244t_bool (tptp.aa_fun8674784841953735804t_bool (tptp.aTP_Lamm_cz A2) R) X3))))))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_nat) (R tptp.fun_int_fun_nat_bool)) (=> (not (tptp.finite_finite_int A2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool R X3) Xa)))))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (not (tptp.finite_finite_int (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun3035398748895483388t_bool (tptp.aTP_Lamm_da A2) R) X3)))))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (R tptp.fun_int_fun_int_bool)) (=> (not (tptp.finite_finite_int A2)) (=> (tptp.finite_finite_int B3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (exists ((Xa tptp.int)) (and (tptp.member_int Xa B3) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R X3) Xa)))))) (exists ((X3 tptp.int)) (and (tptp.member_int X3 B3) (not (tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_db A2) R) X3)))))))))) (forall ((A2 tptp.set_int) (B3 tptp.set_complex) (R tptp.fun_in5750378413879446255x_bool)) (=> (not (tptp.finite_finite_int A2)) (=> (tptp.finite3207457112153483333omplex B3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (exists ((Xa tptp.complex)) (and (tptp.member_complex Xa B3) (tptp.pp (tptp.aa_complex_bool (tptp.aa_int5354780257279585880x_bool R X3) Xa)))))) (exists ((X3 tptp.complex)) (and (tptp.member_complex X3 B3) (not (tptp.finite_finite_int (tptp.collect_int (tptp.aa_com2211550117870696024t_bool (tptp.aa_fun3087709329828230012t_bool (tptp.aTP_Lamm_dc A2) R) X3)))))))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_nat) (R tptp.fun_co2841405903858895691t_bool)) (=> (not (tptp.finite3207457112153483333omplex A2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) B3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_com5335841084339320244t_bool R X3) Xa)))))) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (not (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aa_fun5091585579174883964x_bool (tptp.aTP_Lamm_dd A2) R) X3)))))))))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (tptp.finite_finite_real A2) (=> (tptp.member_real A A2) (exists ((X3 tptp.real)) (and (tptp.member_real X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) A)) (forall ((Xa tptp.real)) (=> (tptp.member_real Xa A2) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (tptp.finite1152437895449049373et_nat A2) (=> (tptp.member_set_nat A A2) (exists ((X3 tptp.set_nat)) (and (tptp.member_set_nat X3 A2) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat X3) A)) (forall ((Xa tptp.set_nat)) (=> (tptp.member_set_nat Xa A2) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (tptp.finite6197958912794628473et_int A2) (=> (tptp.member_set_int A A2) (exists ((X3 tptp.set_int)) (and (tptp.member_set_int X3 A2) (tptp.ord_less_eq_set_int X3 A) (forall ((Xa tptp.set_int)) (=> (tptp.member_set_int Xa A2) (=> (tptp.ord_less_eq_set_int Xa X3) (= X3 Xa))))))))) (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (tptp.finite_finite_rat A2) (=> (tptp.member_rat A A2) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) A)) (forall ((Xa tptp.rat)) (=> (tptp.member_rat Xa A2) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_num) (A tptp.num)) (=> (tptp.finite_finite_num A2) (=> (tptp.member_num A A2) (exists ((X3 tptp.num)) (and (tptp.member_num X3 A2) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) A)) (forall ((Xa tptp.num)) (=> (tptp.member_num Xa A2) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) A2)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) A)) (forall ((Xa tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) A2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (tptp.finite_finite_int A2) (=> (tptp.member_int A A2) (exists ((X3 tptp.int)) (and (tptp.member_int X3 A2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) A)) (forall ((Xa tptp.int)) (=> (tptp.member_int Xa A2) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_real) (A tptp.real)) (=> (tptp.finite_finite_real A2) (=> (tptp.member_real A A2) (exists ((X3 tptp.real)) (and (tptp.member_real X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (forall ((Xa tptp.real)) (=> (tptp.member_real Xa A2) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (tptp.finite1152437895449049373et_nat A2) (=> (tptp.member_set_nat A A2) (exists ((X3 tptp.set_nat)) (and (tptp.member_set_nat X3 A2) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A) X3)) (forall ((Xa tptp.set_nat)) (=> (tptp.member_set_nat Xa A2) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (tptp.finite6197958912794628473et_int A2) (=> (tptp.member_set_int A A2) (exists ((X3 tptp.set_int)) (and (tptp.member_set_int X3 A2) (tptp.ord_less_eq_set_int A X3) (forall ((Xa tptp.set_int)) (=> (tptp.member_set_int Xa A2) (=> (tptp.ord_less_eq_set_int X3 Xa) (= X3 Xa))))))))) (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (tptp.finite_finite_rat A2) (=> (tptp.member_rat A A2) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) X3)) (forall ((Xa tptp.rat)) (=> (tptp.member_rat Xa A2) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_num) (A tptp.num)) (=> (tptp.finite_finite_num A2) (=> (tptp.member_num A A2) (exists ((X3 tptp.num)) (and (tptp.member_num X3 A2) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num A) X3)) (forall ((Xa tptp.num)) (=> (tptp.member_num Xa A2) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) A2)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat A) X3)) (forall ((Xa tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) A2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_int) (A tptp.int)) (=> (tptp.finite_finite_int A2) (=> (tptp.member_int A A2) (exists ((X3 tptp.int)) (and (tptp.member_int X3 A2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) X3)) (forall ((Xa tptp.int)) (=> (tptp.member_int Xa A2) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (tptp.finite3207457112153483333omplex B3) (tptp.finite3207457112153483333omplex A2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (=> (tptp.finite_finite_int B3) (tptp.finite_finite_int A2)))) (forall ((S3 tptp.set_nat) (T3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) T3)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)))))) (forall ((S3 tptp.set_complex) (T3 tptp.set_complex)) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (not (tptp.finite3207457112153483333omplex S3)) (not (tptp.finite3207457112153483333omplex T3))))) (forall ((S3 tptp.set_int) (T3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int S3 T3) (=> (not (tptp.finite_finite_int S3)) (not (tptp.finite_finite_int T3))))) (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex A2 B3) (tptp.finite3207457112153483333omplex A2)))) (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (tptp.finite_finite_int B3) (=> (tptp.ord_less_eq_set_int A2 B3) (tptp.finite_finite_int A2)))) (forall ((T3 tptp.set_int) (S3 tptp.set_int)) (=> (tptp.finite_finite_int T3) (=> (not (tptp.finite_finite_int S3)) (not (tptp.finite_finite_int (tptp.minus_minus_set_int S3 T3)))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex)) (=> (tptp.finite3207457112153483333omplex T3) (=> (not (tptp.finite3207457112153483333omplex S3)) (not (tptp.finite3207457112153483333omplex (tptp.minus_811609699411566653omplex S3 T3)))))) (forall ((T3 tptp.set_nat) (S3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.minus_minus_set_nat S3 T3))))))) (forall ((A2 tptp.set_real)) (=> (tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (tptp.member_real X3 A2) (forall ((Xa tptp.real)) (=> (tptp.member_real Xa A2) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_int)) (=> (tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (tptp.member_set_int X3 A2) (forall ((Xa tptp.set_int)) (=> (tptp.member_set_int Xa A2) (=> (tptp.ord_less_eq_set_int X3 Xa) (= X3 Xa))))))))) (forall ((A2 tptp.set_rat)) (=> (tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 A2) (forall ((Xa tptp.rat)) (=> (tptp.member_rat Xa A2) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_num)) (=> (tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (tptp.member_num X3 A2) (forall ((Xa tptp.num)) (=> (tptp.member_num Xa A2) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (forall ((Xa tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) A2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_int)) (=> (tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (tptp.member_int X3 A2) (forall ((Xa tptp.int)) (=> (tptp.member_int Xa A2) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X3) Xa)) (= X3 Xa))))))))) (forall ((A2 tptp.set_real)) (=> (tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (tptp.member_real X3 A2) (forall ((Xa tptp.real)) (=> (tptp.member_real Xa A2) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_set_int)) (=> (tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X3 tptp.set_int)) (and (tptp.member_set_int X3 A2) (forall ((Xa tptp.set_int)) (=> (tptp.member_set_int Xa A2) (=> (tptp.ord_less_eq_set_int Xa X3) (= X3 Xa))))))))) (forall ((A2 tptp.set_rat)) (=> (tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 A2) (forall ((Xa tptp.rat)) (=> (tptp.member_rat Xa A2) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_num)) (=> (tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (tptp.member_num X3 A2) (forall ((Xa tptp.num)) (=> (tptp.member_num Xa A2) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (forall ((Xa tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) A2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa) X3)) (= X3 Xa))))))))) (forall ((A2 tptp.set_int)) (=> (tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (tptp.member_int X3 A2) (forall ((Xa tptp.int)) (=> (tptp.member_int Xa A2) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa) X3)) (= X3 Xa))))))))) (= (tptp.aa_real_real tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real) (forall ((N2 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) N2)) (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_de N2) C))))) (forall ((I6 tptp.set_real) (X tptp.fun_real_complex) (Y tptp.fun_real_complex)) (let ((_let_1 (tptp.aTP_Lamm_df I6))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool (tptp.aa_fun5520078544946397361l_bool (tptp.aTP_Lamm_dg I6) X) Y))))))) (forall ((I6 tptp.set_nat) (X tptp.fun_nat_complex) (Y tptp.fun_nat_complex)) (let ((_let_1 (tptp.aTP_Lamm_dh I6))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool (tptp.aa_fun5430245816583273541t_bool (tptp.aTP_Lamm_di I6) X) Y)))))))) (forall ((I6 tptp.set_int) (X tptp.fun_int_complex) (Y tptp.fun_int_complex)) (let ((_let_1 (tptp.aTP_Lamm_dj I6))) (=> (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool _let_1 X))) (=> (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool _let_1 Y))) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool (tptp.aa_fun3850298374753145905t_bool (tptp.aTP_Lamm_dk I6) X) Y))))))) (forall ((I6 tptp.set_complex) (X tptp.fun_complex_complex) (Y tptp.fun_complex_complex)) (let ((_let_1 (tptp.aTP_Lamm_dl I6))) (=> (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool _let_1 X))) (=> (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool _let_1 Y))) (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool (tptp.aa_fun6641798613628721963x_bool (tptp.aTP_Lamm_dm I6) X) Y))))))) (forall ((I6 tptp.set_real) (X tptp.fun_real_real) (Y tptp.fun_real_real)) (let ((_let_1 (tptp.aTP_Lamm_dn I6))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool (tptp.aa_fun334843040499603765l_bool (tptp.aTP_Lamm_do I6) X) Y))))))) (forall ((I6 tptp.set_nat) (X tptp.fun_nat_real) (Y tptp.fun_nat_real)) (let ((_let_1 (tptp.aTP_Lamm_dp I6))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool (tptp.aa_fun849216055071118793t_bool (tptp.aTP_Lamm_dq I6) X) Y)))))))) (forall ((I6 tptp.set_int) (X tptp.fun_int_real) (Y tptp.fun_int_real)) (let ((_let_1 (tptp.aTP_Lamm_dr I6))) (=> (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool _let_1 X))) (=> (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool _let_1 Y))) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool (tptp.aa_fun6205147705862377397t_bool (tptp.aTP_Lamm_ds I6) X) Y))))))) (forall ((I6 tptp.set_complex) (X tptp.fun_complex_real) (Y tptp.fun_complex_real)) (let ((_let_1 (tptp.aTP_Lamm_dt I6))) (=> (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool _let_1 X))) (=> (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool _let_1 Y))) (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool (tptp.aa_fun2094807616088678831x_bool (tptp.aTP_Lamm_du I6) X) Y))))))) (forall ((I6 tptp.set_real) (X tptp.fun_real_rat) (Y tptp.fun_real_rat)) (let ((_let_1 (tptp.aTP_Lamm_dv I6))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool (tptp.aa_fun8530242357055030877l_bool (tptp.aTP_Lamm_dw I6) X) Y))))))) (forall ((I6 tptp.set_nat) (X tptp.fun_nat_rat) (Y tptp.fun_nat_rat)) (let ((_let_1 (tptp.aTP_Lamm_dx I6))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_dy I6) X) Y)))))))) (forall ((I6 tptp.set_real) (X tptp.fun_real_complex) (Y tptp.fun_real_complex)) (let ((_let_1 (tptp.aTP_Lamm_dz I6))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun3813300650643916655l_bool (tptp.aa_fun5520078544946397361l_bool (tptp.aTP_Lamm_ea I6) X) Y))))))) (forall ((I6 tptp.set_nat) (X tptp.fun_nat_complex) (Y tptp.fun_nat_complex)) (let ((_let_1 (tptp.aTP_Lamm_eb I6))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun8004580481347240231t_bool (tptp.aa_fun5430245816583273541t_bool (tptp.aTP_Lamm_ec I6) X) Y)))))))) (forall ((I6 tptp.set_int) (X tptp.fun_int_complex) (Y tptp.fun_int_complex)) (let ((_let_1 (tptp.aTP_Lamm_ed I6))) (=> (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool _let_1 X))) (=> (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool _let_1 Y))) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun8146511558608327279t_bool (tptp.aa_fun3850298374753145905t_bool (tptp.aTP_Lamm_ee I6) X) Y))))))) (forall ((I6 tptp.set_complex) (X tptp.fun_complex_complex) (Y tptp.fun_complex_complex)) (let ((_let_1 (tptp.aTP_Lamm_ef I6))) (=> (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool _let_1 X))) (=> (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool _let_1 Y))) (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun9073502203726719595x_bool (tptp.aa_fun6641798613628721963x_bool (tptp.aTP_Lamm_eg I6) X) Y))))))) (forall ((I6 tptp.set_real) (X tptp.fun_real_real) (Y tptp.fun_real_real)) (let ((_let_1 (tptp.aTP_Lamm_eh I6))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun9137271176455094897l_bool (tptp.aa_fun334843040499603765l_bool (tptp.aTP_Lamm_ei I6) X) Y))))))) (forall ((I6 tptp.set_nat) (X tptp.fun_nat_real) (Y tptp.fun_nat_real)) (let ((_let_1 (tptp.aTP_Lamm_ej I6))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun1349230436907296553t_bool (tptp.aa_fun849216055071118793t_bool (tptp.aTP_Lamm_ek I6) X) Y)))))))) (forall ((I6 tptp.set_int) (X tptp.fun_int_real) (Y tptp.fun_int_real)) (let ((_let_1 (tptp.aTP_Lamm_el I6))) (=> (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool _let_1 X))) (=> (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool _let_1 Y))) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_fun1262781554902806129t_bool (tptp.aa_fun6205147705862377397t_bool (tptp.aTP_Lamm_em I6) X) Y))))))) (forall ((I6 tptp.set_complex) (X tptp.fun_complex_real) (Y tptp.fun_complex_real)) (let ((_let_1 (tptp.aTP_Lamm_en I6))) (=> (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool _let_1 X))) (=> (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool _let_1 Y))) (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_fun2898354424061222765x_bool (tptp.aa_fun2094807616088678831x_bool (tptp.aTP_Lamm_eo I6) X) Y))))))) (forall ((I6 tptp.set_real) (X tptp.fun_real_rat) (Y tptp.fun_real_rat)) (let ((_let_1 (tptp.aTP_Lamm_ep I6))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool _let_1 X))) (=> (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool _let_1 Y))) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_fun8987621170725249221l_bool (tptp.aa_fun8530242357055030877l_bool (tptp.aTP_Lamm_eq I6) X) Y))))))) (forall ((I6 tptp.set_nat) (X tptp.fun_nat_rat) (Y tptp.fun_nat_rat)) (let ((_let_1 (tptp.aTP_Lamm_er I6))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 X)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool _let_1 Y)))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_es I6) X) Y)))))))) (forall ((P tptp.fun_nat_fun_nat_bool) (M tptp.nat) (N2 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) (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 P N) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M2) N))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M2) N))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P M) N2))))) (forall ((N2 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.aa_int_fun_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat tptp.suc N2)) 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.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.aa_int_fun_int_int (tptp.bit_concat_bit N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) L)))))) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) _let_46) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real tptp.one_one_real) _let_23) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat tptp.one_one_rat) _let_65) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int tptp.one_one_int) _let_40) (forall ((A tptp.nat) (N2 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) N2))) (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) N2)) (= (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) (N2 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.aa_int_fun_nat_int tptp.power_power_int _let_1) N2))) (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) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int _let_3 A)) _let_2) (tptp.aa_int_int _let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_2))))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2))) (=> (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) N2)) (= (tptp.modulo364778990260209775nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer A) _let_2) (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer (tptp.modulo364778990260209775nteger A _let_2)))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2))) (=> (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) N2)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer A) _let_2) (tptp.divide6298287555418463151nteger A _let_2))))))) (forall ((A tptp.nat) (N2 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) N2))) (=> (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) N2)) (= (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) (N2 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.aa_int_fun_nat_int tptp.power_power_int _let_1) N2))) (=> (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) N2)) (= (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 ((M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) tptp.one_one_nat)) (= M tptp.one_one_nat))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex tptp.zero_zero_complex) A)) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real tptp.zero_zero_real) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat tptp.zero_zero_rat) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (= A tptp.zero_zero_nat))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int tptp.zero_zero_int) A)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) tptp.zero_zero_complex))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) tptp.zero_zero_real))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) tptp.zero_zero_rat))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.zero_zero_nat))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A))) (tptp.pp (tptp.aa_real_bool _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat B) A))) (tptp.pp (tptp.aa_rat_bool _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) A))) (tptp.pp (tptp.aa_nat_bool _let_1 B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) A))) (tptp.pp (tptp.aa_int_bool _let_1 B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))) (tptp.pp (tptp.aa_real_bool _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat A) B))) (tptp.pp (tptp.aa_rat_bool _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))) (tptp.pp (tptp.aa_nat_bool _let_1 B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))) (tptp.pp (tptp.aa_int_bool _let_1 B))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) _let_1)) (= M _let_1)))) (forall ((K tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) K))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger B A)) (tptp.divide6298287555418463151nteger C A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) A))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (or (= K tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger _let_1 A)) (tptp.aa_Cod1783974652533396728nteger _let_1 B))) (or (= C tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C))) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_complex_complex _let_1 A)) (tptp.aa_complex_complex _let_1 B))) (or (= C tptp.zero_zero_complex) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) B)))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B))) (or (= C tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.times_times_rat C))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat _let_1 A)) (tptp.aa_rat_rat _let_1 B))) (or (= C tptp.zero_zero_rat) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A) B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int C))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B))) (or (= C tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (or (= C tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) C))) (or (= C tptp.zero_zero_complex) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) B))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) C))) (or (= C tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A) B))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_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) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A)))) (tptp.pp (tptp.aa_real_bool _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat B) (tptp.aa_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.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.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat C) A)) B))) (tptp.pp (tptp.aa_rat_bool _let_1 B))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)) B))) (tptp.pp (tptp.aa_nat_bool _let_1 B))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)) B))) (tptp.pp (tptp.aa_int_bool _let_1 B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (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 A) (tptp.divide6298287555418463151nteger B A)) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A)) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger B A)) A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)) A) B))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B) C) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A)) A))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat _let_1 A)) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_1 A)) A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A)) tptp.one_one_Code_integer)))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat)))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger A B)) tptp.one_one_Code_integer))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) tptp.one_one_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) tptp.one_one_int))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (= (tptp.divide6298287555418463151nteger (tptp.minus_8373710615458151222nteger A B) C) (tptp.minus_8373710615458151222nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))))) (forall ((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.aa_int_int (tptp.aa_int_fun_int_int 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 ((N2 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.aa_int_fun_int_int (tptp.bit_concat_bit N2) K) L))) (tptp.pp (tptp.aa_int_bool _let_1 L))))) (forall ((N2 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.aa_int_fun_int_int (tptp.bit_concat_bit N2) 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 ((K tptp.num)) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex (tptp.numera6690914467698888265omplex K)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real (tptp.aa_num_real tptp.numeral_numeral_real K)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num)) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (forall ((N2 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 N2)))) (tptp.pp (tptp.aa_nat_bool _let_1 N2))))) (forall ((N2 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 N2))) (not (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger B A)) A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)) A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A)) (tptp.divide6298287555418463151nteger B A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A)))) (forall ((N2 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) N2)) (= (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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B))))) (forall ((N2 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) N2)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2))) (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)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B))) (or (tptp.pp (tptp.aa_nat_bool _let_1 A)) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B))) (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A 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.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A 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.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))) (tptp.pp (tptp.aa_nat_bool _let_2 A)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (= (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1))) (tptp.pp (tptp.aa_int_bool _let_2 A)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_2 (tptp.modulo364778990260209775nteger A _let_1))) (tptp.pp (tptp.aa_Code_integer_bool _let_2 A)))))) (forall ((N2 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) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc N2)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1))))) (forall ((N2 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) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc N2)) _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_1)))))) (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.aa_int_fun_nat_int tptp.power_power_int A) _let_2))) (or _let_3 (and (not _let_3) (tptp.pp (tptp.aa_int_bool _let_1 A))))))))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)) tptp.zero_zero_real)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat)) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))))) (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_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) (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 A) N2)) 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))) N2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) tptp.zero_zero_real))))) (forall ((A tptp.rat) (N2 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) N2)) 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))) N2))) (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) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) 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))) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) tptp.zero_zero_int))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat))) (not (tptp.pp (tptp.aa_nat_bool _let_1 A)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int))) (not (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger A B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)))))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) N2))) (forall ((M tptp.nat) (N2 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) N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))))))) (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.aa_int_fun_nat_int tptp.power_power_int A) _let_2))) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (tptp.pp (tptp.aa_int_bool _let_1 A))))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A tptp.one_one_Code_integer) _let_1) (tptp.divide6298287555418463151nteger A _let_1))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A tptp.one_one_Code_integer) _let_1) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A _let_1) tptp.one_one_Code_integer))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (= (tptp.aa_int_int (tptp.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.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer A) _let_1) (tptp.divide6298287555418463151nteger A _let_1))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.aa_int_int (tptp.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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))) (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) N2)))))) (forall ((A tptp.nat) (N2 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) N2))) (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) N2)))))) (forall ((A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int A) N2))) (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) N2)))))) (forall ((N2 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) N2))) (= (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 N2) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.divide6298287555418463151nteger A _let_1)) tptp.one_one_Code_integer) A)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) _let_1)) tptp.zero_zero_real)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real))) (and _let_2 (= A tptp.zero_zero_real)))))))) (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) _let_1)) (or (and (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat))) (and _let_2 (= A tptp.zero_zero_rat)))))))) (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_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 ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2) tptp.one_one_Code_integer))) (= N2 tptp.zero_zero_nat)))) (forall ((N2 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) N2)) tptp.one_one_nat))) (= N2 tptp.zero_zero_nat)))) (forall ((N2 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.aa_int_fun_nat_int tptp.power_power_int _let_1) N2)) tptp.one_one_int))) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) C)) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) C)) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) A))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) A))) (forall ((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 ((B6 tptp.nat) (C5 tptp.nat)) (and (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B6) C5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B6) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C5) 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 ((B6 tptp.int) (C5 tptp.int)) (and (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B6) C5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B6) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C5) 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) (Y4 tptp.nat)) (=> (= P2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X3) Y4)) (=> (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 Y4) 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) (Y4 tptp.int)) (=> (= P2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X3) Y4)) (=> (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 Y4) B))))))))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex tptp.zero_zero_complex) A)) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real tptp.zero_zero_real) A)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat tptp.zero_zero_rat) A)) (= A tptp.zero_zero_rat))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) A)) (= A tptp.zero_zero_nat))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int tptp.zero_zero_int) A)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer) (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.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.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.times_times_rat A) C)) (tptp.aa_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.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.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.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.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 ((K3 tptp.code_integer)) (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) K3))))) (forall ((B tptp.real) (A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B) A)) (exists ((K3 tptp.real)) (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) K3))))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (exists ((K3 tptp.rat)) (= A (tptp.aa_rat_rat (tptp.times_times_rat B) K3))))) (forall ((B tptp.nat) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (exists ((K3 tptp.nat)) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) K3))))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (exists ((K3 tptp.int)) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) K3))))) (forall ((A tptp.code_integer) (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.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 ((K2 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) K2))))))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B) A)) (not (forall ((K2 tptp.real)) (not (= A (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) K2))))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (not (forall ((K2 tptp.rat)) (not (= A (tptp.aa_rat_rat (tptp.times_times_rat B) K2))))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (not (forall ((K2 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) K2))))))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (not (forall ((K2 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) K2))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B C))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))) (tptp.pp (tptp.aa_real_bool _let_1 C)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat B) C))) (tptp.pp (tptp.aa_rat_bool _let_1 C)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B C))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))) (tptp.pp (tptp.aa_real_bool _let_1 B)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat B) C))) (tptp.pp (tptp.aa_rat_bool _let_1 B)))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 C)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) C))) (tptp.pp (tptp.aa_nat_bool _let_1 B)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool _let_1 C)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) C))) (tptp.pp (tptp.aa_int_bool _let_1 B)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger B C))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real A))) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) C))))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat A))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 C)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.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)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A))) (forall ((A tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex tptp.one_one_complex) A))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real tptp.one_one_real) A))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat tptp.one_one_rat) A))) (forall ((A tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat tptp.one_one_nat) A))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int tptp.one_one_int) A))) (forall ((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) (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 ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 Z)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger Y Z))))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X))) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Z)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z))))))) (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 Z)) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat Y) Z))))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X))) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Z)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Y) Z))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger C B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.minus_8373710615458151222nteger B C)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int C) B))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) C)))))) (forall ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A D) (tptp.divide6298287555418463151nteger B D)) (tptp.divide6298287555418463151nteger A B))))) (forall ((D tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 D)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) D)) (tptp.aa_nat_nat _let_1 B)))))) (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) D)) (tptp.aa_int_int _let_1 B)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (= (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (= A B)))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex C))) (=> (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) C) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 A)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 B)) (= A B)))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real C))) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (= A B)))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat C))) (=> (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) C) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (= A B)))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (= A B)))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= A B)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C))) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (=> (tptp.pp (tptp.aa_Code_integer_bool _let_1 B)) (= (= (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C)) (= A B)))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex C))) (=> (tptp.pp (tptp.aa_complex_bool _let_1 A)) (=> (tptp.pp (tptp.aa_complex_bool _let_1 B)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) C) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) (= A B)))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real C))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) (= A B)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat C))) (=> (tptp.pp (tptp.aa_rat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 B)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) C) (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (= A B)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 A)) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (= A B)))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C))) (=> (tptp.pp (tptp.aa_int_bool _let_1 A)) (=> (tptp.pp (tptp.aa_int_bool _let_1 B)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (= A B)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) N2))))) (forall ((X tptp.nat) (Y tptp.nat) (N2 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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) N2))))) (forall ((X tptp.real) (Y tptp.real) (N2 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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N2))))) (forall ((X tptp.int) (Y tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int X) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) N2))))) (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X) Y)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Y) N2))))) (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)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A))) (=> (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.modulo_modulo_int (tptp.aa_int_int _let_1 B)) C) (tptp.aa_int_int _let_1 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 ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2))))))) (forall ((K tptp.int) (M tptp.int) (N2 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 N2)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int M) N2))))))) (forall ((K tptp.code_integer) (M tptp.code_integer) (N2 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 N2)) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.modulo364778990260209775nteger M N2))))))) (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.aa_int_int (tptp.aa_int_fun_int_int 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.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.aa_int_int (tptp.aa_int_fun_int_int 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 ((K tptp.nat) (M tptp.nat) (N2 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 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))))) (forall ((K tptp.int) (M tptp.int) (N2 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) N2))) (=> (tptp.pp (tptp.aa_int_bool _let_1 N2)) (tptp.pp (tptp.aa_int_bool _let_1 M)))))) (forall ((N2 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 N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)) (tptp.pp (tptp.aa_nat_bool _let_1 M)))))) (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) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) 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 Y4)) 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 Y4)) D)))))))))))))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D3))) (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 Y4)) D3)) (= (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 Y4)) D3))))))))) (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D3))) (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 Y4)) D3) (= (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 Y4)) D3)))))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.ord_le211207098394363844omplex (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_et A)) (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_et B))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_eu A))) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_eu B)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.ord_le7084787975880047091nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_ev A)) (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_ev B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.ord_less_eq_set_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ew A)) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ew B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)))) (forall ((N2 tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int (tptp.bit_concat_bit N2) K))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit M) L) R2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_int_int _let_1 L)) R2)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.ord_less_set_complex (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_et A)) (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_et B))) (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex A) B)) (not (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex B) A)))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_eu A))) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_eu B)))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (not (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.ord_less_set_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ew A)) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ew B))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (not (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.ord_le1307284697595431911nteger (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_ev A)) (tptp.collect_Code_integer (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_ev B))) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)))))) (forall ((I2 tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (tptp.finite_finite_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ew I2))))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int))) (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) (tptp.plus_p5714425477246183910nteger X2 S2))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 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 X2) S2))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 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.plus_plus_rat X2) S2))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 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 X2) S2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 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 X2) S2))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) (tptp.plus_p5714425477246183910nteger X2 S2)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 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 X2) S2)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 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.plus_plus_rat X2) S2)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 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 X2) S2)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 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 X2) S2)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Z3) X2)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) (tptp.plus_p5714425477246183910nteger X2 S2))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X2) Z3)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 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 X2) S2))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) Z3)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 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.plus_plus_rat X2) S2))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) Z3)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 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 X2) S2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Z3)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 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 X2) S2))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) Z3)) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S2 tptp.code_integer)) (exists ((Z3 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) (tptp.plus_p5714425477246183910nteger X2 S2)))))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X2) Z3)) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S2 tptp.real)) (exists ((Z3 tptp.real)) (forall ((X2 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 X2) S2)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) Z3)) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S2 tptp.rat)) (exists ((Z3 tptp.rat)) (forall ((X2 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.plus_plus_rat X2) S2)))))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) Z3)) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S2 tptp.nat)) (exists ((Z3 tptp.nat)) (forall ((X2 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 X2) S2)))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Z3)) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S2 tptp.int)) (exists ((Z3 tptp.int)) (forall ((X2 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 X2) S2)))))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) Z3)) (= _let_1 _let_1)))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (= (tptp.divide6298287555418463151nteger A B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex B) A)) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real B) A)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((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 ((B tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) (tptp.divide6298287555418463151nteger C D)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) D)))))) (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) D)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) D)))))) (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) D)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.divide6298287555418463151nteger B C))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) B)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.divide6298287555418463151nteger A _let_1) (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A B) C))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) A)) (= (tptp.aa_nat_nat _let_1 _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_2) A)) (= (tptp.aa_int_int _let_1 _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.divide6298287555418463151nteger A (tptp.divide6298287555418463151nteger B C)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) C))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger B C)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B) C))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger B C)) A) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A) C)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) C)))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) C)))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B) C) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) A)) (= (tptp.divide6298287555418463151nteger (tptp.plus_p5714425477246183910nteger A B) C) (tptp.plus_p5714425477246183910nteger (tptp.divide6298287555418463151nteger A C) (tptp.divide6298287555418463151nteger B C))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.divide6298287555418463151nteger C B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) B))) (tptp.pp (tptp.aa_nat_bool _let_1 C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) B))) (tptp.pp (tptp.aa_int_bool _let_1 C)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger A B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) C))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) C))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (= (= (tptp.divide6298287555418463151nteger B A) (tptp.divide6298287555418463151nteger C A)) (= B C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) A)) (= B C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) A)) (= B C)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.divide6298287555418463151nteger A B)) N2) (tptp.divide6298287555418463151nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2))))) (forall ((B tptp.nat) (A tptp.nat) (N2 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)) N2) (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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) N2))))) (forall ((B tptp.int) (A tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2))))) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.modulo364778990260209775nteger A B) tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) A) tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (tptp.modulo364778990260209775nteger B A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.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.aa_int_int (tptp.aa_int_fun_int_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 ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2)))))) (forall ((M tptp.nat) (N2 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) N2)) (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 N2)))))) (forall ((M tptp.nat) (N2 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) N2)) (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 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (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 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 N2)) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 M)) B)))))) (forall ((A tptp.nat) (N2 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 N2)) B)) (=> (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 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat _let_1 M)) B)))))) (forall ((A tptp.real) (N2 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 N2)) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (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) (N2 tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2)) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (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) (N2 tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A))) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex _let_1 N2)) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex _let_1 M)) B)))))) (forall ((X tptp.code_integer) (Y tptp.code_integer) (N2 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 N2) M)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) M)))))) (forall ((X tptp.nat) (Y tptp.nat) (N2 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 N2) 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) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Y) M)))))) (forall ((X tptp.real) (Y tptp.real) (N2 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 N2) 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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) M)))))) (forall ((X tptp.int) (Y tptp.int) (N2 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 N2) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) M)))))) (forall ((X tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X) Y)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Y) M)))))) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) (tptp.minus_8373710615458151222nteger A (tptp.modulo364778990260209775nteger A B))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int B) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.modulo364778990260209775nteger A C) (tptp.modulo364778990260209775nteger B C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) (tptp.minus_8373710615458151222nteger A B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X3 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D3))) (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) Y4)) D3))))))) (forall ((M 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) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N2) M)))))) (forall ((M tptp.nat) (N2 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 N2) M))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2)))))) (forall ((M tptp.int) (N2 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 N2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) N2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int N2) M)) (= M N2))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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) N2))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_nat_bool _let_1 M))))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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) N2))) (=> (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 N2) M)) (tptp.pp (tptp.aa_nat_bool _let_1 N2))))))) (forall ((M tptp.nat) (N2 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) N2)) (= (tptp.pp (tptp.aa_nat_bool _let_1 N2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))) (forall ((K tptp.int) (M tptp.int) (N2 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 N2))) (=> (not (= K tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) N2)))))) (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 ((X tptp.real)) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) X))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat X) (tptp.aa_rat_rat (tptp.plus_plus_rat X) X))) (forall ((X tptp.int)) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) X))) (forall ((K tptp.int) (N2 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 N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) M)))) (tptp.pp (tptp.aa_int_bool _let_1 N2))))) (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 ((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_eu M)))))) (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 ((P tptp.fun_Co8822979462182099027r_bool) (L tptp.code_integer)) (= (exists ((X4 tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool P (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger L) X4)))) (exists ((X4 tptp.code_integer)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer L) (tptp.plus_p5714425477246183910nteger X4 tptp.zero_z3403309356797280102nteger))) (tptp.pp (tptp.aa_Code_integer_bool P X4)))))) (forall ((P tptp.fun_complex_bool) (L tptp.complex)) (= (exists ((X4 tptp.complex)) (tptp.pp (tptp.aa_complex_bool P (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex L) X4)))) (exists ((X4 tptp.complex)) (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex L) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X4) tptp.zero_zero_complex))) (tptp.pp (tptp.aa_complex_bool P X4)))))) (forall ((P tptp.fun_real_bool) (L tptp.real)) (= (exists ((X4 tptp.real)) (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real L) X4)))) (exists ((X4 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 X4) tptp.zero_zero_real))) (tptp.pp (tptp.aa_real_bool P X4)))))) (forall ((P tptp.fun_rat_bool) (L tptp.rat)) (= (exists ((X4 tptp.rat)) (tptp.pp (tptp.aa_rat_bool P (tptp.aa_rat_rat (tptp.times_times_rat L) X4)))) (exists ((X4 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.plus_plus_rat X4) tptp.zero_zero_rat))) (tptp.pp (tptp.aa_rat_bool P X4)))))) (forall ((P tptp.fun_nat_bool) (L tptp.nat)) (= (exists ((X4 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat L) X4)))) (exists ((X4 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 X4) tptp.zero_zero_nat))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((P tptp.fun_int_bool) (L tptp.int)) (= (exists ((X4 tptp.int)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) X4)))) (exists ((X4 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 X4) tptp.zero_zero_int))) (tptp.pp (tptp.aa_int_bool P X4)))))) (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 ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) D)) (= (= (tptp.divide6298287555418463151nteger B A) (tptp.divide6298287555418463151nteger D C)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) D)))))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) D)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat D) C)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) D)))))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) D)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int D) C)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D)))))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) B)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.divide6298287555418463151nteger B C))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C)) B)))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) B)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) B)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) B)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.divide6298287555418463151nteger A B)) C)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) C)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B))))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) C)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) B)) (= (= (tptp.divide6298287555418463151nteger B A) C) (= B (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) A)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) B)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) A) C) (= B (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) A)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) B)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) A) C) (= B (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) A)))))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N2))))) (forall ((N2 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 N2))))) (forall ((N2 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 N2))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (= (tptp.divide6298287555418463151nteger A B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((D tptp.code_integer) (D2 tptp.code_integer) (T tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) D2)) (forall ((X2 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger X2 T))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger X2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D2)) T)))))))) (forall ((D tptp.real) (D2 tptp.real) (T tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) D2)) (forall ((X2 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 X2) 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 X2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D2))) T)))))))) (forall ((D tptp.rat) (D2 tptp.rat) (T tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) D2)) (forall ((X2 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.plus_plus_rat X2) T))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X2) (tptp.aa_rat_rat (tptp.times_times_rat K4) D2))) T)))))))) (forall ((D tptp.int) (D2 tptp.int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D2)) (forall ((X2 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 X2) 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 X2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D2))) T)))))))) (forall ((D tptp.code_integer) (D2 tptp.code_integer) (T tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D) D2)) (forall ((X2 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer D))) (= (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger X2 T)))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger X2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger K4) D2)) T))))))))) (forall ((D tptp.real) (D2 tptp.real) (T tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real D) D2)) (forall ((X2 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 X2) 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 X2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real K4) D2))) T))))))))) (forall ((D tptp.rat) (D2 tptp.rat) (T tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat D) D2)) (forall ((X2 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.plus_plus_rat X2) T)))) (not (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X2) (tptp.aa_rat_rat (tptp.times_times_rat K4) D2))) T))))))))) (forall ((D tptp.int) (D2 tptp.int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D2)) (forall ((X2 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 X2) 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 X2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K4) D2))) T))))))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A B) C))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) tptp.one_one_nat)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) tptp.one_one_int)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.divide6298287555418463151nteger B C)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger _let_1 B) C))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) tptp.one_one_nat)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) tptp.one_one_int)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.divide6298287555418463151nteger A B)) C) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) C) B)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B)) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) C)) B)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B)) C) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) B)))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) C)) (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A B) C))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat C) tptp.one_one_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) A)) (= (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat _let_1 B)) C)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int C) tptp.one_one_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) A)) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int _let_1 B)) C)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (= A (tptp.divide6298287555418463151nteger C B)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B) C)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) B)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B) C)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B) C)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (= (tptp.divide6298287555418463151nteger A B) C) (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) B) C) (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) B) C) (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) 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)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.nat) (N2 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) N2)) 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)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) 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)) (= N2 tptp.zero_zero_nat)))) (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.aa_int_int (tptp.aa_int_fun_int_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 ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat K) 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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (=> (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) N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)))))) (forall ((Z tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int Z) N2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) N2))))) (forall ((M 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) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N2) M))))) (forall ((N2 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 N2) 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 N2) 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) N2)))))) (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K2 tptp.nat) (M2 tptp.nat)) (not (= X (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat K2) M2)))))) (tptp.pp (tptp.aa_Code_integer_bool _let_133 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_nat_bool _let_132 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_int_bool _let_131 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.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.code_integer)) (not (= A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B2))))))) (forall ((A tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B2))))))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A)) (not (forall ((B2 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B2))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))) (=> (not (tptp.pp (tptp.aa_Code_integer_bool _let_1 B))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.plus_p5714425477246183910nteger A B))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 A))) (=> (not (tptp.pp (tptp.aa_nat_bool _let_1 B))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (not (tptp.pp (tptp.aa_int_bool _let_1 A))) (=> (not (tptp.pp (tptp.aa_int_bool _let_1 B))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) A)) (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat B) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B) tptp.one_one_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B) tptp.one_one_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) B))))) (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer)) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B2 tptp.code_integer)) (=> (not (= B2 tptp.zero_z3403309356797280102nteger)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B2) tptp.one_one_Code_integer)) (=> (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer A) B2) (=> (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer B2) A) (=> (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B2) tptp.one_one_Code_integer) (not (= (tptp.divide6298287555418463151nteger C A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) B2))))))))))))) (forall ((A tptp.nat) (C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat A) tptp.one_one_nat)) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B2 tptp.zero_zero_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat B2) tptp.one_one_nat)) (=> (= (tptp.aa_nat_nat _let_1 A) B2) (=> (= (tptp.aa_nat_nat _let_1 B2) A) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat A) B2) tptp.one_one_nat) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat C) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) B2)))))))))))))) (forall ((A tptp.int) (C tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int A) tptp.one_one_int)) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B2 tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int B2) tptp.one_one_int)) (=> (= (tptp.aa_int_int _let_1 A) B2) (=> (= (tptp.aa_int_int _let_1 B2) A) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B2) tptp.one_one_int) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int C) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B2)))))))))))))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_133 tptp.one_one_Code_integer))) (not (tptp.pp (tptp.aa_nat_bool _let_132 tptp.one_one_nat))) (not (tptp.pp (tptp.aa_int_bool _let_131 tptp.one_one_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1))) (= (= A B) (and (= (tptp.pp (tptp.aa_Code_integer_bool _let_2 A)) (tptp.pp (tptp.aa_Code_integer_bool _let_2 B))) (= (tptp.divide6298287555418463151nteger A _let_1) (tptp.divide6298287555418463151nteger B _let_1))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (= A B) (and (= (tptp.pp (tptp.aa_nat_bool _let_2 A)) (tptp.pp (tptp.aa_nat_bool _let_2 B))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat B) _let_1))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (= (= A B) (and (= (tptp.pp (tptp.aa_int_bool _let_2 A)) (tptp.pp (tptp.aa_int_bool _let_2 B))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B) _let_1))))))) (forall ((X tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer _let_1 N2))) (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) N2))))))) (forall ((X tptp.nat) (M tptp.nat) (N2 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 N2))) (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) N2))))))) (forall ((X tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2))) (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) N2))))))) (forall ((N2 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) N2)) (= X tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) N2))))) (forall ((N2 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) N2)) (= 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) N2))))) (forall ((N2 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) N2)) (= 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) N2))))) (forall ((N2 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) N2)) (= 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) N2))))) (forall ((N2 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) N2)) (= 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.aa_int_fun_nat_int tptp.power_power_int X) N2))))) (forall ((N2 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) N2)) (= X tptp.one_one_complex)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2))))) (forall ((N2 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 N2)) (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 _let_1))))))))) (forall ((M 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) 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) N2)) M)) (= N2 tptp.one_one_nat)))) (forall ((M 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) 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 N2) M)) M)) (= N2 tptp.one_one_nat)))) (forall ((Q2 tptp.nat) (N2 tptp.nat) (R2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R2) M))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M))) (let ((_let_3 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Q2))) (=> (tptp.pp (tptp.aa_nat_bool _let_3 N2)) (=> (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 N2) Q2))) (tptp.pp (tptp.aa_nat_bool _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_1) Q2))))))))))) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat I2))) (=> (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 N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) I2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((R2 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat R2) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R2) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) R2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2) R2))))) (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.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 ((D tptp.int) (D2 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D2)) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X2) 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 X2) D2)) T))))))))) (forall ((D tptp.int) (D2 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) D2)) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 B3) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xb3) Xa3))))))) (=> (not (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X2) 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 X2) D2)) T)))))))))) (forall ((D tptp.int) (D2 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) D2)) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int X2))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int _let_1 T))) (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 D2)) T)))))))))) (forall ((D tptp.int) (D2 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) D2)) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int X2))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (tptp.member_int Xa3 (tptp.set_or1266510415728281911st_int tptp.one_one_int D2)) (forall ((Xb3 tptp.int)) (=> (tptp.member_int Xb3 A2) (not (= X2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xb3) Xa3))))))) (=> (not (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int _let_1 T)))) (not (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_1 D2)) T))))))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.divide6298287555418463151nteger A _let_1)) A)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)) A)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1) tptp.zero_zero_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (= (tptp.modulo364778990260209775nteger A _let_1) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1) tptp.one_one_nat)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1) tptp.one_one_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (= (tptp.modulo364778990260209775nteger A _let_1) tptp.one_one_Code_integer)))) (forall ((N2 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))) N2))) (=> (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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2)))))) (forall ((N2 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))) N2))) (=> (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) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)))))) (forall ((N2 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))) N2))) (=> (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.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)))))) (forall ((N2 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))) N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_se8260200283734997820nteger M A))) (or (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (= M tptp.zero_zero_nat))))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int M) A))) (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (= M tptp.zero_zero_nat))))) (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat M) A))) (or (tptp.pp (tptp.aa_nat_bool _let_1 A)) (= M tptp.zero_zero_nat))))) (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_se2793503036327961859nteger M A))) (and (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (not (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.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.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_se1345352211410354436nteger M A))) (not (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 A)) (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int M) A))) (not (= (tptp.pp (tptp.aa_int_bool _let_1 A)) (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat M) A))) (not (= (tptp.pp (tptp.aa_nat_bool _let_1 A)) (= M tptp.zero_zero_nat)))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) L))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L)))))) (forall ((A tptp.code_integer)) (=> (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B2 tptp.code_integer)) (not (= A (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) B2) tptp.one_one_Code_integer))))))) (forall ((A tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B2 tptp.nat)) (not (= A (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B2)) tptp.one_one_nat))))))) (forall ((A tptp.int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A))) (not (forall ((B2 tptp.int)) (not (= A (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) B2)) tptp.one_one_int))))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.modulo364778990260209775nteger A _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.modulo364778990260209775nteger A _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))) (forall ((N2 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))) N2)) (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) N2))))) (forall ((N2 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))) N2)) (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) N2))))) (forall ((N2 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))) N2)) (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.aa_int_fun_nat_int tptp.power_power_int A) N2))))) (forall ((N2 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))) N2))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))) (tptp.pp (tptp.aa_real_bool _let_1 A)))))) (forall ((N2 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))) N2))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))) (forall ((N2 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))) N2))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (tptp.pp (tptp.aa_int_bool _let_1 A)))))) (forall ((A tptp.real) (N2 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))) N2)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_real_bool _let_1 A)))))))) (forall ((A tptp.rat) (N2 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))) N2)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A)))))))) (forall ((A tptp.int) (N2 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))) N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (or _let_2 (and (not _let_2) (tptp.pp (tptp.aa_int_bool _let_1 A)))))))) (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N tptp.nat)) (not (= X (tptp.aa_nat_nat tptp.suc N))))))) (forall ((A tptp.real) (N2 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))) N2)))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))) (or (= N2 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) (N2 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))) N2)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (or (= N2 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) (N2 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))) N2)))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (or (= N2 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 ((P tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P B2) A3)))) (=> (forall ((A3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A3) tptp.zero_zero_nat))) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool P A3))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 B2)) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A3) B2)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool P A) B)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.divide6298287555418463151nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer _let_2 M) tptp.one_one_Code_integer) (tptp.aa_nat_Code_integer _let_2 N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((M tptp.nat) (N2 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 N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((M tptp.nat) (N2 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_fun_nat_int 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 N2)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))) (forall ((A tptp.real) (N2 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))) N2)))) (= (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) N2)) 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) N2)) (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) (N2 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))) N2)))) (= (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) N2)) 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) N2)) (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) (N2 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))) N2)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) 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) N2)) (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 ((N2 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 N2) (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 N2) _let_3)) _let_2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (tptp.aa_nat_Code_integer _let_2 N2))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) (tptp.divide6298287555418463151nteger (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer _let_2 M) tptp.one_one_Code_integer) _let_3))) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))))))) (forall ((M tptp.nat) (N2 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 N2))) (= (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) N2)))))))) (forall ((M tptp.nat) (N2 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_fun_nat_int tptp.power_power_int _let_1))) (let ((_let_3 (tptp.aa_nat_int _let_2 N2))) (= (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) N2)))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (tptp.aa_nat_Code_integer _let_2 N2))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_3 (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) (tptp.aa_nat_Code_integer _let_2 M)) _let_4))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (tptp.pp (tptp.aa_Code_integer_bool _let_3 (tptp.divide6298287555418463151nteger A (tptp.aa_nat_Code_integer _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))))))) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2))) (= (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 N2) 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) N2)) (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 N2) M))))))))))))) (forall ((A tptp.int) (M tptp.nat) (N2 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_fun_nat_int 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 N2))) (= (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 N2) 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) N2)) (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 N2) M))))))))))))) (forall ((X6 tptp.set_real)) (=> (not (= X6 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 X6) (exists ((Xa tptp.real)) (and (tptp.member_real Xa X6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) Xa)))))) (not (tptp.finite_finite_real X6))))) (forall ((X6 tptp.set_rat)) (=> (not (= X6 tptp.bot_bot_set_rat)) (=> (forall ((X3 tptp.rat)) (=> (tptp.member_rat X3 X6) (exists ((Xa tptp.rat)) (and (tptp.member_rat Xa X6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X3) Xa)))))) (not (tptp.finite_finite_rat X6))))) (forall ((X6 tptp.set_num)) (=> (not (= X6 tptp.bot_bot_set_num)) (=> (forall ((X3 tptp.num)) (=> (tptp.member_num X3 X6) (exists ((Xa tptp.num)) (and (tptp.member_num Xa X6) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num X3) Xa)))))) (not (tptp.finite_finite_num X6))))) (forall ((X6 tptp.set_nat)) (=> (not (= X6 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) X6)) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) X6)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X3) Xa)))))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat X6)))))) (forall ((X6 tptp.set_int)) (=> (not (= X6 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 X6) (exists ((Xa tptp.int)) (and (tptp.member_int Xa X6) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X3) Xa)))))) (not (tptp.finite_finite_int X6))))) (forall ((S3 tptp.set_real)) (=> (tptp.finite_finite_real S3) (=> (not (= S3 tptp.bot_bot_set_real)) (exists ((X3 tptp.real)) (and (tptp.member_real X3 S3) (not (exists ((Xa tptp.real)) (and (tptp.member_real Xa S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Xa) X3)))))))))) (forall ((S3 tptp.set_rat)) (=> (tptp.finite_finite_rat S3) (=> (not (= S3 tptp.bot_bot_set_rat)) (exists ((X3 tptp.rat)) (and (tptp.member_rat X3 S3) (not (exists ((Xa tptp.rat)) (and (tptp.member_rat Xa S3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Xa) X3)))))))))) (forall ((S3 tptp.set_num)) (=> (tptp.finite_finite_num S3) (=> (not (= S3 tptp.bot_bot_set_num)) (exists ((X3 tptp.num)) (and (tptp.member_num X3 S3) (not (exists ((Xa tptp.num)) (and (tptp.member_num Xa S3) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Xa) X3)))))))))) (forall ((S3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (=> (not (= S3 tptp.bot_bot_set_nat)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S3)) (not (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) S3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xa) X3)))))))))) (forall ((S3 tptp.set_int)) (=> (tptp.finite_finite_int S3) (=> (not (= S3 tptp.bot_bot_set_int)) (exists ((X3 tptp.int)) (and (tptp.member_int X3 S3) (not (exists ((Xa tptp.int)) (and (tptp.member_int Xa S3) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Xa) X3)))))))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.nat_triangle N2) (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 N2) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))))) (=> (= (tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat tptp.suc _let_3))) (let ((_let_5 (tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_7 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) _let_2)))) (=> (= X _let_2) (not (and (=> _let_7 (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_3) _let_5) _let_5))) (=> (not _let_7) (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_4) _let_5) (tptp.vEBT_vebt_buildup _let_4))))))))))))))))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat A) (tptp.plus_p5714425477246183910nteger (tptp.zero_n356916108424825756nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.divide6298287555418463151nteger A _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1) A))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) A))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A) _let_1)))))) (forall ((X tptp.fun_Pr2602117396471556196at_nat) (X22 tptp.product_prod_nat_nat)) (= (tptp.size_o8335143837870341156at_nat X (tptp.some_P7363390416028606310at_nat X22)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_Pro4243173770044397973at_nat X X22)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X tptp.fun_nat_nat) (X22 tptp.nat)) (= (tptp.size_option_nat X (tptp.some_nat X22)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat X X22)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((X tptp.fun_num_nat) (X22 tptp.num)) (= (tptp.size_option_num X (tptp.some_num X22)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat X X22)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.bit_ri6519982836138164636nteger (tptp.aa_nat_nat tptp.suc N2) A) (tptp.plus_p5714425477246183910nteger (tptp.modulo364778990260209775nteger A _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_ri6519982836138164636nteger N2 (tptp.divide6298287555418463151nteger A _let_1))))))) (forall ((N2 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_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N2)) 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.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_ri631733984087533419it_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.nat_set_decode X))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) (tptp.nat_set_decode (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (tptp.minus_minus_set_real X Y) tptp.bot_bot_set_real) (tptp.ord_less_eq_set_real X Y))) (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (tptp.minus_minus_set_nat X Y) tptp.bot_bot_set_nat) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat X) Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (tptp.minus_minus_set_int X Y) tptp.bot_bot_set_int) (tptp.ord_less_eq_set_int X Y))) (forall ((I2 tptp.nat) (N2 tptp.nat) (P tptp.fun_nat_bool) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N2)) (=> (tptp.pp (tptp.aa_nat_bool P X)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat (tptp.nth_nat (tptp.replicate_nat N2 X)) I2)))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (P tptp.fun_int_bool) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N2)) (=> (tptp.pp (tptp.aa_int_bool P X)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int (tptp.nth_int (tptp.replicate_int N2 X)) I2)))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (P tptp.fun_VEBT_VEBT_bool) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N2)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool P X)) (tptp.pp (tptp.aa_VEBT_VEBT_bool P (tptp.nth_VEBT_VEBT (tptp.replicate_VEBT_VEBT N2 X) I2)))))) (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.zero_n356916108424825756nteger P)) (tptp.zero_n356916108424825756nteger Q))) (=> (tptp.pp P) (tptp.pp Q)))) (= (tptp.zero_n1201886186963655149omplex tptp.fFalse) tptp.zero_zero_complex) (= (tptp.zero_n3304061248610475627l_real tptp.fFalse) tptp.zero_zero_real) (= (tptp.zero_n2052037380579107095ol_rat tptp.fFalse) tptp.zero_zero_rat) (= (tptp.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.zero_n356916108424825756nteger tptp.fFalse) tptp.zero_z3403309356797280102nteger) (forall ((P tptp.bool)) (= (= (tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (= (tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (= (tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (= (tptp.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.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.zero_n356916108424825756nteger P)) (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.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.zero_n356916108424825756nteger tptp.fTrue) tptp.one_one_Code_integer) (forall ((N2 tptp.nat)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((M tptp.nat) (X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (tptp.replicate_VEBT_VEBT M X) (tptp.replicate_VEBT_VEBT N2 Y)) (and (= M N2) (=> (not (= M tptp.zero_zero_nat)) (= X Y))))) (forall ((N2 tptp.nat) (X tptp.vEBT_VEBT)) (= (tptp.size_s6755466524823107622T_VEBT (tptp.replicate_VEBT_VEBT N2 X)) N2)) (forall ((N2 tptp.nat) (X tptp.bool)) (= (tptp.size_size_list_bool (tptp.replicate_bool N2 X)) N2)) (forall ((N2 tptp.nat) (X tptp.int)) (= (tptp.size_size_list_int (tptp.replicate_int N2 X)) N2)) (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.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.fdisj P) Q)) (tptp.ord_max_Code_integer (tptp.zero_n356916108424825756nteger P) (tptp.zero_n356916108424825756nteger Q)))) (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.zero_n356916108424825756nteger P))) (tptp.pp P))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)) (not (tptp.pp P)))) (forall ((P tptp.bool)) (= (tptp.zero_n1201886186963655149omplex (tptp.aa_bool_bool tptp.fNot P)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) (tptp.zero_n1201886186963655149omplex P)))) (forall ((P tptp.bool)) (= (tptp.zero_n3304061248610475627l_real (tptp.aa_bool_bool tptp.fNot P)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.zero_n3304061248610475627l_real P)))) (forall ((P tptp.bool)) (= (tptp.zero_n2052037380579107095ol_rat (tptp.aa_bool_bool tptp.fNot P)) (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.one_one_rat) (tptp.zero_n2052037380579107095ol_rat P)))) (forall ((P tptp.bool)) (= (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot P)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P)))) (forall ((P tptp.bool)) (= (tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot P)) (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer (tptp.zero_n356916108424825756nteger P)))) (forall ((N2 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) N2) (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 N2) _let_1)))))) (forall ((N2 tptp.nat)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)) (forall ((K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)) (forall ((N2 tptp.nat) (A tptp.int) (P tptp.fun_int_bool)) (= (forall ((X4 tptp.int)) (=> (tptp.member_int X4 (tptp.set_int2 (tptp.replicate_int N2 A))) (tptp.pp (tptp.aa_int_bool P X4)))) (or (tptp.pp (tptp.aa_int_bool P A)) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (= (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 (tptp.replicate_VEBT_VEBT N2 A)))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X4)))) (or (tptp.pp (tptp.aa_VEBT_VEBT_bool P A)) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.int) (P tptp.fun_int_bool)) (= (exists ((X4 tptp.int)) (and (tptp.member_int X4 (tptp.set_int2 (tptp.replicate_int N2 A))) (tptp.pp (tptp.aa_int_bool P X4)))) (and (tptp.pp (tptp.aa_int_bool P A)) (not (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P tptp.fun_VEBT_VEBT_bool)) (= (exists ((X4 tptp.vEBT_VEBT)) (and (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 (tptp.replicate_VEBT_VEBT N2 A)))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X4)))) (and (tptp.pp (tptp.aa_VEBT_VEBT_bool P A)) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (tptp.member_complex X (tptp.set_complex2 (tptp.replicate_complex N2 Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (tptp.member_real X (tptp.set_real2 (tptp.replicate_real N2 Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.set_nat) (N2 tptp.nat) (Y tptp.set_nat)) (= (tptp.member_set_nat X (tptp.set_set_nat2 (tptp.replicate_set_nat N2 Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X) (tptp.set_nat2 (tptp.replicate_nat N2 Y)))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (tptp.member_int X (tptp.set_int2 (tptp.replicate_int N2 Y))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X) (tptp.set_VEBT_VEBT2 (tptp.replicate_VEBT_VEBT N2 Y)))) (and (= X Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N2)) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.replicate_nat N2 X)) I2) X))) (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N2)) (= (tptp.aa_nat_int (tptp.nth_int (tptp.replicate_int N2 X)) I2) X))) (forall ((I2 tptp.nat) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) N2)) (= (tptp.nth_VEBT_VEBT (tptp.replicate_VEBT_VEBT N2 X) I2) X))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (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 N2)) _let_1)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N2)) (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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) (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 ((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.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.zero_n356916108424825756nteger P2)))) (tptp.pp P2))) (forall ((B tptp.bool)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat B)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((B tptp.bool)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int B)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_zero_int)) (forall ((B tptp.bool)) (= (tptp.divide6298287555418463151nteger (tptp.zero_n356916108424825756nteger B) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)) (forall ((X tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) (tptp.nat_set_decode X))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) X))))) (forall ((N2 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))) N2)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N2) tptp.zero_zero_nat)))) (forall ((N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N2) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N2) tptp.zero_zero_nat)))) (forall ((N2 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))) N2)) (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N2) tptp.zero_zero_nat)))) (forall ((N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N2) tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (tptp.divide6298287555418463151nteger tptp.one_one_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat N2) tptp.zero_zero_nat)))) (forall ((N2 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))) N2)) (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) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int tptp.one_one_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (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) N2)))) (forall ((N2 tptp.nat)) (= (tptp.modulo364778990260209775nteger tptp.one_one_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat N2) M)) (= M N2)))) (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.zero_n356916108424825756nteger P2) (tptp.zero_n356916108424825756nteger Q2)) (= (tptp.pp P2) (tptp.pp Q2)))) (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.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.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.fconj P) Q)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.zero_n356916108424825756nteger P)) (tptp.zero_n356916108424825756nteger Q)))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2))) (= (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 ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2))) (= (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 ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2))) (= (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 ((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.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.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n1201886186963655149omplex P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n3304061248610475627l_real P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.zero_n2052037380579107095ol_rat P2))) (let ((_let_2 (tptp.pp P2))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((P2 tptp.bool)) (let ((_let_1 (tptp.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.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.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.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 ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (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))) (= X3 X))) (= (tptp.replicate_VEBT_VEBT (tptp.size_s6755466524823107622T_VEBT Xs) X) Xs))) (forall ((Xs tptp.list_bool) (X tptp.bool)) (=> (forall ((X3 tptp.bool)) (=> (tptp.member_bool X3 (tptp.set_bool2 Xs)) (= (tptp.pp X3) (tptp.pp X)))) (= (tptp.replicate_bool (tptp.size_size_list_bool Xs) X) Xs))) (forall ((Xs tptp.list_int) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.set_int2 Xs)) (= X3 X))) (= (tptp.replicate_int (tptp.size_size_list_int Xs) X) Xs))) (forall ((Xs tptp.list_complex) (N2 tptp.nat) (X tptp.complex)) (=> (= (tptp.size_s3451745648224563538omplex Xs) N2) (=> (forall ((Y4 tptp.complex)) (=> (tptp.member_complex Y4 (tptp.set_complex2 Xs)) (= Y4 X))) (= Xs (tptp.replicate_complex N2 X))))) (forall ((Xs tptp.list_real) (N2 tptp.nat) (X tptp.real)) (=> (= (tptp.size_size_list_real Xs) N2) (=> (forall ((Y4 tptp.real)) (=> (tptp.member_real Y4 (tptp.set_real2 Xs)) (= Y4 X))) (= Xs (tptp.replicate_real N2 X))))) (forall ((Xs tptp.list_set_nat) (N2 tptp.nat) (X tptp.set_nat)) (=> (= (tptp.size_s3254054031482475050et_nat Xs) N2) (=> (forall ((Y4 tptp.set_nat)) (=> (tptp.member_set_nat Y4 (tptp.set_set_nat2 Xs)) (= Y4 X))) (= Xs (tptp.replicate_set_nat N2 X))))) (forall ((Xs tptp.list_nat) (N2 tptp.nat) (X tptp.nat)) (=> (= (tptp.size_size_list_nat Xs) N2) (=> (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Y4) (tptp.set_nat2 Xs))) (= Y4 X))) (= Xs (tptp.replicate_nat N2 X))))) (forall ((Xs tptp.list_VEBT_VEBT) (N2 tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (tptp.size_s6755466524823107622T_VEBT Xs) N2) (=> (forall ((Y4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT Y4) (tptp.set_VEBT_VEBT2 Xs))) (= Y4 X))) (= Xs (tptp.replicate_VEBT_VEBT N2 X))))) (forall ((Xs tptp.list_bool) (N2 tptp.nat) (X tptp.bool)) (=> (= (tptp.size_size_list_bool Xs) N2) (=> (forall ((Y4 tptp.bool)) (=> (tptp.member_bool Y4 (tptp.set_bool2 Xs)) (= (tptp.pp Y4) (tptp.pp X)))) (= Xs (tptp.replicate_bool N2 X))))) (forall ((Xs tptp.list_int) (N2 tptp.nat) (X tptp.int)) (=> (= (tptp.size_size_list_int Xs) N2) (=> (forall ((Y4 tptp.int)) (=> (tptp.member_int Y4 (tptp.set_int2 Xs)) (= Y4 X))) (= Xs (tptp.replicate_int N2 X))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.nat_set_decode M)) (tptp.nat_set_decode N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) A))) (tptp.modulo364778990260209775nteger A _let_1)))) (forall ((N2 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_ri631733984087533419it_int N2) K)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.bit_ri6519982836138164636nteger M A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int M) A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((P tptp.fun_nat_bool) (A tptp.nat)) (=> (forall ((A3 tptp.nat)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat A3) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) A3) (tptp.pp (tptp.aa_nat_bool P A3)))) (=> (forall ((A3 tptp.nat) (B2 tptp.bool)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat B2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A3)))) (=> (tptp.pp (tptp.aa_nat_bool P A3)) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1) A3) (tptp.pp (tptp.aa_nat_bool P _let_2))))))) (tptp.pp (tptp.aa_nat_bool P A))))) (forall ((P tptp.fun_int_bool) (A tptp.int)) (=> (forall ((A3 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A3) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) A3) (tptp.pp (tptp.aa_int_bool P A3)))) (=> (forall ((A3 tptp.int) (B2 tptp.bool)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int B2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A3)))) (=> (tptp.pp (tptp.aa_int_bool P A3)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2) _let_1) A3) (tptp.pp (tptp.aa_int_bool P _let_2))))))) (tptp.pp (tptp.aa_int_bool P A))))) (forall ((P tptp.fun_Co8822979462182099027r_bool) (A tptp.code_integer)) (=> (forall ((A3 tptp.code_integer)) (=> (= (tptp.divide6298287555418463151nteger A3 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) A3) (tptp.pp (tptp.aa_Code_integer_bool P A3)))) (=> (forall ((A3 tptp.code_integer) (B2 tptp.bool)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.plus_p5714425477246183910nteger (tptp.zero_n356916108424825756nteger B2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) A3)))) (=> (tptp.pp (tptp.aa_Code_integer_bool P A3)) (=> (= (tptp.divide6298287555418463151nteger _let_2 _let_1) A3) (tptp.pp (tptp.aa_Code_integer_bool P _let_2))))))) (tptp.pp (tptp.aa_Code_integer_bool P A))))) (forall ((K tptp.int) (N2 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_ri631733984087533419it_int N2) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((N2 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_ri631733984087533419it_int N2) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) K)))) (forall ((M tptp.nat) (N2 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 N2)) (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) N2))) _let_2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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.modulo_modulo_int _let_2) (tptp.aa_nat_int _let_1 N2)) (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) N2))) _let_2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (= (tptp.modulo364778990260209775nteger _let_2 (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.zero_n356916108424825756nteger (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))) _let_2))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2)) K)) (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_ri631733984087533419it_int N2) 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 N2)))))))) (forall ((X tptp.fun_nat_nat)) (= (tptp.size_option_nat X tptp.none_nat) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X tptp.fun_Pr2602117396471556196at_nat)) (= (tptp.size_o8335143837870341156at_nat X tptp.none_P5556105721700978146at_nat) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X tptp.fun_num_nat)) (= (tptp.size_option_num X tptp.none_num) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (forall ((X tptp.nat)) (= (tptp.nat_set_decode X) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_ex X)))) (forall ((M tptp.nat) (N2 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 N2)) (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 N2) M)))) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2)) (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 N2) M)))) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_nat_Code_integer _let_1 M))) (= (tptp.divide6298287555418463151nteger _let_2 (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.zero_n356916108424825756nteger (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer _let_2) tptp.zero_z3403309356797280102nteger))) (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)))) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2))))))) (forall ((Va tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (tptp.aa_nat_nat tptp.suc _let_3))) (let ((_let_5 (tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1))) (let ((_let_7 (tptp.vEBT_vebt_buildup _let_2))) (let ((_let_8 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) _let_2)))) (and (=> _let_8 (= _let_7 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_3) _let_5) _let_5))) (=> (not _let_8) (= _let_7 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_2 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_4) _let_5) (tptp.vEBT_vebt_buildup _let_4)))))))))))))) (forall ((Q2 tptp.int) (R2 tptp.int)) (= (tptp.aa_Pro6799258434465214121nt_int tptp.adjust_div (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Q2) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int R2) tptp.zero_zero_int)))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.modulo364778990260209775nteger A _let_1))) (let ((_let_3 (tptp.bit_ri6519982836138164636nteger N2 A))) (let ((_let_4 (= N2 tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_2))) (=> (not _let_4) (= _let_3 (tptp.plus_p5714425477246183910nteger _let_2 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.bit_ri6519982836138164636nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat) (tptp.divide6298287555418463151nteger A _let_1)))))))))))) (forall ((N2 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.aa_int_fun_int_int tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) A))) (let ((_let_4 (= N2 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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)))))))))))) (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse)))) (=> (= (tptp.vEBT_vebt_buildup X) Y) (=> (tptp.pp (tptp.aa_nat_bool _let_2 X)) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (tptp.pp (tptp.aa_nat_bool _let_2 tptp.zero_zero_nat))))) (=> (=> (= X _let_1) (=> _let_3 (not (tptp.pp (tptp.aa_nat_bool _let_2 _let_1))))) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc Va2)))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (tptp.aa_nat_nat tptp.suc _let_3))) (let ((_let_5 (tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2))) (let ((_let_7 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) _let_1)))) (=> (= X _let_1) (=> (and (=> _let_7 (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_3) _let_5) _let_5))) (=> (not _let_7) (= Y (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat _let_1 (tptp.replicate_VEBT_VEBT (tptp.aa_nat_nat _let_6 _let_4) _let_5) (tptp.vEBT_vebt_buildup _let_4))))) (not (tptp.pp (tptp.aa_nat_bool (tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))) (forall ((R2 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex R2))) (=> (not (= R2 tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) (tptp.aa_complex_complex _let_1 C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex B) (tptp.aa_complex_complex _let_1 D)))))))) (forall ((R2 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (=> (not (= R2 tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_real_real _let_1 C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) (tptp.aa_real_real _let_1 D)))))))) (forall ((R2 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.times_times_rat R2))) (=> (not (= R2 tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (tptp.aa_rat_rat (tptp.plus_plus_rat A) (tptp.aa_rat_rat _let_1 C)) (tptp.aa_rat_rat (tptp.plus_plus_rat B) (tptp.aa_rat_rat _let_1 D)))))))) (forall ((R2 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R2))) (=> (not (= R2 tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat _let_1 C)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat B) (tptp.aa_nat_nat _let_1 D)))))))) (forall ((R2 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int R2))) (=> (not (= R2 tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_int_int _let_1 C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int B) (tptp.aa_int_int _let_1 D)))))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.artanh_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) X)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((M tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M) N2)) (= (tptp.groups4538972089207619220nt_int tptp.aTP_Lamm_aj (tptp.set_or1266510415728281911st_int M N2)) (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 N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int N2) tptp.one_one_int))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int M) tptp.one_one_int)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((L tptp.num) (Qr tptp.product_prod_nat_nat)) (= (tptp.unique5026877609467782581ep_nat L Qr) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat (tptp.aTP_Lamm_ey L)) Qr))) (forall ((L tptp.num) (Qr tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int L) Qr) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_ez L)) Qr))) (forall ((L tptp.num) (Qr tptp.produc8923325533196201883nteger)) (= (tptp.unique4921790084139445826nteger L Qr) (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_fa L) Qr))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (tptp.ord_less_eq_set_int A2 B3) (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int B3) (tptp.uminus1532241313380277803et_int A2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int A2) (tptp.uminus1532241313380277803et_int B3)) (tptp.ord_less_eq_set_int B3 A2))) (forall ((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.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int X) (tptp.uminus1532241313380277803et_int Y)) (tptp.ord_less_eq_set_int Y X))) (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.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((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) (N2 tptp.num)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))) (= M N2))) (forall ((M tptp.num) (N2 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 N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (= M N2))) (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.aa_com3342990543769683525omplex tptp.times_times_complex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 B))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.times_times_rat A))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B))))) (forall ((A tptp.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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.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.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger A B)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)) B)) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.plus_p5714425477246183910nteger A B)) B)) (forall ((A tptp.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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B)) B)) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat A) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger A (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B)) B)) (forall ((A tptp.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.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) (tptp.aa_rat_rat (tptp.minus_minus_rat B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.minus_8373710615458151222nteger A B)) (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.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.divide6298287555418463151nteger A B))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int tptp.uminus_uminus_int X)) Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) Y)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X) Y)))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X) Y)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real X))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.uminus_uminus_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int X))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int Y))) (tptp.pp (tptp.aa_int_bool _let_1 Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex X))) (= (tptp.pp (tptp.aa_complex_bool _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Y))) (tptp.pp (tptp.aa_complex_bool _let_1 Y))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat X))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat Y))) (tptp.pp (tptp.aa_rat_bool _let_1 Y))))) (forall ((X tptp.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 ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_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.aa_int_int (tptp.aa_int_fun_int_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 ((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 ((A2 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int tptp.aTP_Lamm_bm A2) tptp.zero_zero_int)) (forall ((A2 tptp.set_complex)) (= (tptp.groups7754918857620584856omplex tptp.aTP_Lamm_bi A2) tptp.zero_zero_complex)) (forall ((A2 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_bl) A2) tptp.zero_zero_nat)) (forall ((A2 tptp.set_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real tptp.aTP_Lamm_fb) A2) tptp.zero_zero_real)) (forall ((F tptp.fun_na1668100129766719005at_nat) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B)) (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F A) B))) (forall ((F tptp.fun_na4786964484885125043t_bool) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B)) (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F A) B))) (forall ((F tptp.fun_in1696471567231710611nt_int) (A tptp.int) (B tptp.int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F A) B))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B)))) (forall ((F tptp.fun_int_fun_int_int) (A tptp.int) (B tptp.int)) (= (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int F 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)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real A))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.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.aa_rat_rat tptp.uminus_uminus_rat A))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.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.aa_rat_rat tptp.uminus_uminus_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.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.aa_rat_rat 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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.code_integer)) (= (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)) (forall ((A tptp.code_integer)) (= (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.zero_zero_complex) A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.zero_zero_rat) A) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (forall ((A tptp.code_integer)) (= (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.zero_zero_complex) B) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.zero_zero_rat) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (forall ((B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N2))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real M))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (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) (N2 tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N2))) (let ((_let_2 (tptp.numera6690914467698888265omplex M))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger _let_2 _let_1)))))) (forall ((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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (tptp.aa_rat_rat tptp.uminus_uminus_rat Z))) (forall ((Z tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Z))) (forall ((Z tptp.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.aa_com3342990543769683525omplex tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Z))) (forall ((Z tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat Z) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat Z))) (forall ((Z tptp.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 ((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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.plus_plus_rat A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.plus_p5714425477246183910nteger A B))) (forall ((A tptp.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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B) (tptp.aa_rat_rat (tptp.minus_minus_rat B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B) (tptp.minus_8373710615458151222nteger B A))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int A))) (forall ((A tptp.code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (forall ((X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.uminus_uminus_real X))) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat X))) (forall ((B tptp.int) (A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger (tptp.minus_8373710615458151222nteger B A) B) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real tptp.ln_ln_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))))))) (= (tptp.aa_real_real tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (tptp.bit_ri6519982836138164636nteger N2 _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) _let_1) _let_1))) (forall ((S3 tptp.set_real) (A tptp.real) (B tptp.fun_real_complex)) (let ((_let_1 (tptp.groups5754745047067104278omplex (tptp.aa_fun2233226938935547116omplex (tptp.aTP_Lamm_fc A) B) S3))) (let ((_let_2 (tptp.member_real A S3))) (=> (tptp.finite_finite_real S3) (and (=> _let_2 (= _let_1 (tptp.aa_real_complex B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex))))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_complex)) (let ((_let_1 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_fd A) B)) S3))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S3)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_complex B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B tptp.fun_int_complex)) (let ((_let_1 (tptp.groups3049146728041665814omplex (tptp.aa_fun3088484340408535532omplex (tptp.aTP_Lamm_fe A) B) S3))) (let ((_let_2 (tptp.member_int A S3))) (=> (tptp.finite_finite_int S3) (and (=> _let_2 (= _let_1 (tptp.aa_int_complex B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B tptp.fun_real_real)) (let ((_let_1 (tptp.groups8097168146408367636l_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_ff A) B) S3))) (let ((_let_2 (tptp.member_real A S3))) (=> (tptp.finite_finite_real S3) (and (=> _let_2 (= _let_1 (tptp.aa_real_real B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B tptp.fun_int_real)) (let ((_let_1 (tptp.groups8778361861064173332t_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_fg A) B) S3))) (let ((_let_2 (tptp.member_int A S3))) (=> (tptp.finite_finite_int S3) (and (=> _let_2 (= _let_1 (tptp.aa_int_real B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real))))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B tptp.fun_complex_real)) (let ((_let_1 (tptp.groups5808333547571424918x_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_fh A) B) S3))) (let ((_let_2 (tptp.member_complex A S3))) (=> (tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= _let_1 (tptp.aa_complex_real B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B tptp.fun_real_rat)) (let ((_let_1 (tptp.groups1300246762558778688al_rat (tptp.aa_fun2468082234287226944al_rat (tptp.aTP_Lamm_fi A) B) S3))) (let ((_let_2 (tptp.member_real A S3))) (=> (tptp.finite_finite_real S3) (and (=> _let_2 (= _let_1 (tptp.aa_real_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_fj A) B) S3))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S3)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B tptp.fun_int_rat)) (let ((_let_1 (tptp.groups3906332499630173760nt_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_fk A) B) S3))) (let ((_let_2 (tptp.member_int A S3))) (=> (tptp.finite_finite_int S3) (and (=> _let_2 (= _let_1 (tptp.aa_int_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B tptp.fun_complex_rat)) (let ((_let_1 (tptp.groups5058264527183730370ex_rat (tptp.aa_fun7622890401989837636ex_rat (tptp.aTP_Lamm_fl A) B) S3))) (let ((_let_2 (tptp.member_complex A S3))) (=> (tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= _let_1 (tptp.aa_complex_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B tptp.fun_real_complex)) (let ((_let_1 (tptp.groups5754745047067104278omplex (tptp.aa_fun2233226938935547116omplex (tptp.aTP_Lamm_fm A) B) S3))) (let ((_let_2 (tptp.member_real A S3))) (=> (tptp.finite_finite_real S3) (and (=> _let_2 (= _let_1 (tptp.aa_real_complex B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex))))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_complex)) (let ((_let_1 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_fn A) B)) S3))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S3)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_complex B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B tptp.fun_int_complex)) (let ((_let_1 (tptp.groups3049146728041665814omplex (tptp.aa_fun3088484340408535532omplex (tptp.aTP_Lamm_fo A) B) S3))) (let ((_let_2 (tptp.member_int A S3))) (=> (tptp.finite_finite_int S3) (and (=> _let_2 (= _let_1 (tptp.aa_int_complex B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B tptp.fun_real_real)) (let ((_let_1 (tptp.groups8097168146408367636l_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_fp A) B) S3))) (let ((_let_2 (tptp.member_real A S3))) (=> (tptp.finite_finite_real S3) (and (=> _let_2 (= _let_1 (tptp.aa_real_real B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B tptp.fun_int_real)) (let ((_let_1 (tptp.groups8778361861064173332t_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_fq A) B) S3))) (let ((_let_2 (tptp.member_int A S3))) (=> (tptp.finite_finite_int S3) (and (=> _let_2 (= _let_1 (tptp.aa_int_real B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real))))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B tptp.fun_complex_real)) (let ((_let_1 (tptp.groups5808333547571424918x_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_fr A) B) S3))) (let ((_let_2 (tptp.member_complex A S3))) (=> (tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= _let_1 (tptp.aa_complex_real B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real))))))) (forall ((S3 tptp.set_real) (A tptp.real) (B tptp.fun_real_rat)) (let ((_let_1 (tptp.groups1300246762558778688al_rat (tptp.aa_fun2468082234287226944al_rat (tptp.aTP_Lamm_fs A) B) S3))) (let ((_let_2 (tptp.member_real A S3))) (=> (tptp.finite_finite_real S3) (and (=> _let_2 (= _let_1 (tptp.aa_real_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S3 tptp.set_nat) (A tptp.nat) (B tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_ft A) B) S3))) (let ((_let_2 (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A) S3)))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (and (=> _let_2 (= _let_1 (tptp.aa_nat_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S3 tptp.set_int) (A tptp.int) (B tptp.fun_int_rat)) (let ((_let_1 (tptp.groups3906332499630173760nt_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_fu A) B) S3))) (let ((_let_2 (tptp.member_int A S3))) (=> (tptp.finite_finite_int S3) (and (=> _let_2 (= _let_1 (tptp.aa_int_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((S3 tptp.set_complex) (A tptp.complex) (B tptp.fun_complex_rat)) (let ((_let_1 (tptp.groups5058264527183730370ex_rat (tptp.aa_fun7622890401989837636ex_rat (tptp.aTP_Lamm_fv A) B) S3))) (let ((_let_2 (tptp.member_complex A S3))) (=> (tptp.finite3207457112153483333omplex S3) (and (=> _let_2 (= _let_1 (tptp.aa_complex_rat B A))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat))))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real K))) (= (tptp.aa_real_real tptp.neg_numeral_dbl_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.neg_numeral_dbl_real _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int K))) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.neg_numeral_dbl_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex K))) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (= (tptp.neg_nu8804712462038260780nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.neg_nu8804712462038260780nteger _let_1))))) (= (tptp.aa_real_real _let_127 tptp.one_one_real) tptp.zero_zero_real) (= (tptp.aa_int_int _let_126 tptp.one_one_int) tptp.zero_zero_int) (= (tptp.aa_complex_complex _let_125 tptp.one_one_complex) tptp.zero_zero_complex) (= (tptp.aa_rat_rat _let_124 tptp.one_one_rat) tptp.zero_zero_rat) (= (tptp.plus_p5714425477246183910nteger _let_77 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_real_real _let_130 _let_53) tptp.zero_zero_real) (= (tptp.aa_int_int _let_129 _let_79) tptp.zero_zero_int) (= (tptp.aa_complex_complex _let_45 _let_50) tptp.zero_zero_complex) (= (tptp.aa_rat_rat _let_128 _let_78) tptp.zero_zero_rat) (= (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer _let_77) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_real_real _let_123 _let_53) tptp.zero_zero_real) (= (tptp.aa_int_int _let_122 _let_79) tptp.zero_zero_int) (= (tptp.aa_complex_complex _let_121 _let_50) tptp.zero_zero_complex) (= (tptp.aa_rat_rat _let_120 _let_78) tptp.zero_zero_rat) (= (tptp.minus_8373710615458151222nteger _let_77 _let_77) tptp.zero_z3403309356797280102nteger) (forall ((N2 tptp.num)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2)) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))) (= N2 tptp.one))) (forall ((N2 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 N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (= N2 tptp.one))) (forall ((N2 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)) N2)))) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (tptp.aa_int_int _let_1 (tptp.aa_int_int _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2)))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (tptp.aa_Cod1783974652533396728nteger _let_1 (tptp.aa_Cod1783974652533396728nteger _let_1 A)) A))) (forall ((N2 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)) N2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1) tptp.one_one_real))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) tptp.one_one_int))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2))) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real U)))) (let ((_let_2 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (tptp.ord_max_Code_integer _let_1 _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat U)))) (let ((_let_2 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int U)))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (let ((_let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real U)))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real V))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (let ((_let_3 (tptp.ord_max_Code_integer _let_1 _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat U)))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (let ((_let_3 (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int U)))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int V))) (let ((_let_3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real U))) (let ((_let_2 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger U))) (let ((_let_2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (tptp.ord_max_Code_integer _let_1 _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat U))) (let ((_let_2 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) _let_2)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))) (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int U))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V)))) (let ((_let_3 (tptp.aa_int_int (tptp.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.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))))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W)) Y)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num V) W))) Y))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_num_real tptp.numeral_numeral_real N2)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 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 N2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) (tptp.numera6690914467698888265omplex N2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 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 N2))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.numera6690914467698888265omplex M)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 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 N2))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_num_real tptp.numeral_numeral_real N2)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 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 N2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) (tptp.numera6690914467698888265omplex N2)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 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 N2))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex M)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2))) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2))))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real W)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int W)) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)) Y)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W)) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real V)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex V)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real V))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int V))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex V))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat V))) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W))) Y)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger V))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W))) Y)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num V) W))) Y))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) M)))) (forall ((M tptp.num) (N2 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 N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N2) M)))) (forall ((M tptp.num) (N2 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 N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num N2) M)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))))) (not (= M tptp.one)))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat (tptp.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.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) B))))) (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.times_times_rat A) _let_1)) B))))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (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.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.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.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (tptp.aa_rat_rat (tptp.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.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (not (= M tptp.one)))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)))))) (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat (tptp.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.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) _let_1)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) B))))) (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) _let_1)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) _let_1) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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.aa_rat_rat tptp.uminus_uminus_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1)))) (= (tptp.aa_real_real _let_127 _let_53) _let_113) (= (tptp.aa_int_int _let_126 _let_79) _let_112) (= (tptp.aa_complex_complex _let_125 _let_50) _let_111) (= (tptp.aa_rat_rat _let_124 _let_78) _let_110) (= (tptp.plus_p5714425477246183910nteger _let_77 _let_77) _let_109) (= (tptp.aa_real_real _let_123 tptp.one_one_real) _let_113) (= (tptp.aa_int_int _let_122 tptp.one_one_int) _let_112) (= (tptp.aa_complex_complex _let_121 tptp.one_one_complex) _let_111) (= (tptp.aa_rat_rat _let_120 tptp.one_one_rat) _let_110) (= (tptp.minus_8373710615458151222nteger _let_77 tptp.one_one_Code_integer) _let_109) (= (tptp.aa_real_real _let_119 _let_53) _let_23) (= (tptp.aa_int_int _let_118 _let_79) _let_40) (= (tptp.aa_complex_complex _let_117 _let_50) _let_46) (= (tptp.aa_rat_rat _let_116 _let_78) _let_65) (= (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer _let_77) _let_35) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_79) _let_40) _let_79) (= (tptp.divide6298287555418463151nteger _let_77 _let_35) _let_77) _let_115 _let_114 _let_115 _let_114 (forall ((A tptp.real) (N2 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))) N2))) (= (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) (N2 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))) N2))) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_1)))) (forall ((A tptp.complex) (N2 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))) N2))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) _let_1) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) _let_1)))) (forall ((A tptp.rat) (N2 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))) N2))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)))) (forall ((A tptp.code_integer) (N2 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))) N2))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2)))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N2) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N2) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2)))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N2) (tptp.aa_nat_rat (tptp.power_power_rat A) N2)))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N2) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real A)) N2) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2))))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N2) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2))))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))))) (forall ((M tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M))) tptp.one_one_complex) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one))))) (forall ((N2 tptp.num)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 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 N2))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N2)) (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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) (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.neg_numeral_dbl_real _let_53) _let_113) (= (tptp.aa_int_int tptp.neg_numeral_dbl_int _let_79) _let_112) (= (tptp.aa_complex_complex tptp.neg_nu7009210354673126013omplex _let_50) _let_111) (= (tptp.aa_rat_rat tptp.neg_numeral_dbl_rat _let_78) _let_110) (= (tptp.neg_nu8804712462038260780nteger _let_77) _let_109) (forall ((N2 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))) N2)) tptp.one_one_real)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_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))) N2)) tptp.one_one_int)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) tptp.one_one_complex)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) tptp.one_one_rat)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) tptp.one_one_Code_integer)) (forall ((N2 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))) N2)) (= (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)) N2) tptp.one_one_real))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2) tptp.one_one_int))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2) tptp.one_one_complex))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2) tptp.one_one_rat))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2) tptp.one_one_Code_integer))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) N2) _let_1)))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1) N2) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex _let_1) N2) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N2) _let_1)))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2) _let_1)))) (forall ((A tptp.code_integer)) (= (tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.modulo364778990260209775nteger A (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2))) (= (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 ((F tptp.fun_int_int) (A2 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_fw F) A2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.groups4538972089207619220nt_int F A2)))) (forall ((F tptp.fun_complex_complex) (A2 tptp.set_complex)) (= (tptp.groups7754918857620584856omplex (tptp.aTP_Lamm_fx F) A2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.groups7754918857620584856omplex F A2)))) (forall ((F tptp.fun_nat_real) (A2 tptp.set_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_fy F)) A2) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2)))) (forall ((G tptp.fun_int_fun_int_int) (B3 tptp.set_int) (A2 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_fz G) B3) A2) (tptp.groups4538972089207619220nt_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_gb G) A2) B3))) (forall ((G tptp.fun_co7673397065115134084omplex) (B3 tptp.set_complex) (A2 tptp.set_complex)) (= (tptp.groups7754918857620584856omplex (tptp.aa_set7743095458595710203omplex (tptp.aTP_Lamm_gc G) B3) A2) (tptp.groups7754918857620584856omplex (tptp.aa_set7743095458595710203omplex (tptp.aTP_Lamm_ge G) A2) B3))) (forall ((G tptp.fun_nat_fun_nat_nat) (B3 tptp.set_nat) (A2 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_gf G) B3)) A2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_gh G) A2)) B3))) (forall ((G tptp.fun_nat_fun_nat_real) (B3 tptp.set_nat) (A2 tptp.set_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_set1166323925324055613t_real (tptp.aTP_Lamm_gi G) B3)) A2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_set1166323925324055613t_real (tptp.aTP_Lamm_gk G) A2)) B3))) (forall ((H tptp.fun_bool_bool) (F tptp.fun_int_fun_int_bool) (Prod tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_bool_bool H (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) Prod))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_gl H) F)) Prod)))) (forall ((H tptp.fun_bool_int) (F tptp.fun_int_fun_int_bool) (Prod tptp.product_prod_int_int)) (= (tptp.aa_bool_int H (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) Prod)) (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int (tptp.aa_fun5341983444565040691nt_int (tptp.aTP_Lamm_gm H) F)) Prod))) (forall ((H tptp.fun_int_bool) (F tptp.fun_int_fun_int_int) (Prod tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_int_bool H (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int F) Prod))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_fun980369494830392501t_bool (tptp.aTP_Lamm_gn H) F)) Prod)))) (forall ((H tptp.fun_int_int) (F tptp.fun_int_fun_int_int) (Prod tptp.product_prod_int_int)) (= (tptp.aa_int_int H (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int F) Prod)) (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int (tptp.aa_fun6119123525526402106nt_int (tptp.aTP_Lamm_go H) F)) Prod))) (forall ((H tptp.fun_Pr803113274115125473t_bool) (F tptp.fun_in1696471567231710611nt_int) (Prod tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool H (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int F) Prod))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_fun395975271853239642t_bool (tptp.aTP_Lamm_gp H) F)) Prod)))) (forall ((H tptp.fun_Pr982841511892225912nt_int) (F tptp.fun_in1696471567231710611nt_int) (Prod tptp.product_prod_int_int)) (= (tptp.aa_Pro6799258434465214121nt_int H (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int F) Prod)) (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int (tptp.aa_fun7461304428735181397nt_int (tptp.aTP_Lamm_gq H) F)) Prod))) (forall ((H tptp.fun_bo7720638723722887333nt_int) (F tptp.fun_int_fun_int_bool) (Prod tptp.product_prod_int_int)) (= (tptp.aa_boo6976928504896087454nt_int H (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) Prod)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_fun9101259627203045662nt_int (tptp.aTP_Lamm_gr H) F)) Prod))) (forall ((H tptp.fun_in4211310926729683942nt_int) (F tptp.fun_int_fun_int_int) (Prod tptp.product_prod_int_int)) (= (tptp.aa_int7462565939943104719nt_int H (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int F) Prod)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_fun1034830265760468567nt_int (tptp.aTP_Lamm_gs H) F)) Prod))) (forall ((H tptp.fun_Pr2478283820680522243nt_int) (F tptp.fun_in1696471567231710611nt_int) (Prod tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int H (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int F) Prod)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_fun4152872853588681340nt_int (tptp.aTP_Lamm_gt H) F)) Prod))) (forall ((H tptp.fun_fu6897202038601531823t_bool) (F tptp.fun_na4786964484885125043t_bool) (Prod tptp.product_prod_nat_nat)) (= (tptp.aa_fun830836278467416944t_bool H (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool F) Prod)) (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool (tptp.aa_fun3491305611276047780t_bool (tptp.aTP_Lamm_gu H) F)) Prod))) (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.aa_rat_rat tptp.uminus_uminus_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int tptp.uminus_uminus_int B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (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.aa_rat_rat tptp.uminus_uminus_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int B)) A)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real 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.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int tptp.uminus_uminus_int A))))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int Y) X) (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int X) Y))) (forall ((Y tptp.set_int) (X tptp.set_int)) (=> (tptp.ord_less_eq_set_int Y (tptp.uminus1532241313380277803et_int X)) (tptp.ord_less_eq_set_int X (tptp.uminus1532241313380277803et_int Y)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (tptp.ord_less_eq_set_int X Y) (tptp.ord_less_eq_set_int (tptp.uminus1532241313380277803et_int Y) (tptp.uminus1532241313380277803et_int X)))) (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.aa_rat_rat tptp.uminus_uminus_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (forall ((A tptp.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.aa_rat_rat tptp.uminus_uminus_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) A)))) (forall ((A tptp.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) 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.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat 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 ((M tptp.num) (N2 tptp.num)) (not (= (tptp.aa_num_real tptp.numeral_numeral_real M) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))))) (forall ((M tptp.num) (N2 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 N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (tptp.numera6690914467698888265omplex M) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (tptp.aa_num_rat tptp.numeral_numeral_rat M) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_num_real tptp.numeral_numeral_real N2)))) (forall ((M tptp.num) (N2 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 N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex M)) (tptp.numera6690914467698888265omplex N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B) (tptp.aa_rat_rat (tptp.times_times_rat A) (tptp.aa_rat_rat 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.aa_com3342990543769683525omplex tptp.times_times_complex A) A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) B)) (or (= A B) (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.times_times_rat A) A) (tptp.aa_rat_rat (tptp.times_times_rat B) B)) (or (= A B) (= A (tptp.aa_rat_rat 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))))) (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.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger A B)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.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.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.plus_p5714425477246183910nteger A B)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex K) A)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex K)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A))))) (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (tptp.aa_rat_rat (tptp.plus_plus_rat K) A)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A2) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat K)) (tptp.aa_rat_rat tptp.uminus_uminus_rat A))))) (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (tptp.plus_p5714425477246183910nteger K A)) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A2) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))))) (not (= tptp.one_one_real _let_53)) (not (= tptp.one_one_int _let_79)) (not (= tptp.one_one_complex _let_50)) (not (= tptp.one_one_rat _let_78)) (not (= tptp.one_one_Code_integer _let_77)) (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.minus_8373710615458151222nteger A B)))) (forall ((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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B))) (forall ((B tptp.rat) (A tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) A) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B) A) (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) (tptp.aa_int_int tptp.uminus_uminus_int B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (forall ((A tptp.real) (B tptp.real)) (= (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.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B))) (forall ((A tptp.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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B))) (forall ((A tptp.real) (B tptp.real)) (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)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A))) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 B)) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))))) (forall ((F tptp.fun_na1668100129766719005at_nat) (X1 tptp.nat) (X22 tptp.nat)) (= (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X1) X22)) (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F X1) X22))) (forall ((F tptp.fun_na4786964484885125043t_bool) (X1 tptp.nat) (X22 tptp.nat)) (= (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X1) X22)) (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F X1) X22))) (forall ((F tptp.fun_in1696471567231710611nt_int) (X1 tptp.int) (X22 tptp.int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X22)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F X1) X22))) (forall ((F tptp.fun_int_fun_int_bool) (X1 tptp.int) (X22 tptp.int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X22))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F X1) X22)))) (forall ((F tptp.fun_int_fun_int_int) (X1 tptp.int) (X22 tptp.int)) (= (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X1) X22)) (tptp.aa_int_int (tptp.aa_int_fun_int_int F X1) X22))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_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.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) (A5 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A5) B)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int A5)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (A5 tptp.code_integer)) (=> (= (tptp.modulo364778990260209775nteger A B) (tptp.modulo364778990260209775nteger A5 B)) (= (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A5) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) B) (tptp.aa_int_int (tptp.aa_int_fun_int_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 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.modulo364778990260209775nteger A B)) B) (tptp.modulo364778990260209775nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (forall ((K5 tptp.set_complex) (F tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 K5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F I3)) (tptp.aa_complex_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups5058264527183730370ex_rat F K5)) (tptp.groups5058264527183730370ex_rat G K5))))) (forall ((K5 tptp.set_real) (F tptp.fun_real_rat) (G tptp.fun_real_rat)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 K5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F I3)) (tptp.aa_real_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1300246762558778688al_rat F K5)) (tptp.groups1300246762558778688al_rat G K5))))) (forall ((K5 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F I3)) (tptp.aa_nat_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F K5)) (tptp.groups2906978787729119204at_rat G K5))))) (forall ((K5 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 K5) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F I3)) (tptp.aa_int_rat G I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F K5)) (tptp.groups3906332499630173760nt_rat G K5))))) (forall ((K5 tptp.set_complex) (F tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 K5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F I3)) (tptp.aa_complex_nat G I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups5693394587270226106ex_nat F K5)) (tptp.groups5693394587270226106ex_nat G K5))))) (forall ((K5 tptp.set_real) (F tptp.fun_real_nat) (G tptp.fun_real_nat)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 K5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat F I3)) (tptp.aa_real_nat G I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1935376822645274424al_nat F K5)) (tptp.groups1935376822645274424al_nat G K5))))) (forall ((K5 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 K5) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F I3)) (tptp.aa_int_nat G I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups4541462559716669496nt_nat F K5)) (tptp.groups4541462559716669496nt_nat G K5))))) (forall ((K5 tptp.set_complex) (F tptp.fun_complex_int) (G tptp.fun_complex_int)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 K5) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_complex_int F I3)) (tptp.aa_complex_int G I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups5690904116761175830ex_int F K5)) (tptp.groups5690904116761175830ex_int G K5))))) (forall ((K5 tptp.set_real) (F tptp.fun_real_int) (G tptp.fun_real_int)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 K5) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int F I3)) (tptp.aa_real_int G I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups1932886352136224148al_int F K5)) (tptp.groups1932886352136224148al_int G K5))))) (forall ((K5 tptp.set_nat) (F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) K5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F I3)) (tptp.aa_nat_int G I3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F K5)) (tptp.groups3539618377306564664at_int G K5))))) (forall ((F tptp.fun_int_int) (A2 tptp.set_int) (G tptp.fun_int_int) (B3 tptp.set_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups4538972089207619220nt_int F A2)) (tptp.groups4538972089207619220nt_int G B3)) (tptp.groups4538972089207619220nt_int (tptp.aa_set7310040872927613301nt_int (tptp.aa_fun8076508010538293575nt_int (tptp.aTP_Lamm_gw F) G) B3) A2))) (forall ((F tptp.fun_complex_complex) (A2 tptp.set_complex) (G tptp.fun_complex_complex) (B3 tptp.set_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.groups7754918857620584856omplex F A2)) (tptp.groups7754918857620584856omplex G B3)) (tptp.groups7754918857620584856omplex (tptp.aa_set7743095458595710203omplex (tptp.aa_fun1583801116089702097omplex (tptp.aTP_Lamm_gy F) G) B3) A2))) (forall ((F tptp.fun_nat_nat) (A2 tptp.set_nat) (G tptp.fun_nat_nat) (B3 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) B3)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_set6537093552120046177at_nat (tptp.aa_fun4561837934398617467at_nat (tptp.aTP_Lamm_ha F) G) B3)) A2))) (forall ((F tptp.fun_nat_real) (A2 tptp.set_nat) (G tptp.fun_nat_real) (B3 tptp.set_nat)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) B3)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_set1166323925324055613t_real (tptp.aa_fun1400677770452585267t_real (tptp.aTP_Lamm_hc F) G) B3)) A2))) (forall ((F tptp.fun_int_int) (A2 tptp.set_int) (R2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups4538972089207619220nt_int F A2)) R2) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_hd F) R2) A2))) (forall ((F tptp.fun_complex_complex) (A2 tptp.set_complex) (R2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.groups7754918857620584856omplex F A2)) R2) (tptp.groups7754918857620584856omplex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_he F) R2) A2))) (forall ((F tptp.fun_nat_nat) (A2 tptp.set_nat) (R2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) R2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_hf F) R2)) A2))) (forall ((F tptp.fun_nat_real) (A2 tptp.set_nat) (R2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2)) R2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_hg F) R2)) A2))) (forall ((R2 tptp.int) (F tptp.fun_int_int) (A2 tptp.set_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R2) (tptp.groups4538972089207619220nt_int F A2)) (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_hh R2) F) A2))) (forall ((R2 tptp.complex) (F tptp.fun_complex_complex) (A2 tptp.set_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex R2) (tptp.groups7754918857620584856omplex F A2)) (tptp.groups7754918857620584856omplex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_hi R2) F) A2))) (forall ((R2 tptp.nat) (F tptp.fun_nat_nat) (A2 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat R2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hj R2) F)) A2))) (forall ((R2 tptp.real) (F tptp.fun_nat_real) (A2 tptp.set_nat)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hk R2) F)) A2))) (forall ((G tptp.fun_int_int) (H tptp.fun_int_int) (A2 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_hl G) H) A2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G A2)) (tptp.groups4538972089207619220nt_int H A2)))) (forall ((G tptp.fun_complex_complex) (H tptp.fun_complex_complex) (A2 tptp.set_complex)) (= (tptp.groups7754918857620584856omplex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_hm G) H) A2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.groups7754918857620584856omplex G A2)) (tptp.groups7754918857620584856omplex H A2)))) (forall ((G tptp.fun_nat_nat) (H tptp.fun_nat_nat) (A2 tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hn G) H)) A2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) A2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat H) A2)))) (forall ((G tptp.fun_nat_real) (H tptp.fun_nat_real) (A2 tptp.set_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ho G) H)) A2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) A2)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real H) A2)))) (forall ((F tptp.fun_int_int) (G tptp.fun_int_int) (A2 tptp.set_int)) (= (tptp.groups4538972089207619220nt_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_hp F) G) A2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups4538972089207619220nt_int F A2)) (tptp.groups4538972089207619220nt_int G A2)))) (forall ((F tptp.fun_complex_complex) (G tptp.fun_complex_complex) (A2 tptp.set_complex)) (= (tptp.groups7754918857620584856omplex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_hq F) G) A2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.groups7754918857620584856omplex F A2)) (tptp.groups7754918857620584856omplex G A2)))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real) (A2 tptp.set_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hr F) G)) A2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) A2)))) (forall ((F tptp.fun_complex_complex) (A2 tptp.set_complex) (R2 tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.groups7754918857620584856omplex F A2)) R2) (tptp.groups7754918857620584856omplex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_hs F) R2) A2))) (forall ((F tptp.fun_nat_real) (A2 tptp.set_nat) (R2 tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2)) R2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ht F) R2)) A2))) (forall ((A2 tptp.set_real) (B3 tptp.set_int) (G tptp.fun_real_fun_int_int) (R tptp.fun_re8661203372455305201t_bool)) (=> (tptp.finite_finite_real A2) (=> (tptp.finite_finite_int B3) (= (tptp.groups1932886352136224148al_int (tptp.aa_fun529217645232493962al_int (tptp.aa_fun5832317237790237469al_int (tptp.aTP_Lamm_hv B3) G) R) A2) (tptp.groups4538972089207619220nt_int (tptp.aa_fun5532095235224157706nt_int (tptp.aa_fun4786959800906006429nt_int (tptp.aTP_Lamm_hx A2) G) R) B3))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_int) (G tptp.fun_nat_fun_int_int) (R tptp.fun_nat_fun_int_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (tptp.finite_finite_int B3) (= (tptp.groups3539618377306564664at_int (tptp.aa_fun3504929462025808522at_int (tptp.aa_fun3325927984641084153at_int (tptp.aTP_Lamm_hz B3) G) R) A2) (tptp.groups4538972089207619220nt_int (tptp.aa_fun4504283173926863078nt_int (tptp.aa_fun5512849559334105941nt_int (tptp.aTP_Lamm_ib A2) G) R) B3))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_int) (G tptp.fun_co333780937270390912nt_int) (R tptp.fun_co2381122952212249071t_bool)) (=> (tptp.finite3207457112153483333omplex A2) (=> (tptp.finite_finite_int B3) (= (tptp.groups5690904116761175830ex_int (tptp.aa_fun3700423334941611530ex_int (tptp.aa_fun3520494530470439451ex_int (tptp.aTP_Lamm_id B3) G) R) A2) (tptp.groups4538972089207619220nt_int (tptp.aa_fun855801025254967176nt_int (tptp.aa_fun315996177946036377nt_int (tptp.aTP_Lamm_ig A2) G) R) B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_complex) (G tptp.fun_re7208826350674946562omplex) (R tptp.fun_re3010880487650781423x_bool)) (=> (tptp.finite_finite_real A2) (=> (tptp.finite3207457112153483333omplex B3) (= (tptp.groups5754745047067104278omplex (tptp.aa_fun4873726854752153866omplex (tptp.aa_fun883667864959905433omplex (tptp.aTP_Lamm_ii B3) G) R) A2) (tptp.groups7754918857620584856omplex (tptp.aa_fun8128191506076533516omplex (tptp.aa_fun840110154952133019omplex (tptp.aTP_Lamm_ik A2) G) R) B3))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_complex) (G tptp.fun_na1591161823130732966omplex) (R tptp.fun_na5941084329111710283x_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (tptp.finite3207457112153483333omplex B3) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_fun2700696402887535882omplex (tptp.aa_fun8019143150332516725omplex (tptp.aTP_Lamm_im B3) G) R)) A2) (tptp.groups7754918857620584856omplex (tptp.aa_fun1613615970879741416omplex (tptp.aa_fun7586814990830484307omplex (tptp.aTP_Lamm_io A2) G) R) B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_complex) (G tptp.fun_in1307110748760623106omplex) (R tptp.fun_in5750378413879446255x_bool)) (=> (tptp.finite_finite_int A2) (=> (tptp.finite3207457112153483333omplex B3) (= (tptp.groups3049146728041665814omplex (tptp.aa_fun751309451324587018omplex (tptp.aa_fun3438240386181387033omplex (tptp.aTP_Lamm_iq B3) G) R) A2) (tptp.groups7754918857620584856omplex (tptp.aa_fun2686559102040213132omplex (tptp.aa_fun5422379709423809691omplex (tptp.aTP_Lamm_is A2) G) R) B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (G tptp.fun_real_fun_nat_nat) (R tptp.fun_re9121486324101951821t_bool)) (=> (tptp.finite_finite_real A2) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups1935376822645274424al_nat (tptp.aa_fun5804151645385689226al_nat (tptp.aa_fun8436216498351771861al_nat (tptp.aTP_Lamm_iu B3) G) R) A2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5672750458368166062at_nat (tptp.aa_fun6824837968375615225at_nat (tptp.aTP_Lamm_iw A2) G) R)) B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_nat) (G tptp.fun_int_fun_nat_nat) (R tptp.fun_int_fun_nat_bool)) (=> (tptp.finite_finite_int A2) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun5132377469993263754nt_nat (tptp.aa_fun348247319442030677nt_nat (tptp.aTP_Lamm_iy B3) G) R) A2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun4133023758092209198at_nat (tptp.aa_fun7384697781603784697at_nat (tptp.aTP_Lamm_ja A2) G) R)) B3))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_nat) (G tptp.fun_co636942507509095880at_nat) (R tptp.fun_co2841405903858895691t_bool)) (=> (tptp.finite3207457112153483333omplex A2) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups5693394587270226106ex_nat (tptp.aa_fun9050545535516344074ex_nat (tptp.aa_fun2757644259618170323ex_nat (tptp.aTP_Lamm_jc B3) G) R) A2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun996456248398975532at_nat (tptp.aa_fun8754082201773474805at_nat (tptp.aTP_Lamm_je A2) G) R)) B3))))) (forall ((A2 tptp.set_real) (B3 tptp.set_nat) (G tptp.fun_re4238438383274954274t_real) (R tptp.fun_re9121486324101951821t_bool)) (=> (tptp.finite_finite_real A2) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (= (tptp.groups8097168146408367636l_real (tptp.aa_fun7981600115099051494l_real (tptp.aa_fun2847282595593119957l_real (tptp.aTP_Lamm_jf B3) G) R) A2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun555827300007793674t_real (tptp.aa_fun8353879187736340217t_real (tptp.aTP_Lamm_jh A2) G) R)) B3))))) (forall ((F tptp.fun_int_int) (A tptp.int) (A2 tptp.set_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_ji F) A) A2)) A) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.groups4538972089207619220nt_int F A2)) A))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (A2 tptp.set_nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jj F) A)) A2)) A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) A))) (forall ((F tptp.fun_na1668100129766719005at_nat) (G tptp.fun_Pr2477239776880934807at_nat)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat F X3) Y4) (tptp.aa_Pro8023792847356852296at_nat G (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y4)))) (= (tptp.produc4528391901023682385at_nat F) G))) (forall ((F tptp.fun_na4786964484885125043t_bool) (G tptp.fun_Pr248683899324676269t_bool)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool F X3) Y4) (tptp.aa_Pro595088089689268830t_bool G (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y4)))) (= (tptp.produc5023667602222594023t_bool F) G))) (forall ((F tptp.fun_in1696471567231710611nt_int) (G tptp.fun_Pr2478283820680522243nt_int)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int F X3) Y4) (tptp.aa_Pro6970504127699319548nt_int G (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y4)))) (= (tptp.produc4245557441103728435nt_int F) G))) (forall ((F tptp.fun_int_fun_int_bool) (G tptp.fun_Pr803113274115125473t_bool)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F X3) Y4)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool G (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y4))))) (= (tptp.produc8560705615207772305t_bool F) G))) (forall ((F tptp.fun_int_fun_int_int) (G tptp.fun_Pr982841511892225912nt_int)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int F X3) Y4) (tptp.aa_Pro6799258434465214121nt_int G (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y4)))) (= (tptp.produc8211389475949308722nt_int F) G))) (forall ((F tptp.fun_Pr2477239776880934807at_nat)) (= (tptp.produc4528391901023682385at_nat (tptp.aTP_Lamm_jk F)) F)) (forall ((F tptp.fun_Pr248683899324676269t_bool)) (= (tptp.produc5023667602222594023t_bool (tptp.aTP_Lamm_jl F)) F)) (forall ((F tptp.fun_Pr2478283820680522243nt_int)) (= (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_jm F)) F)) (forall ((F tptp.fun_Pr803113274115125473t_bool)) (= (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_jn F)) F)) (forall ((F tptp.fun_Pr982841511892225912nt_int)) (= (tptp.produc8211389475949308722nt_int (tptp.aTP_Lamm_jo F)) F)) (forall ((Q tptp.fun_fu7919257609373989805t_bool) (P tptp.fun_na1668100129766719005at_nat) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_fun4519828053337421206t_bool Q (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat P) Z))) (not (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (= Z (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y4)) (not (tptp.pp (tptp.aa_fun4519828053337421206t_bool Q (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat P X3) Y4))))))))) (forall ((Q tptp.fun_fu5641360819561228055l_bool) (P tptp.fun_na4786964484885125043t_bool) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_fun8663595511526100224l_bool Q (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool P) Z))) (not (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (= Z (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y4)) (not (tptp.pp (tptp.aa_fun8663595511526100224l_bool Q (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool P X3) Y4))))))))) (forall ((Q tptp.fun_Pr803113274115125473t_bool) (P tptp.fun_in1696471567231710611nt_int) (Z tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int P) Z))) (not (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (= Z (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y4)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Q (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int P X3) Y4))))))))) (forall ((Q tptp.fun_bool_bool) (P tptp.fun_int_fun_int_bool) (Z tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_bool_bool Q (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool P) Z))) (not (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (= Z (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y4)) (not (tptp.pp (tptp.aa_bool_bool Q (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P X3) Y4))))))))) (forall ((Q tptp.fun_int_bool) (P tptp.fun_int_fun_int_int) (Z tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_int_bool Q (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int P) Z))) (not (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (= Z (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y4)) (not (tptp.pp (tptp.aa_int_bool Q (tptp.aa_int_int (tptp.aa_int_fun_int_int P X3) Y4))))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_real)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.groups5808333547571424918x_real F A2))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_real)) (=> (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.zero_zero_real) (tptp.aa_real_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.groups8097168146408367636l_real F A2))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_real)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.groups8778361861064173332t_real F A2))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups5058264527183730370ex_rat F A2))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_rat)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups1300246762558778688al_rat F A2))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups2906978787729119204at_rat F A2))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.groups3906332499630173760nt_rat F A2))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.groups5693394587270226106ex_nat F A2))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_nat)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.groups1935376822645274424al_nat F A2))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.groups4541462559716669496nt_nat F A2))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_real)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F X3)) tptp.zero_zero_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups5808333547571424918x_real F A2)) tptp.zero_zero_real)))) (forall ((A2 tptp.set_real) (F tptp.fun_real_real)) (=> (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.aa_real_real F X3)) tptp.zero_zero_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8097168146408367636l_real F A2)) tptp.zero_zero_real)))) (forall ((A2 tptp.set_int) (F tptp.fun_int_real)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F X3)) tptp.zero_zero_real)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8778361861064173332t_real F A2)) tptp.zero_zero_real)))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F X3)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups5058264527183730370ex_rat F A2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.set_real) (F tptp.fun_real_rat)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F X3)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1300246762558778688al_rat F A2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F A2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.set_int) (F tptp.fun_int_rat)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) tptp.zero_zero_rat)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F A2)) tptp.zero_zero_rat)))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F X3)) tptp.zero_zero_nat)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups5693394587270226106ex_nat F A2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.set_real) (F tptp.fun_real_nat)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat F X3)) tptp.zero_zero_nat)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1935376822645274424al_nat F A2)) tptp.zero_zero_nat)))) (forall ((A2 tptp.set_int) (F tptp.fun_int_nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F X3)) tptp.zero_zero_nat)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups4541462559716669496nt_nat F A2)) tptp.zero_zero_nat)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.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 ((F tptp.fun_real_rat) (I6 tptp.set_real) (G tptp.fun_real_rat) (I2 tptp.real)) (=> (= (tptp.groups1300246762558778688al_rat F I6) (tptp.groups1300246762558778688al_rat G I6)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F I3)) (tptp.aa_real_rat G I3))))) (=> (tptp.member_real I2 I6) (=> (tptp.finite_finite_real I6) (= (tptp.aa_real_rat F I2) (tptp.aa_real_rat G I2))))))) (forall ((F tptp.fun_nat_rat) (I6 tptp.set_nat) (G tptp.fun_nat_rat) (I2 tptp.nat)) (=> (= (tptp.groups2906978787729119204at_rat F I6) (tptp.groups2906978787729119204at_rat G I6)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F I3)) (tptp.aa_nat_rat G I3))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) I6)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I6)) (= (tptp.aa_nat_rat F I2) (tptp.aa_nat_rat G I2))))))) (forall ((F tptp.fun_int_rat) (I6 tptp.set_int) (G tptp.fun_int_rat) (I2 tptp.int)) (=> (= (tptp.groups3906332499630173760nt_rat F I6) (tptp.groups3906332499630173760nt_rat G I6)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F I3)) (tptp.aa_int_rat G I3))))) (=> (tptp.member_int I2 I6) (=> (tptp.finite_finite_int I6) (= (tptp.aa_int_rat F I2) (tptp.aa_int_rat G I2))))))) (forall ((F tptp.fun_complex_rat) (I6 tptp.set_complex) (G tptp.fun_complex_rat) (I2 tptp.complex)) (=> (= (tptp.groups5058264527183730370ex_rat F I6) (tptp.groups5058264527183730370ex_rat G I6)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F I3)) (tptp.aa_complex_rat G I3))))) (=> (tptp.member_complex I2 I6) (=> (tptp.finite3207457112153483333omplex I6) (= (tptp.aa_complex_rat F I2) (tptp.aa_complex_rat G I2))))))) (forall ((F tptp.fun_real_nat) (I6 tptp.set_real) (G tptp.fun_real_nat) (I2 tptp.real)) (=> (= (tptp.groups1935376822645274424al_nat F I6) (tptp.groups1935376822645274424al_nat G I6)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat F I3)) (tptp.aa_real_nat G I3))))) (=> (tptp.member_real I2 I6) (=> (tptp.finite_finite_real I6) (= (tptp.aa_real_nat F I2) (tptp.aa_real_nat G I2))))))) (forall ((F tptp.fun_int_nat) (I6 tptp.set_int) (G tptp.fun_int_nat) (I2 tptp.int)) (=> (= (tptp.groups4541462559716669496nt_nat F I6) (tptp.groups4541462559716669496nt_nat G I6)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F I3)) (tptp.aa_int_nat G I3))))) (=> (tptp.member_int I2 I6) (=> (tptp.finite_finite_int I6) (= (tptp.aa_int_nat F I2) (tptp.aa_int_nat G I2))))))) (forall ((F tptp.fun_complex_nat) (I6 tptp.set_complex) (G tptp.fun_complex_nat) (I2 tptp.complex)) (=> (= (tptp.groups5693394587270226106ex_nat F I6) (tptp.groups5693394587270226106ex_nat G I6)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F I3)) (tptp.aa_complex_nat G I3))))) (=> (tptp.member_complex I2 I6) (=> (tptp.finite3207457112153483333omplex I6) (= (tptp.aa_complex_nat F I2) (tptp.aa_complex_nat G I2))))))) (forall ((F tptp.fun_real_int) (I6 tptp.set_real) (G tptp.fun_real_int) (I2 tptp.real)) (=> (= (tptp.groups1932886352136224148al_int F I6) (tptp.groups1932886352136224148al_int G I6)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_real_int F I3)) (tptp.aa_real_int G I3))))) (=> (tptp.member_real I2 I6) (=> (tptp.finite_finite_real I6) (= (tptp.aa_real_int F I2) (tptp.aa_real_int G I2))))))) (forall ((F tptp.fun_nat_int) (I6 tptp.set_nat) (G tptp.fun_nat_int) (I2 tptp.nat)) (=> (= (tptp.groups3539618377306564664at_int F I6) (tptp.groups3539618377306564664at_int G I6)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F I3)) (tptp.aa_nat_int G I3))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) I6)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I6)) (= (tptp.aa_nat_int F I2) (tptp.aa_nat_int G I2))))))) (forall ((F tptp.fun_complex_int) (I6 tptp.set_complex) (G tptp.fun_complex_int) (I2 tptp.complex)) (=> (= (tptp.groups5690904116761175830ex_int F I6) (tptp.groups5690904116761175830ex_int G I6)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_complex_int F I3)) (tptp.aa_complex_int G I3))))) (=> (tptp.member_complex I2 I6) (=> (tptp.finite3207457112153483333omplex I6) (= (tptp.aa_complex_int F I2) (tptp.aa_complex_int G I2))))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))))) (forall ((M tptp.num) (N2 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 N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_num_real tptp.numeral_numeral_real N2)))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((M tptp.num) (N2 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 N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2)))))) (forall ((M tptp.num) (N2 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 N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_num_real tptp.numeral_numeral_real N2)))) (forall ((M tptp.num) (N2 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 N2)))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))) (forall ((M tptp.num) (N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))) (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (tptp.plus_p5714425477246183910nteger A B) tptp.zero_z3403309356797280102nteger) (= B (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.code_integer)) (= (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) (= (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (tptp.aa_rat_rat (tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (tptp.plus_p5714425477246183910nteger A B) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B))) (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.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (= (tptp.aa_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.plus_p5714425477246183910nteger A B) tptp.zero_z3403309356797280102nteger))) (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.aa_complex_complex tptp.uminus1482373934393186551omplex A) B) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) B) (= (tptp.aa_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.plus_p5714425477246183910nteger A B) tptp.zero_z3403309356797280102nteger))) (not (tptp.pp (tptp.aa_real_bool _let_108 _let_53))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) _let_77))) (not (tptp.pp (tptp.aa_rat_bool _let_107 _let_78))) (not (tptp.pp (tptp.aa_int_bool _let_106 _let_79))) (tptp.pp (tptp.aa_real_bool _let_100 tptp.one_one_real)) (tptp.pp (tptp.aa_Code_integer_bool _let_99 tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_rat_bool _let_98 tptp.one_one_rat)) (tptp.pp (tptp.aa_int_bool _let_97 tptp.one_one_int)) (not (= tptp.zero_zero_real _let_53)) (not (= tptp.zero_zero_int _let_79)) (not (= tptp.zero_zero_complex _let_50)) (not (= tptp.zero_zero_rat _let_78)) (not (= tptp.zero_z3403309356797280102nteger _let_77)) (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real tptp.uminus_uminus_real _let_1))))) (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int W))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int tptp.uminus_uminus_int X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int X) (tptp.aa_int_int tptp.uminus_uminus_int _let_1))))) (forall ((W tptp.num) (X tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1))))) (forall ((W tptp.num) (X tptp.rat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_1) (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.times_times_rat X) (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1))))) (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger W))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1))))) (not (tptp.pp (tptp.aa_real_bool _let_105 _let_53))) (not (tptp.pp (tptp.aa_int_bool _let_104 _let_79))) (not (tptp.pp (tptp.aa_rat_bool _let_103 _let_78))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) _let_77))) (tptp.pp (tptp.aa_real_bool _let_94 tptp.one_one_real)) (tptp.pp (tptp.aa_int_bool _let_93 tptp.one_one_int)) (tptp.pp (tptp.aa_rat_bool _let_92 tptp.one_one_rat)) (tptp.pp (tptp.aa_Code_integer_bool _let_91 tptp.one_one_Code_integer)) (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)))) (forall ((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)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 B)) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B)) (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((N2 tptp.num)) (not (= (tptp.aa_num_real tptp.numeral_numeral_real N2) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((N2 tptp.num)) (not (= (tptp.aa_num_int tptp.numeral_numeral_int N2) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((N2 tptp.num)) (not (= (tptp.numera6690914467698888265omplex N2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (forall ((N2 tptp.num)) (not (= (tptp.aa_num_rat tptp.numeral_numeral_rat N2) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((N2 tptp.num)) (not (= (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((N2 tptp.num)) (not (= tptp.one_one_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))))) (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.aa_com3342990543769683525omplex tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((X tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((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 ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (=> (= B3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real K) B)) (= (tptp.aa_real_real _let_1 B3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.uminus_uminus_real K)) (tptp.aa_real_real _let_1 B)))))) (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int A))) (=> (= B3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) B)) (= (tptp.aa_int_int _let_1 B3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.uminus_uminus_int K)) (tptp.aa_int_int _let_1 B)))))) (forall ((B3 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A))) (=> (= B3 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex K) B)) (= (tptp.aa_complex_complex _let_1 B3) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex K)) (tptp.aa_complex_complex _let_1 B)))))) (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.minus_minus_rat A))) (=> (= B3 (tptp.aa_rat_rat (tptp.plus_plus_rat K) B)) (= (tptp.aa_rat_rat _let_1 B3) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat K)) (tptp.aa_rat_rat _let_1 B)))))) (forall ((B3 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (= B3 (tptp.plus_p5714425477246183910nteger K B)) (= (tptp.minus_8373710615458151222nteger A B3) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K) (tptp.minus_8373710615458151222nteger A B))))) (forall ((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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.plus_plus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A B) (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat A) B) (tptp.aa_rat_rat (tptp.plus_plus_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger A B) (tptp.plus_p5714425477246183910nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)))) (forall ((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.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex B) A)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) B) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A) B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.divide6298287555418463151nteger A B))))) (forall ((B tptp.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)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A))) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex B) A)) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 B)))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (tptp.divide_divide_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat B) A)) (= (tptp.aa_rat_rat _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat _let_1 B)))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer B) A)) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.divide6298287555418463151nteger A B))))) (forall ((A2 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) (tptp.uminus5710092332889474511et_nat A2))) (= A2 tptp.bot_bot_set_nat))) (forall ((A2 tptp.set_real)) (= (tptp.ord_less_eq_set_real A2 (tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))) (forall ((A2 tptp.set_int)) (= (tptp.ord_less_eq_set_int A2 (tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))) (forall ((U tptp.real) (X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real U) U))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) X)))) (forall ((M tptp.int) (N2 tptp.int)) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int M) N2) 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) (N2 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) N2) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N2 tptp.one_one_int)) (and (= M _let_1) (= N2 _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 ((A2 tptp.set_real) (G tptp.fun_real_complex) (P tptp.fun_real_bool)) (=> (tptp.finite_finite_real A2) (= (tptp.groups5754745047067104278omplex G (tptp.collect_real (tptp.aa_fun6476784834714468668l_bool (tptp.aTP_Lamm_bc A2) P))) (tptp.groups5754745047067104278omplex (tptp.aa_fun6813637976755515871omplex (tptp.aTP_Lamm_jp G) P) A2)))) (forall ((A2 tptp.set_nat) (G tptp.fun_nat_complex) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex G) (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bg A2) P))) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_fun8588439219086927967omplex (tptp.aTP_Lamm_jq G) P)) A2)))) (forall ((A2 tptp.set_int) (G tptp.fun_int_complex) (P tptp.fun_int_bool)) (=> (tptp.finite_finite_int A2) (= (tptp.groups3049146728041665814omplex G (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bh A2) P))) (tptp.groups3049146728041665814omplex (tptp.aa_fun3606824691168040799omplex (tptp.aTP_Lamm_jr G) P) A2)))) (forall ((A2 tptp.set_real) (G tptp.fun_real_real) (P tptp.fun_real_bool)) (=> (tptp.finite_finite_real A2) (= (tptp.groups8097168146408367636l_real G (tptp.collect_real (tptp.aa_fun6476784834714468668l_bool (tptp.aTP_Lamm_bc A2) P))) (tptp.groups8097168146408367636l_real (tptp.aa_fun6348708079608492509l_real (tptp.aTP_Lamm_js G) P) A2)))) (forall ((A2 tptp.set_int) (G tptp.fun_int_real) (P tptp.fun_int_bool)) (=> (tptp.finite_finite_int A2) (= (tptp.groups8778361861064173332t_real G (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bh A2) P))) (tptp.groups8778361861064173332t_real (tptp.aa_fun6974987029372589917t_real (tptp.aTP_Lamm_jt G) P) A2)))) (forall ((A2 tptp.set_complex) (G tptp.fun_complex_real) (P tptp.fun_complex_bool)) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5808333547571424918x_real G (tptp.collect_complex (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_be A2) P))) (tptp.groups5808333547571424918x_real (tptp.aa_fun2902006202505214429x_real (tptp.aTP_Lamm_ju G) P) A2)))) (forall ((A2 tptp.set_real) (G tptp.fun_real_rat) (P tptp.fun_real_bool)) (=> (tptp.finite_finite_real A2) (= (tptp.groups1300246762558778688al_rat G (tptp.collect_real (tptp.aa_fun6476784834714468668l_bool (tptp.aTP_Lamm_bc A2) P))) (tptp.groups1300246762558778688al_rat (tptp.aa_fun7219699593533116937al_rat (tptp.aTP_Lamm_jv G) P) A2)))) (forall ((A2 tptp.set_nat) (G tptp.fun_nat_rat) (P tptp.fun_nat_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (tptp.groups2906978787729119204at_rat G (tptp.collect_nat (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bg A2) P))) (tptp.groups2906978787729119204at_rat (tptp.aa_fun5656162108953708681at_rat (tptp.aTP_Lamm_jw G) P) A2)))) (forall ((A2 tptp.set_int) (G tptp.fun_int_rat) (P tptp.fun_int_bool)) (=> (tptp.finite_finite_int A2) (= (tptp.groups3906332499630173760nt_rat G (tptp.collect_int (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bh A2) P))) (tptp.groups3906332499630173760nt_rat (tptp.aa_fun4400602662665189257nt_rat (tptp.aTP_Lamm_jx G) P) A2)))) (forall ((A2 tptp.set_complex) (G tptp.fun_complex_rat) (P tptp.fun_complex_bool)) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5058264527183730370ex_rat G (tptp.collect_complex (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_be A2) P))) (tptp.groups5058264527183730370ex_rat (tptp.aa_fun5529999419959482889ex_rat (tptp.aTP_Lamm_jy G) P) A2)))) (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_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 ((S2 tptp.set_int) (T tptp.set_int) (G tptp.fun_int_real) (I2 tptp.fun_int_int) (F tptp.fun_int_real)) (=> (tptp.finite_finite_int S2) (=> (tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 T) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real G X3))))) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S2) (exists ((Xa tptp.int)) (and (tptp.member_int Xa T) (= (tptp.aa_int_int I2 Xa) X3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F X3)) (tptp.aa_int_real G Xa))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8778361861064173332t_real F S2)) (tptp.groups8778361861064173332t_real G T)))))))) (forall ((S2 tptp.set_int) (T tptp.set_complex) (G tptp.fun_complex_real) (I2 tptp.fun_complex_int) (F tptp.fun_int_real)) (=> (tptp.finite_finite_int S2) (=> (tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 T) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real G X3))))) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S2) (exists ((Xa tptp.complex)) (and (tptp.member_complex Xa T) (= (tptp.aa_complex_int I2 Xa) X3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F X3)) (tptp.aa_complex_real G Xa))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8778361861064173332t_real F S2)) (tptp.groups5808333547571424918x_real G T)))))))) (forall ((S2 tptp.set_complex) (T tptp.set_int) (G tptp.fun_int_real) (I2 tptp.fun_int_complex) (F tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex S2) (=> (tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 T) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real G X3))))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S2) (exists ((Xa tptp.int)) (and (tptp.member_int Xa T) (= (tptp.aa_int_complex I2 Xa) X3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F X3)) (tptp.aa_int_real G Xa))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups5808333547571424918x_real F S2)) (tptp.groups8778361861064173332t_real G T)))))))) (forall ((S2 tptp.set_complex) (T tptp.set_complex) (G tptp.fun_complex_real) (I2 tptp.fun_complex_complex) (F tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex S2) (=> (tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 T) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real G X3))))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S2) (exists ((Xa tptp.complex)) (and (tptp.member_complex Xa T) (= (tptp.aa_complex_complex I2 Xa) X3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F X3)) (tptp.aa_complex_real G Xa))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups5808333547571424918x_real F S2)) (tptp.groups5808333547571424918x_real G T)))))))) (forall ((S2 tptp.set_nat) (T tptp.set_nat) (G tptp.fun_nat_rat) (I2 tptp.fun_nat_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat G X3))))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S2)) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) T)) (= (tptp.aa_nat_nat I2 Xa) X3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F S2)) (tptp.groups2906978787729119204at_rat G T)))))))) (forall ((S2 tptp.set_nat) (T tptp.set_int) (G tptp.fun_int_rat) (I2 tptp.fun_int_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 T) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat G X3))))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S2)) (exists ((Xa tptp.int)) (and (tptp.member_int Xa T) (= (tptp.aa_int_nat I2 Xa) X3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_int_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F S2)) (tptp.groups3906332499630173760nt_rat G T)))))))) (forall ((S2 tptp.set_nat) (T tptp.set_complex) (G tptp.fun_complex_rat) (I2 tptp.fun_complex_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 T) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat G X3))))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S2)) (exists ((Xa tptp.complex)) (and (tptp.member_complex Xa T) (= (tptp.aa_complex_nat I2 Xa) X3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_complex_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F S2)) (tptp.groups5058264527183730370ex_rat G T)))))))) (forall ((S2 tptp.set_int) (T tptp.set_nat) (G tptp.fun_nat_rat) (I2 tptp.fun_nat_int) (F tptp.fun_int_rat)) (=> (tptp.finite_finite_int S2) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) T)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat G X3))))) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S2) (exists ((Xa tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa) T)) (= (tptp.aa_nat_int I2 Xa) X3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) (tptp.aa_nat_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F S2)) (tptp.groups2906978787729119204at_rat G T)))))))) (forall ((S2 tptp.set_int) (T tptp.set_int) (G tptp.fun_int_rat) (I2 tptp.fun_int_int) (F tptp.fun_int_rat)) (=> (tptp.finite_finite_int S2) (=> (tptp.finite_finite_int T) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 T) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat G X3))))) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S2) (exists ((Xa tptp.int)) (and (tptp.member_int Xa T) (= (tptp.aa_int_int I2 Xa) X3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F S2)) (tptp.groups3906332499630173760nt_rat G T)))))))) (forall ((S2 tptp.set_int) (T tptp.set_complex) (G tptp.fun_complex_rat) (I2 tptp.fun_complex_int) (F tptp.fun_int_rat)) (=> (tptp.finite_finite_int S2) (=> (tptp.finite3207457112153483333omplex T) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 T) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat G X3))))) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S2) (exists ((Xa tptp.complex)) (and (tptp.member_complex Xa T) (= (tptp.aa_complex_int I2 Xa) X3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) (tptp.aa_complex_rat G Xa))))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups3906332499630173760nt_rat F S2)) (tptp.groups5058264527183730370ex_rat G T)))))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real A2) (=> (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.zero_zero_real) (tptp.aa_real_real F X3))))) (= (= (tptp.groups8097168146408367636l_real F A2) tptp.zero_zero_real) (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A2) (= (tptp.aa_real_real F X4) tptp.zero_zero_real))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_real)) (=> (tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F X3))))) (= (= (tptp.groups8778361861064173332t_real F A2) tptp.zero_zero_real) (forall ((X4 tptp.int)) (=> (tptp.member_int X4 A2) (= (tptp.aa_int_real F X4) tptp.zero_zero_real))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F X3))))) (= (= (tptp.groups5808333547571424918x_real F A2) tptp.zero_zero_real) (forall ((X4 tptp.complex)) (=> (tptp.member_complex X4 A2) (= (tptp.aa_complex_real F X4) tptp.zero_zero_real))))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F X3))))) (= (= (tptp.groups1300246762558778688al_rat F A2) tptp.zero_zero_rat) (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A2) (= (tptp.aa_real_rat F X4) tptp.zero_zero_rat))))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F X3))))) (= (= (tptp.groups2906978787729119204at_rat F A2) tptp.zero_zero_rat) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A2)) (= (tptp.aa_nat_rat F X4) tptp.zero_zero_rat))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F X3))))) (= (= (tptp.groups3906332499630173760nt_rat F A2) tptp.zero_zero_rat) (forall ((X4 tptp.int)) (=> (tptp.member_int X4 A2) (= (tptp.aa_int_rat F X4) tptp.zero_zero_rat))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F X3))))) (= (= (tptp.groups5058264527183730370ex_rat F A2) tptp.zero_zero_rat) (forall ((X4 tptp.complex)) (=> (tptp.member_complex X4 A2) (= (tptp.aa_complex_rat F X4) tptp.zero_zero_rat))))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_nat)) (=> (tptp.finite_finite_real A2) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F X3))))) (= (= (tptp.groups1935376822645274424al_nat F A2) tptp.zero_zero_nat) (forall ((X4 tptp.real)) (=> (tptp.member_real X4 A2) (= (tptp.aa_real_nat F X4) tptp.zero_zero_nat))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F X3))))) (= (= (tptp.groups4541462559716669496nt_nat F A2) tptp.zero_zero_nat) (forall ((X4 tptp.int)) (=> (tptp.member_int X4 A2) (= (tptp.aa_int_nat F X4) tptp.zero_zero_nat))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F X3))))) (= (= (tptp.groups5693394587270226106ex_nat F A2) tptp.zero_zero_nat) (forall ((X4 tptp.complex)) (=> (tptp.member_complex X4 A2) (= (tptp.aa_complex_nat F X4) tptp.zero_zero_nat))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_real) (G tptp.fun_int_real)) (=> (tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F X3)) (tptp.aa_int_real G X3))))) (=> (exists ((X2 tptp.int)) (and (tptp.member_int X2 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X2)) (tptp.aa_int_real G X2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups8778361861064173332t_real F A2)) (tptp.groups8778361861064173332t_real G A2))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F X3)) (tptp.aa_complex_real G X3))))) (=> (exists ((X2 tptp.complex)) (and (tptp.member_complex X2 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real F X2)) (tptp.aa_complex_real G X2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups5808333547571424918x_real F A2)) (tptp.groups5808333547571424918x_real G A2))))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat G X3))))) (=> (exists ((X2 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X2) A2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X2)) (tptp.aa_nat_rat G X2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups2906978787729119204at_rat F A2)) (tptp.groups2906978787729119204at_rat G A2))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat G X3))))) (=> (exists ((X2 tptp.int)) (and (tptp.member_int X2 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X2)) (tptp.aa_int_rat G X2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups3906332499630173760nt_rat F A2)) (tptp.groups3906332499630173760nt_rat G A2))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F X3)) (tptp.aa_complex_rat G X3))))) (=> (exists ((X2 tptp.complex)) (and (tptp.member_complex X2 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_complex_rat F X2)) (tptp.aa_complex_rat G X2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups5058264527183730370ex_rat F A2)) (tptp.groups5058264527183730370ex_rat G A2))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F X3)) (tptp.aa_int_nat G X3))))) (=> (exists ((X2 tptp.int)) (and (tptp.member_int X2 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat F X2)) (tptp.aa_int_nat G X2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups4541462559716669496nt_nat F A2)) (tptp.groups4541462559716669496nt_nat G A2))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F X3)) (tptp.aa_complex_nat G X3))))) (=> (exists ((X2 tptp.complex)) (and (tptp.member_complex X2 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_complex_nat F X2)) (tptp.aa_complex_nat G X2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups5693394587270226106ex_nat F A2)) (tptp.groups5693394587270226106ex_nat G A2))))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F X3)) (tptp.aa_nat_int G X3))))) (=> (exists ((X2 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X2) A2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int F X2)) (tptp.aa_nat_int G X2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups3539618377306564664at_int F A2)) (tptp.groups3539618377306564664at_int G A2))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_int) (G tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex A2) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_complex_int F X3)) (tptp.aa_complex_int G X3))))) (=> (exists ((X2 tptp.complex)) (and (tptp.member_complex X2 A2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_complex_int F X2)) (tptp.aa_complex_int G X2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups5690904116761175830ex_int F A2)) (tptp.groups5690904116761175830ex_int G A2))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_int) (G tptp.fun_int_int)) (=> (tptp.finite_finite_int A2) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int F X3)) (tptp.aa_int_int G X3))))) (=> (exists ((X2 tptp.int)) (and (tptp.member_int X2 A2) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int F X2)) (tptp.aa_int_int G X2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups4538972089207619220nt_int F A2)) (tptp.groups4538972089207619220nt_int G A2))))))) (forall ((R tptp.fun_co1378794544173401837x_bool) (S3 tptp.set_nat) (H tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R tptp.zero_zero_complex) tptp.zero_zero_complex)) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R X15) X23)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R Y15) Y23))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X15) Y15)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X23) Y23))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S3)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R (tptp.aa_nat_complex H X3)) (tptp.aa_nat_complex G X3))))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex H) S3)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex G) S3)))))))) (forall ((R tptp.fun_co1378794544173401837x_bool) (S3 tptp.set_int) (H tptp.fun_int_complex) (G tptp.fun_int_complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R tptp.zero_zero_complex) tptp.zero_zero_complex)) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R X15) X23)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R Y15) Y23))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X15) Y15)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X23) Y23))))) (=> (tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S3) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R (tptp.aa_int_complex H X3)) (tptp.aa_int_complex G X3))))) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool R (tptp.groups3049146728041665814omplex H S3)) (tptp.groups3049146728041665814omplex G S3)))))))) (forall ((R tptp.fun_re1255401033344146673l_bool) (S3 tptp.set_int) (H tptp.fun_int_real) (G tptp.fun_int_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R tptp.zero_zero_real) tptp.zero_zero_real)) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R X15) X23)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R Y15) Y23))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X15) Y15)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X23) Y23))))) (=> (tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R (tptp.aa_int_real H X3)) (tptp.aa_int_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R (tptp.groups8778361861064173332t_real H S3)) (tptp.groups8778361861064173332t_real G S3)))))))) (forall ((R tptp.fun_re1255401033344146673l_bool) (S3 tptp.set_complex) (H tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R tptp.zero_zero_real) tptp.zero_zero_real)) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R X15) X23)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R Y15) Y23))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X15) Y15)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X23) Y23))))) (=> (tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R (tptp.aa_complex_real H X3)) (tptp.aa_complex_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool R (tptp.groups5808333547571424918x_real H S3)) (tptp.groups5808333547571424918x_real G S3)))))))) (forall ((R tptp.fun_rat_fun_rat_bool) (S3 tptp.set_nat) (H tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R tptp.zero_zero_rat) tptp.zero_zero_rat)) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R X15) X23)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R Y15) Y23))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_rat_rat (tptp.plus_plus_rat X15) Y15)) (tptp.aa_rat_rat (tptp.plus_plus_rat X23) Y23))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_nat_rat H X3)) (tptp.aa_nat_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.groups2906978787729119204at_rat H S3)) (tptp.groups2906978787729119204at_rat G S3)))))))) (forall ((R tptp.fun_rat_fun_rat_bool) (S3 tptp.set_int) (H tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R tptp.zero_zero_rat) tptp.zero_zero_rat)) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R X15) X23)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R Y15) Y23))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_rat_rat (tptp.plus_plus_rat X15) Y15)) (tptp.aa_rat_rat (tptp.plus_plus_rat X23) Y23))))) (=> (tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_int_rat H X3)) (tptp.aa_int_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.groups3906332499630173760nt_rat H S3)) (tptp.groups3906332499630173760nt_rat G S3)))))))) (forall ((R tptp.fun_rat_fun_rat_bool) (S3 tptp.set_complex) (H tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R tptp.zero_zero_rat) tptp.zero_zero_rat)) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R X15) X23)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R Y15) Y23))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_rat_rat (tptp.plus_plus_rat X15) Y15)) (tptp.aa_rat_rat (tptp.plus_plus_rat X23) Y23))))) (=> (tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.aa_complex_rat H X3)) (tptp.aa_complex_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool R (tptp.groups5058264527183730370ex_rat H S3)) (tptp.groups5058264527183730370ex_rat G S3)))))))) (forall ((R tptp.fun_nat_fun_nat_bool) (S3 tptp.set_int) (H tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R tptp.zero_zero_nat) tptp.zero_zero_nat)) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X15) X23)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R Y15) Y23))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X15) Y15)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X23) Y23))))) (=> (tptp.finite_finite_int S3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R (tptp.aa_int_nat H X3)) (tptp.aa_int_nat G X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R (tptp.groups4541462559716669496nt_nat H S3)) (tptp.groups4541462559716669496nt_nat G S3)))))))) (forall ((R tptp.fun_nat_fun_nat_bool) (S3 tptp.set_complex) (H tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R tptp.zero_zero_nat) tptp.zero_zero_nat)) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R X15) X23)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R Y15) Y23))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X15) Y15)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X23) Y23))))) (=> (tptp.finite3207457112153483333omplex S3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R (tptp.aa_complex_nat H X3)) (tptp.aa_complex_nat G X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R (tptp.groups5693394587270226106ex_nat H S3)) (tptp.groups5693394587270226106ex_nat G S3)))))))) (forall ((R tptp.fun_int_fun_int_bool) (S3 tptp.set_nat) (H tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R tptp.zero_zero_int) tptp.zero_zero_int)) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R X15) X23)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R Y15) Y23))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X15) Y15)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X23) Y23))))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R (tptp.aa_nat_int H X3)) (tptp.aa_nat_int G X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool R (tptp.groups3539618377306564664at_int H S3)) (tptp.groups3539618377306564664at_int G S3)))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real F X3)) (tptp.aa_complex_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups5808333547571424918x_real F A2)) (tptp.groups5808333547571424918x_real G A2))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_real) (G tptp.fun_int_real)) (=> (tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real F X3)) (tptp.aa_int_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups8778361861064173332t_real F A2)) (tptp.groups8778361861064173332t_real G A2))))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_real) (G tptp.fun_real_real)) (=> (tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X3)) (tptp.aa_real_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups8097168146408367636l_real F A2)) (tptp.groups8097168146408367636l_real G A2))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_complex_rat F X3)) (tptp.aa_complex_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups5058264527183730370ex_rat F A2)) (tptp.groups5058264527183730370ex_rat G A2))))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_rat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat F X3)) (tptp.aa_nat_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups2906978787729119204at_rat F A2)) (tptp.groups2906978787729119204at_rat G A2))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_rat) (G tptp.fun_int_rat)) (=> (tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_int_rat F X3)) (tptp.aa_int_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups3906332499630173760nt_rat F A2)) (tptp.groups3906332499630173760nt_rat G A2))))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_rat) (G tptp.fun_real_rat)) (=> (tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_real_rat F X3)) (tptp.aa_real_rat G X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups1300246762558778688al_rat F A2)) (tptp.groups1300246762558778688al_rat G A2))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_complex_nat F X3)) (tptp.aa_complex_nat G X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups5693394587270226106ex_nat F A2)) (tptp.groups5693394587270226106ex_nat G A2))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_nat) (G tptp.fun_int_nat)) (=> (tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat F X3)) (tptp.aa_int_nat G X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups4541462559716669496nt_nat F A2)) (tptp.groups4541462559716669496nt_nat G A2))))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_nat) (G tptp.fun_real_nat)) (=> (tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_real_nat F X3)) (tptp.aa_real_nat G X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups1935376822645274424al_nat F A2)) (tptp.groups1935376822645274424al_nat G A2))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.ln_ln_real X)) X)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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 ((S4 tptp.set_real) (T4 tptp.set_real) (S3 tptp.set_real) (I2 tptp.fun_real_real) (J tptp.fun_real_real) (T3 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real S4) (=> (tptp.finite_finite_real T4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (= (tptp.aa_real_real I2 (tptp.aa_real_real J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (tptp.member_real (tptp.aa_real_real J A3) (tptp.minus_minus_set_real T3 T4)))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real T3 T4)) (= (tptp.aa_real_real J (tptp.aa_real_real I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real T3 T4)) (tptp.member_real (tptp.aa_real_real I2 B2) (tptp.minus_minus_set_real S3 S4)))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S4) (= (tptp.aa_real_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 T4) (= (tptp.aa_real_complex H B2) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S3) (= (tptp.aa_real_complex H (tptp.aa_real_real J A3)) (tptp.aa_real_complex G A3)))) (= (tptp.groups5754745047067104278omplex G S3) (tptp.groups5754745047067104278omplex H T3)))))))))))) (forall ((S4 tptp.set_real) (T4 tptp.set_int) (S3 tptp.set_real) (I2 tptp.fun_int_real) (J tptp.fun_real_int) (T3 tptp.set_int) (G tptp.fun_real_complex) (H tptp.fun_int_complex)) (=> (tptp.finite_finite_real S4) (=> (tptp.finite_finite_int T4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (= (tptp.aa_int_real I2 (tptp.aa_real_int J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (tptp.member_int (tptp.aa_real_int J A3) (tptp.minus_minus_set_int T3 T4)))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 (tptp.minus_minus_set_int T3 T4)) (= (tptp.aa_real_int J (tptp.aa_int_real I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 (tptp.minus_minus_set_int T3 T4)) (tptp.member_real (tptp.aa_int_real I2 B2) (tptp.minus_minus_set_real S3 S4)))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S4) (= (tptp.aa_real_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 T4) (= (tptp.aa_int_complex H B2) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S3) (= (tptp.aa_int_complex H (tptp.aa_real_int J A3)) (tptp.aa_real_complex G A3)))) (= (tptp.groups5754745047067104278omplex G S3) (tptp.groups3049146728041665814omplex H T3)))))))))))) (forall ((S4 tptp.set_int) (T4 tptp.set_real) (S3 tptp.set_int) (I2 tptp.fun_real_int) (J tptp.fun_int_real) (T3 tptp.set_real) (G tptp.fun_int_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_int S4) (=> (tptp.finite_finite_real T4) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (= (tptp.aa_real_int I2 (tptp.aa_int_real J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (tptp.member_real (tptp.aa_int_real J A3) (tptp.minus_minus_set_real T3 T4)))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real T3 T4)) (= (tptp.aa_int_real J (tptp.aa_real_int I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real T3 T4)) (tptp.member_int (tptp.aa_real_int I2 B2) (tptp.minus_minus_set_int S3 S4)))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S4) (= (tptp.aa_int_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 T4) (= (tptp.aa_real_complex H B2) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S3) (= (tptp.aa_real_complex H (tptp.aa_int_real J A3)) (tptp.aa_int_complex G A3)))) (= (tptp.groups3049146728041665814omplex G S3) (tptp.groups5754745047067104278omplex H T3)))))))))))) (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S3 tptp.set_int) (I2 tptp.fun_int_int) (J tptp.fun_int_int) (T3 tptp.set_int) (G tptp.fun_int_complex) (H tptp.fun_int_complex)) (=> (tptp.finite_finite_int S4) (=> (tptp.finite_finite_int T4) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (= (tptp.aa_int_int I2 (tptp.aa_int_int J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (tptp.member_int (tptp.aa_int_int J A3) (tptp.minus_minus_set_int T3 T4)))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 (tptp.minus_minus_set_int T3 T4)) (= (tptp.aa_int_int J (tptp.aa_int_int I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 (tptp.minus_minus_set_int T3 T4)) (tptp.member_int (tptp.aa_int_int I2 B2) (tptp.minus_minus_set_int S3 S4)))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S4) (= (tptp.aa_int_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 T4) (= (tptp.aa_int_complex H B2) tptp.zero_zero_complex))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S3) (= (tptp.aa_int_complex H (tptp.aa_int_int J A3)) (tptp.aa_int_complex G A3)))) (= (tptp.groups3049146728041665814omplex G S3) (tptp.groups3049146728041665814omplex H T3)))))))))))) (forall ((S4 tptp.set_real) (T4 tptp.set_real) (S3 tptp.set_real) (I2 tptp.fun_real_real) (J tptp.fun_real_real) (T3 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real S4) (=> (tptp.finite_finite_real T4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (= (tptp.aa_real_real I2 (tptp.aa_real_real J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (tptp.member_real (tptp.aa_real_real J A3) (tptp.minus_minus_set_real T3 T4)))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real T3 T4)) (= (tptp.aa_real_real J (tptp.aa_real_real I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real T3 T4)) (tptp.member_real (tptp.aa_real_real I2 B2) (tptp.minus_minus_set_real S3 S4)))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S4) (= (tptp.aa_real_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 T4) (= (tptp.aa_real_real H B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S3) (= (tptp.aa_real_real H (tptp.aa_real_real J A3)) (tptp.aa_real_real G A3)))) (= (tptp.groups8097168146408367636l_real G S3) (tptp.groups8097168146408367636l_real H T3)))))))))))) (forall ((S4 tptp.set_real) (T4 tptp.set_int) (S3 tptp.set_real) (I2 tptp.fun_int_real) (J tptp.fun_real_int) (T3 tptp.set_int) (G tptp.fun_real_real) (H tptp.fun_int_real)) (=> (tptp.finite_finite_real S4) (=> (tptp.finite_finite_int T4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (= (tptp.aa_int_real I2 (tptp.aa_real_int J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (tptp.member_int (tptp.aa_real_int J A3) (tptp.minus_minus_set_int T3 T4)))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 (tptp.minus_minus_set_int T3 T4)) (= (tptp.aa_real_int J (tptp.aa_int_real I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 (tptp.minus_minus_set_int T3 T4)) (tptp.member_real (tptp.aa_int_real I2 B2) (tptp.minus_minus_set_real S3 S4)))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S4) (= (tptp.aa_real_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 T4) (= (tptp.aa_int_real H B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S3) (= (tptp.aa_int_real H (tptp.aa_real_int J A3)) (tptp.aa_real_real G A3)))) (= (tptp.groups8097168146408367636l_real G S3) (tptp.groups8778361861064173332t_real H T3)))))))))))) (forall ((S4 tptp.set_real) (T4 tptp.set_complex) (S3 tptp.set_real) (I2 tptp.fun_complex_real) (J tptp.fun_real_complex) (T3 tptp.set_complex) (G tptp.fun_real_real) (H tptp.fun_complex_real)) (=> (tptp.finite_finite_real S4) (=> (tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (= (tptp.aa_complex_real I2 (tptp.aa_real_complex J A3)) A3))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real S3 S4)) (tptp.member_complex (tptp.aa_real_complex J A3) (tptp.minus_811609699411566653omplex T3 T4)))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex T3 T4)) (= (tptp.aa_real_complex J (tptp.aa_complex_real I2 B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex T3 T4)) (tptp.member_real (tptp.aa_complex_real I2 B2) (tptp.minus_minus_set_real S3 S4)))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S4) (= (tptp.aa_real_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 T4) (= (tptp.aa_complex_real H B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 S3) (= (tptp.aa_complex_real H (tptp.aa_real_complex J A3)) (tptp.aa_real_real G A3)))) (= (tptp.groups8097168146408367636l_real G S3) (tptp.groups5808333547571424918x_real H T3)))))))))))) (forall ((S4 tptp.set_int) (T4 tptp.set_real) (S3 tptp.set_int) (I2 tptp.fun_real_int) (J tptp.fun_int_real) (T3 tptp.set_real) (G tptp.fun_int_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_int S4) (=> (tptp.finite_finite_real T4) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (= (tptp.aa_real_int I2 (tptp.aa_int_real J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (tptp.member_real (tptp.aa_int_real J A3) (tptp.minus_minus_set_real T3 T4)))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real T3 T4)) (= (tptp.aa_int_real J (tptp.aa_real_int I2 B2)) B2))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real T3 T4)) (tptp.member_int (tptp.aa_real_int I2 B2) (tptp.minus_minus_set_int S3 S4)))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S4) (= (tptp.aa_int_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 T4) (= (tptp.aa_real_real H B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S3) (= (tptp.aa_real_real H (tptp.aa_int_real J A3)) (tptp.aa_int_real G A3)))) (= (tptp.groups8778361861064173332t_real G S3) (tptp.groups8097168146408367636l_real H T3)))))))))))) (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S3 tptp.set_int) (I2 tptp.fun_int_int) (J tptp.fun_int_int) (T3 tptp.set_int) (G tptp.fun_int_real) (H tptp.fun_int_real)) (=> (tptp.finite_finite_int S4) (=> (tptp.finite_finite_int T4) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (= (tptp.aa_int_int I2 (tptp.aa_int_int J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (tptp.member_int (tptp.aa_int_int J A3) (tptp.minus_minus_set_int T3 T4)))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 (tptp.minus_minus_set_int T3 T4)) (= (tptp.aa_int_int J (tptp.aa_int_int I2 B2)) B2))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 (tptp.minus_minus_set_int T3 T4)) (tptp.member_int (tptp.aa_int_int I2 B2) (tptp.minus_minus_set_int S3 S4)))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S4) (= (tptp.aa_int_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.int)) (=> (tptp.member_int B2 T4) (= (tptp.aa_int_real H B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S3) (= (tptp.aa_int_real H (tptp.aa_int_int J A3)) (tptp.aa_int_real G A3)))) (= (tptp.groups8778361861064173332t_real G S3) (tptp.groups8778361861064173332t_real H T3)))))))))))) (forall ((S4 tptp.set_int) (T4 tptp.set_complex) (S3 tptp.set_int) (I2 tptp.fun_complex_int) (J tptp.fun_int_complex) (T3 tptp.set_complex) (G tptp.fun_int_real) (H tptp.fun_complex_real)) (=> (tptp.finite_finite_int S4) (=> (tptp.finite3207457112153483333omplex T4) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (= (tptp.aa_complex_int I2 (tptp.aa_int_complex J A3)) A3))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 (tptp.minus_minus_set_int S3 S4)) (tptp.member_complex (tptp.aa_int_complex J A3) (tptp.minus_811609699411566653omplex T3 T4)))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex T3 T4)) (= (tptp.aa_int_complex J (tptp.aa_complex_int I2 B2)) B2))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex T3 T4)) (tptp.member_int (tptp.aa_complex_int I2 B2) (tptp.minus_minus_set_int S3 S4)))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S4) (= (tptp.aa_int_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 T4) (= (tptp.aa_complex_real H B2) tptp.zero_zero_real))) (=> (forall ((A3 tptp.int)) (=> (tptp.member_int A3 S3) (= (tptp.aa_complex_real H (tptp.aa_int_complex J A3)) (tptp.aa_int_real G A3)))) (= (tptp.groups8778361861064173332t_real G S3) (tptp.groups5808333547571424918x_real H T3)))))))))))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))) tptp.zero_zero_real))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat))) (forall ((N2 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 N2))) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2)))))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))))) (forall ((N2 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 N2)))))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))) tptp.zero_zero_real))) (forall ((N2 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 N2))) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2)))))) (forall ((N2 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 N2)))))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat N2)))))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2)))))) (not (tptp.pp (tptp.aa_real_bool _let_71 _let_53))) (not (tptp.pp (tptp.aa_Code_integer_bool _let_36 _let_77))) (not (tptp.pp (tptp.aa_rat_bool _let_102 _let_78))) (not (tptp.pp (tptp.aa_int_bool _let_101 _let_79))) (tptp.pp (tptp.aa_real_bool _let_100 tptp.zero_zero_real)) (tptp.pp (tptp.aa_Code_integer_bool _let_99 tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_rat_bool _let_98 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_int_bool _let_97 tptp.zero_zero_int)) (not (tptp.pp (tptp.aa_real_bool _let_72 _let_53))) (not (tptp.pp (tptp.aa_int_bool _let_96 _let_79))) (not (tptp.pp (tptp.aa_rat_bool _let_95 _let_78))) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) _let_77))) (tptp.pp (tptp.aa_real_bool _let_94 tptp.zero_zero_real)) (tptp.pp (tptp.aa_int_bool _let_93 tptp.zero_zero_int)) (tptp.pp (tptp.aa_rat_bool _let_92 tptp.zero_zero_rat)) (tptp.pp (tptp.aa_Code_integer_bool _let_91 tptp.zero_z3403309356797280102nteger)) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) tptp.one_one_real))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) tptp.one_one_rat))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) tptp.one_one_int))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_num_real tptp.numeral_numeral_real M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M))) tptp.one_one_real))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) tptp.one_one_int))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M))) tptp.one_one_rat))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_num_real tptp.numeral_numeral_real M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat M)))) (forall ((M tptp.num)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real M)) (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat M)))))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))))) (forall ((B tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real tptp.one))) B) (tptp.aa_real_real tptp.uminus_uminus_real B))) (forall ((B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) B) (tptp.aa_int_int tptp.uminus_uminus_int B))) (forall ((B tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex tptp.one))) B) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one))) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (forall ((B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one))) 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.aa_num_real tptp.numeral_numeral_real tptp.one))) (tptp.aa_real_real tptp.uminus_uminus_real B))) (forall ((B tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one))) (tptp.aa_int_int tptp.uminus_uminus_int B))) (forall ((B tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex tptp.one))) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.rat)) (= (tptp.aa_rat_rat (tptp.times_times_rat B) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat tptp.one))) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (forall ((B tptp.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger B) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one))) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) B) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C) B) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B))) (= (tptp.aa_rat_rat (tptp.times_times_rat C) B) (tptp.aa_rat_rat 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.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) C) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C) B))))) (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) C) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat A) (tptp.aa_rat_rat (tptp.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.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) A) (and (=> (not _let_1) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat B) (tptp.aa_rat_rat (tptp.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.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C))) (and (=> (not _let_1) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (tptp.aa_rat_rat (tptp.times_times_rat A) C) (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))) (= (tptp.aa_real_real tptp.uminus_uminus_real _let_90) _let_53) (= (tptp.aa_int_int tptp.uminus_uminus_int _let_89) _let_79) (= (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_88) _let_50) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_87) _let_78) (= (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)) _let_77) (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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B))))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat A) B) (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B))))) (forall ((A tptp.real) (N2 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)) N2) (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)) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N2) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (tptp.aa_nat_rat (tptp.power_power_rat A) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)))) (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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int X)) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) _let_1) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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.aa_rat_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.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)))) (forall ((S2 tptp.set_real) (F tptp.fun_real_real) (B3 tptp.real) (I2 tptp.real)) (=> (tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F I3))))) (=> (= (tptp.groups8097168146408367636l_real F S2) B3) (=> (tptp.member_real I2 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F I2)) B3))))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_real) (B3 tptp.real) (I2 tptp.int)) (=> (tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F I3))))) (=> (= (tptp.groups8778361861064173332t_real F S2) B3) (=> (tptp.member_int I2 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real F I2)) B3))))))) (forall ((S2 tptp.set_complex) (F tptp.fun_complex_real) (B3 tptp.real) (I2 tptp.complex)) (=> (tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F I3))))) (=> (= (tptp.groups5808333547571424918x_real F S2) B3) (=> (tptp.member_complex I2 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real F I2)) B3))))))) (forall ((S2 tptp.set_real) (F tptp.fun_real_rat) (B3 tptp.rat) (I2 tptp.real)) (=> (tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F I3))))) (=> (= (tptp.groups1300246762558778688al_rat F S2) B3) (=> (tptp.member_real I2 S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_real_rat F I2)) B3))))))) (forall ((S2 tptp.set_nat) (F tptp.fun_nat_rat) (B3 tptp.rat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (=> (= (tptp.groups2906978787729119204at_rat F S2) B3) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F I2)) B3))))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_rat) (B3 tptp.rat) (I2 tptp.int)) (=> (tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (=> (= (tptp.groups3906332499630173760nt_rat F S2) B3) (=> (tptp.member_int I2 S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat F I2)) B3))))))) (forall ((S2 tptp.set_complex) (F tptp.fun_complex_rat) (B3 tptp.rat) (I2 tptp.complex)) (=> (tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F I3))))) (=> (= (tptp.groups5058264527183730370ex_rat F S2) B3) (=> (tptp.member_complex I2 S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_complex_rat F I2)) B3))))))) (forall ((S2 tptp.set_real) (F tptp.fun_real_nat) (B3 tptp.nat) (I2 tptp.real)) (=> (tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F I3))))) (=> (= (tptp.groups1935376822645274424al_nat F S2) B3) (=> (tptp.member_real I2 S2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat F I2)) B3))))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_nat) (B3 tptp.nat) (I2 tptp.int)) (=> (tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 S2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (=> (= (tptp.groups4541462559716669496nt_nat F S2) B3) (=> (tptp.member_int I2 S2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat F I2)) B3))))))) (forall ((S2 tptp.set_complex) (F tptp.fun_complex_nat) (B3 tptp.nat) (I2 tptp.complex)) (=> (tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 S2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F I3))))) (=> (= (tptp.groups5693394587270226106ex_nat F S2) B3) (=> (tptp.member_complex I2 S2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat F I2)) B3))))))) (forall ((S2 tptp.set_real) (F tptp.fun_real_real) (I2 tptp.real)) (=> (tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F I3))))) (=> (= (tptp.groups8097168146408367636l_real F S2) tptp.zero_zero_real) (=> (tptp.member_real I2 S2) (= (tptp.aa_real_real F I2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_real) (I2 tptp.int)) (=> (tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F I3))))) (=> (= (tptp.groups8778361861064173332t_real F S2) tptp.zero_zero_real) (=> (tptp.member_int I2 S2) (= (tptp.aa_int_real F I2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_complex) (F tptp.fun_complex_real) (I2 tptp.complex)) (=> (tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 S2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F I3))))) (=> (= (tptp.groups5808333547571424918x_real F S2) tptp.zero_zero_real) (=> (tptp.member_complex I2 S2) (= (tptp.aa_complex_real F I2) tptp.zero_zero_real)))))) (forall ((S2 tptp.set_real) (F tptp.fun_real_rat) (I2 tptp.real)) (=> (tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F I3))))) (=> (= (tptp.groups1300246762558778688al_rat F S2) tptp.zero_zero_rat) (=> (tptp.member_real I2 S2) (= (tptp.aa_real_rat F I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_nat) (F tptp.fun_nat_rat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S2)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) S2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (=> (= (tptp.groups2906978787729119204at_rat F S2) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) S2)) (= (tptp.aa_nat_rat F I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_rat) (I2 tptp.int)) (=> (tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (=> (= (tptp.groups3906332499630173760nt_rat F S2) tptp.zero_zero_rat) (=> (tptp.member_int I2 S2) (= (tptp.aa_int_rat F I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_complex) (F tptp.fun_complex_rat) (I2 tptp.complex)) (=> (tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 S2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F I3))))) (=> (= (tptp.groups5058264527183730370ex_rat F S2) tptp.zero_zero_rat) (=> (tptp.member_complex I2 S2) (= (tptp.aa_complex_rat F I2) tptp.zero_zero_rat)))))) (forall ((S2 tptp.set_real) (F tptp.fun_real_nat) (I2 tptp.real)) (=> (tptp.finite_finite_real S2) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 S2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F I3))))) (=> (= (tptp.groups1935376822645274424al_nat F S2) tptp.zero_zero_nat) (=> (tptp.member_real I2 S2) (= (tptp.aa_real_nat F I2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_int) (F tptp.fun_int_nat) (I2 tptp.int)) (=> (tptp.finite_finite_int S2) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 S2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (=> (= (tptp.groups4541462559716669496nt_nat F S2) tptp.zero_zero_nat) (=> (tptp.member_int I2 S2) (= (tptp.aa_int_nat F I2) tptp.zero_zero_nat)))))) (forall ((S2 tptp.set_complex) (F tptp.fun_complex_nat) (I2 tptp.complex)) (=> (tptp.finite3207457112153483333omplex S2) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 S2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F I3))))) (=> (= (tptp.groups5693394587270226106ex_nat F S2) tptp.zero_zero_nat) (=> (tptp.member_complex I2 S2) (= (tptp.aa_complex_nat F I2) tptp.zero_zero_nat)))))) (forall ((A2 tptp.set_int) (G tptp.fun_int_complex)) (=> (tptp.finite_finite_int A2) (= (tptp.groups3049146728041665814omplex G (tptp.minus_minus_set_int A2 (tptp.collect_int (tptp.aTP_Lamm_jz G)))) (tptp.groups3049146728041665814omplex G A2)))) (forall ((A2 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.finite_finite_int A2) (= (tptp.groups8778361861064173332t_real G (tptp.minus_minus_set_int A2 (tptp.collect_int (tptp.aTP_Lamm_ka G)))) (tptp.groups8778361861064173332t_real G A2)))) (forall ((A2 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5808333547571424918x_real G (tptp.minus_811609699411566653omplex A2 (tptp.collect_complex (tptp.aTP_Lamm_kb G)))) (tptp.groups5808333547571424918x_real G A2)))) (forall ((A2 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.finite_finite_int A2) (= (tptp.groups3906332499630173760nt_rat G (tptp.minus_minus_set_int A2 (tptp.collect_int (tptp.aTP_Lamm_kc G)))) (tptp.groups3906332499630173760nt_rat G A2)))) (forall ((A2 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5058264527183730370ex_rat G (tptp.minus_811609699411566653omplex A2 (tptp.collect_complex (tptp.aTP_Lamm_kd G)))) (tptp.groups5058264527183730370ex_rat G A2)))) (forall ((A2 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.finite_finite_int A2) (= (tptp.groups4541462559716669496nt_nat G (tptp.minus_minus_set_int A2 (tptp.collect_int (tptp.aTP_Lamm_ke G)))) (tptp.groups4541462559716669496nt_nat G A2)))) (forall ((A2 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5693394587270226106ex_nat G (tptp.minus_811609699411566653omplex A2 (tptp.collect_complex (tptp.aTP_Lamm_kf G)))) (tptp.groups5693394587270226106ex_nat G A2)))) (forall ((A2 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5690904116761175830ex_int G (tptp.minus_811609699411566653omplex A2 (tptp.collect_complex (tptp.aTP_Lamm_kg G)))) (tptp.groups5690904116761175830ex_int G A2)))) (forall ((A2 tptp.set_nat) (G tptp.fun_nat_complex)) (let ((_let_1 (tptp.groups2073611262835488442omplex G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (tptp.aa_set_nat_complex _let_1 (tptp.minus_minus_set_nat A2 (tptp.collect_nat (tptp.aTP_Lamm_kh G)))) (tptp.aa_set_nat_complex _let_1 A2))))) (forall ((A2 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (tptp.groups2906978787729119204at_rat G (tptp.minus_minus_set_nat A2 (tptp.collect_nat (tptp.aTP_Lamm_ki G)))) (tptp.groups2906978787729119204at_rat G A2)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A))) (let ((_let_2 (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 (= _let_2 tptp.zero_zero_int))) (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) B))))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A) B))) (let ((_let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int 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 ((I6 tptp.set_real) (I2 tptp.real) (F tptp.fun_real_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.finite_finite_real I6) (=> (tptp.member_real I2 I6) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real F I2))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups8097168146408367636l_real F I6))))))))) (forall ((I6 tptp.set_int) (I2 tptp.int) (F tptp.fun_int_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.finite_finite_int I6) (=> (tptp.member_int I2 I6) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_int_real F I2))) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups8778361861064173332t_real F I6))))))))) (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F tptp.fun_complex_real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.finite3207457112153483333omplex I6) (=> (tptp.member_complex I2 I6) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real F I2))) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F I3))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.groups5808333547571424918x_real F I6))))))))) (forall ((I6 tptp.set_real) (I2 tptp.real) (F tptp.fun_real_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.finite_finite_real I6) (=> (tptp.member_real I2 I6) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_real_rat F I2))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups1300246762558778688al_rat F I6))))))))) (forall ((I6 tptp.set_nat) (I2 tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I6)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) I6)) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_nat_rat F I2))) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups2906978787729119204at_rat F I6))))))))) (forall ((I6 tptp.set_int) (I2 tptp.int) (F tptp.fun_int_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.finite_finite_int I6) (=> (tptp.member_int I2 I6) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_int_rat F I2))) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups3906332499630173760nt_rat F I6))))))))) (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F tptp.fun_complex_rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (=> (tptp.finite3207457112153483333omplex I6) (=> (tptp.member_complex I2 I6) (=> (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_complex_rat F I2))) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F I3))))) (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.groups5058264527183730370ex_rat F I6))))))))) (forall ((I6 tptp.set_real) (I2 tptp.real) (F tptp.fun_real_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.finite_finite_real I6) (=> (tptp.member_real I2 I6) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_real_nat F I2))) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F I3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups1935376822645274424al_nat F I6))))))))) (forall ((I6 tptp.set_int) (I2 tptp.int) (F tptp.fun_int_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.finite_finite_int I6) (=> (tptp.member_int I2 I6) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_int_nat F I2))) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups4541462559716669496nt_nat F I6))))))))) (forall ((I6 tptp.set_complex) (I2 tptp.complex) (F tptp.fun_complex_nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.finite3207457112153483333omplex I6) (=> (tptp.member_complex I2 I6) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_complex_nat F I2))) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F I3))))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.groups5693394587270226106ex_nat F I6))))))))) (forall ((I6 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_complex_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.groups5808333547571424918x_real F I6))))))) (forall ((I6 tptp.set_int) (F tptp.fun_int_real)) (=> (tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_int_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.groups8778361861064173332t_real F I6))))))) (forall ((I6 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F I3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.groups8097168146408367636l_real F I6))))))) (forall ((I6 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups5058264527183730370ex_rat F I6))))))) (forall ((I6 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I6)) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups2906978787729119204at_rat F I6))))))) (forall ((I6 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_int_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups3906332499630173760nt_rat F I6))))))) (forall ((I6 tptp.set_real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_real_rat F I3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.groups1300246762558778688al_rat F I6))))))) (forall ((I6 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups5693394587270226106ex_nat F I6))))))) (forall ((I6 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_int_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups4541462559716669496nt_nat F I6))))))) (forall ((I6 tptp.set_real) (F tptp.fun_real_nat)) (=> (tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_real_nat F I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.groups1935376822645274424al_nat F I6))))))) (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 ((T3 tptp.set_real) (S3 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_complex G X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_complex G X3) (tptp.aa_real_complex H X3)))) (= (tptp.groups5754745047067104278omplex G T3) (tptp.groups5754745047067104278omplex H S3))))))) (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_real G X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_real G X3) (tptp.aa_real_real H X3)))) (= (tptp.groups8097168146408367636l_real G T3) (tptp.groups8097168146408367636l_real H S3))))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_real) (H tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_real G X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (= (tptp.aa_complex_real G X3) (tptp.aa_complex_real H X3)))) (= (tptp.groups5808333547571424918x_real G T3) (tptp.groups5808333547571424918x_real H S3))))))) (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G tptp.fun_real_rat) (H tptp.fun_real_rat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_rat G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_rat G X3) (tptp.aa_real_rat H X3)))) (= (tptp.groups1300246762558778688al_rat G T3) (tptp.groups1300246762558778688al_rat H S3))))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_rat) (H tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_rat G X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (= (tptp.aa_complex_rat G X3) (tptp.aa_complex_rat H X3)))) (= (tptp.groups5058264527183730370ex_rat G T3) (tptp.groups5058264527183730370ex_rat H S3))))))) (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G tptp.fun_real_nat) (H tptp.fun_real_nat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_nat G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_nat G X3) (tptp.aa_real_nat H X3)))) (= (tptp.groups1935376822645274424al_nat G T3) (tptp.groups1935376822645274424al_nat H S3))))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_nat) (H tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_nat G X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (= (tptp.aa_complex_nat G X3) (tptp.aa_complex_nat H X3)))) (= (tptp.groups5693394587270226106ex_nat G T3) (tptp.groups5693394587270226106ex_nat H S3))))))) (forall ((T3 tptp.set_real) (S3 tptp.set_real) (G tptp.fun_real_int) (H tptp.fun_real_int)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_int G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_int G X3) (tptp.aa_real_int H X3)))) (= (tptp.groups1932886352136224148al_int G T3) (tptp.groups1932886352136224148al_int H S3))))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_int) (H tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_int G X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (= (tptp.aa_complex_int G X3) (tptp.aa_complex_int H X3)))) (= (tptp.groups5690904116761175830ex_int G T3) (tptp.groups5690904116761175830ex_int H S3))))))) (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) T3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.minus_minus_set_nat T3 S3))) (= (tptp.aa_nat_complex G X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S3)) (= (tptp.aa_nat_complex G X3) (tptp.aa_nat_complex H X3)))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex G) T3) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex H) S3))))))) (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H tptp.fun_real_complex) (G tptp.fun_real_complex)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_complex H X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_complex G X3) (tptp.aa_real_complex H X3)))) (= (tptp.groups5754745047067104278omplex G S3) (tptp.groups5754745047067104278omplex H T3))))))) (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H tptp.fun_real_real) (G tptp.fun_real_real)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_real H X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_real G X3) (tptp.aa_real_real H X3)))) (= (tptp.groups8097168146408367636l_real G S3) (tptp.groups8097168146408367636l_real H T3))))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H tptp.fun_complex_real) (G tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_real H X3) tptp.zero_zero_real))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (= (tptp.aa_complex_real G X3) (tptp.aa_complex_real H X3)))) (= (tptp.groups5808333547571424918x_real G S3) (tptp.groups5808333547571424918x_real H T3))))))) (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H tptp.fun_real_rat) (G tptp.fun_real_rat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_rat H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_rat G X3) (tptp.aa_real_rat H X3)))) (= (tptp.groups1300246762558778688al_rat G S3) (tptp.groups1300246762558778688al_rat H T3))))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H tptp.fun_complex_rat) (G tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_rat H X3) tptp.zero_zero_rat))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (= (tptp.aa_complex_rat G X3) (tptp.aa_complex_rat H X3)))) (= (tptp.groups5058264527183730370ex_rat G S3) (tptp.groups5058264527183730370ex_rat H T3))))))) (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H tptp.fun_real_nat) (G tptp.fun_real_nat)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_nat H X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_nat G X3) (tptp.aa_real_nat H X3)))) (= (tptp.groups1935376822645274424al_nat G S3) (tptp.groups1935376822645274424al_nat H T3))))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H tptp.fun_complex_nat) (G tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_nat H X3) tptp.zero_zero_nat))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (= (tptp.aa_complex_nat G X3) (tptp.aa_complex_nat H X3)))) (= (tptp.groups5693394587270226106ex_nat G S3) (tptp.groups5693394587270226106ex_nat H T3))))))) (forall ((T3 tptp.set_real) (S3 tptp.set_real) (H tptp.fun_real_int) (G tptp.fun_real_int)) (=> (tptp.finite_finite_real T3) (=> (tptp.ord_less_eq_set_real S3 T3) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.minus_minus_set_real T3 S3)) (= (tptp.aa_real_int H X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (= (tptp.aa_real_int G X3) (tptp.aa_real_int H X3)))) (= (tptp.groups1932886352136224148al_int G S3) (tptp.groups1932886352136224148al_int H T3))))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (H tptp.fun_complex_int) (G tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_int H X3) tptp.zero_zero_int))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (= (tptp.aa_complex_int G X3) (tptp.aa_complex_int H X3)))) (= (tptp.groups5690904116761175830ex_int G S3) (tptp.groups5690904116761175830ex_int H T3))))))) (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (H tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) T3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.minus_minus_set_nat T3 S3))) (= (tptp.aa_nat_complex H X3) tptp.zero_zero_complex))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S3)) (= (tptp.aa_nat_complex G X3) (tptp.aa_nat_complex H X3)))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex G) S3) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex H) T3))))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_real G X3) tptp.zero_zero_real))) (= (tptp.groups5808333547571424918x_real G T3) (tptp.groups5808333547571424918x_real G S3)))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups5058264527183730370ex_rat G T3) (tptp.groups5058264527183730370ex_rat G S3)))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_nat G X3) tptp.zero_zero_nat))) (= (tptp.groups5693394587270226106ex_nat G T3) (tptp.groups5693394587270226106ex_nat G S3)))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_int G X3) tptp.zero_zero_int))) (= (tptp.groups5690904116761175830ex_int G T3) (tptp.groups5690904116761175830ex_int G S3)))))) (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G tptp.fun_nat_complex)) (let ((_let_1 (tptp.groups2073611262835488442omplex G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) T3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.minus_minus_set_nat T3 S3))) (= (tptp.aa_nat_complex G X3) tptp.zero_zero_complex))) (= (tptp.aa_set_nat_complex _let_1 T3) (tptp.aa_set_nat_complex _let_1 S3))))))) (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) T3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.minus_minus_set_nat T3 S3))) (= (tptp.aa_nat_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups2906978787729119204at_rat G T3) (tptp.groups2906978787729119204at_rat G S3)))))) (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) T3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.minus_minus_set_nat T3 S3))) (= (tptp.aa_nat_int G X3) tptp.zero_zero_int))) (= (tptp.groups3539618377306564664at_int G T3) (tptp.groups3539618377306564664at_int G S3)))))) (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G tptp.fun_int_complex)) (=> (tptp.finite_finite_int T3) (=> (tptp.ord_less_eq_set_int S3 T3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.minus_minus_set_int T3 S3)) (= (tptp.aa_int_complex G X3) tptp.zero_zero_complex))) (= (tptp.groups3049146728041665814omplex G T3) (tptp.groups3049146728041665814omplex G S3)))))) (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.finite_finite_int T3) (=> (tptp.ord_less_eq_set_int S3 T3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.minus_minus_set_int T3 S3)) (= (tptp.aa_int_real G X3) tptp.zero_zero_real))) (= (tptp.groups8778361861064173332t_real G T3) (tptp.groups8778361861064173332t_real G S3)))))) (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.finite_finite_int T3) (=> (tptp.ord_less_eq_set_int S3 T3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.minus_minus_set_int T3 S3)) (= (tptp.aa_int_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups3906332499630173760nt_rat G T3) (tptp.groups3906332499630173760nt_rat G S3)))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_real G X3) tptp.zero_zero_real))) (= (tptp.groups5808333547571424918x_real G S3) (tptp.groups5808333547571424918x_real G T3)))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups5058264527183730370ex_rat G S3) (tptp.groups5058264527183730370ex_rat G T3)))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_nat G X3) tptp.zero_zero_nat))) (= (tptp.groups5693394587270226106ex_nat G S3) (tptp.groups5693394587270226106ex_nat G T3)))))) (forall ((T3 tptp.set_complex) (S3 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex T3) (=> (tptp.ord_le211207098394363844omplex S3 T3) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 (tptp.minus_811609699411566653omplex T3 S3)) (= (tptp.aa_complex_int G X3) tptp.zero_zero_int))) (= (tptp.groups5690904116761175830ex_int G S3) (tptp.groups5690904116761175830ex_int G T3)))))) (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G tptp.fun_nat_complex)) (let ((_let_1 (tptp.groups2073611262835488442omplex G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) T3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.minus_minus_set_nat T3 S3))) (= (tptp.aa_nat_complex G X3) tptp.zero_zero_complex))) (= (tptp.aa_set_nat_complex _let_1 S3) (tptp.aa_set_nat_complex _let_1 T3))))))) (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) T3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.minus_minus_set_nat T3 S3))) (= (tptp.aa_nat_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups2906978787729119204at_rat G S3) (tptp.groups2906978787729119204at_rat G T3)))))) (forall ((T3 tptp.set_nat) (S3 tptp.set_nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat T3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) T3)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) (tptp.minus_minus_set_nat T3 S3))) (= (tptp.aa_nat_int G X3) tptp.zero_zero_int))) (= (tptp.groups3539618377306564664at_int G S3) (tptp.groups3539618377306564664at_int G T3)))))) (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G tptp.fun_int_complex)) (=> (tptp.finite_finite_int T3) (=> (tptp.ord_less_eq_set_int S3 T3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.minus_minus_set_int T3 S3)) (= (tptp.aa_int_complex G X3) tptp.zero_zero_complex))) (= (tptp.groups3049146728041665814omplex G S3) (tptp.groups3049146728041665814omplex G T3)))))) (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.finite_finite_int T3) (=> (tptp.ord_less_eq_set_int S3 T3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.minus_minus_set_int T3 S3)) (= (tptp.aa_int_real G X3) tptp.zero_zero_real))) (= (tptp.groups8778361861064173332t_real G S3) (tptp.groups8778361861064173332t_real G T3)))))) (forall ((T3 tptp.set_int) (S3 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.finite_finite_int T3) (=> (tptp.ord_less_eq_set_int S3 T3) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 (tptp.minus_minus_set_int T3 S3)) (= (tptp.aa_int_rat G X3) tptp.zero_zero_rat))) (= (tptp.groups3906332499630173760nt_rat G S3) (tptp.groups3906332499630173760nt_rat G T3)))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_complex H B2) tptp.zero_zero_complex))) (=> (= (tptp.groups5754745047067104278omplex G C2) (tptp.groups5754745047067104278omplex H C2)) (= (tptp.groups5754745047067104278omplex G A2) (tptp.groups5754745047067104278omplex H B3))))))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_real H B2) tptp.zero_zero_real))) (=> (= (tptp.groups8097168146408367636l_real G C2) (tptp.groups8097168146408367636l_real H C2)) (= (tptp.groups8097168146408367636l_real G A2) (tptp.groups8097168146408367636l_real H B3))))))))) (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G tptp.fun_complex_real) (H tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex C2) (=> (tptp.ord_le211207098394363844omplex A2 C2) (=> (tptp.ord_le211207098394363844omplex B3 C2) (=> (forall ((A3 tptp.complex)) (=> (tptp.member_complex A3 (tptp.minus_811609699411566653omplex C2 A2)) (= (tptp.aa_complex_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex C2 B3)) (= (tptp.aa_complex_real H B2) tptp.zero_zero_real))) (=> (= (tptp.groups5808333547571424918x_real G C2) (tptp.groups5808333547571424918x_real H C2)) (= (tptp.groups5808333547571424918x_real G A2) (tptp.groups5808333547571424918x_real H B3))))))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_rat) (H tptp.fun_real_rat)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_rat H B2) tptp.zero_zero_rat))) (=> (= (tptp.groups1300246762558778688al_rat G C2) (tptp.groups1300246762558778688al_rat H C2)) (= (tptp.groups1300246762558778688al_rat G A2) (tptp.groups1300246762558778688al_rat H B3))))))))) (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G tptp.fun_complex_rat) (H tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex C2) (=> (tptp.ord_le211207098394363844omplex A2 C2) (=> (tptp.ord_le211207098394363844omplex B3 C2) (=> (forall ((A3 tptp.complex)) (=> (tptp.member_complex A3 (tptp.minus_811609699411566653omplex C2 A2)) (= (tptp.aa_complex_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex C2 B3)) (= (tptp.aa_complex_rat H B2) tptp.zero_zero_rat))) (=> (= (tptp.groups5058264527183730370ex_rat G C2) (tptp.groups5058264527183730370ex_rat H C2)) (= (tptp.groups5058264527183730370ex_rat G A2) (tptp.groups5058264527183730370ex_rat H B3))))))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_nat) (H tptp.fun_real_nat)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_nat G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_nat H B2) tptp.zero_zero_nat))) (=> (= (tptp.groups1935376822645274424al_nat G C2) (tptp.groups1935376822645274424al_nat H C2)) (= (tptp.groups1935376822645274424al_nat G A2) (tptp.groups1935376822645274424al_nat H B3))))))))) (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G tptp.fun_complex_nat) (H tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex C2) (=> (tptp.ord_le211207098394363844omplex A2 C2) (=> (tptp.ord_le211207098394363844omplex B3 C2) (=> (forall ((A3 tptp.complex)) (=> (tptp.member_complex A3 (tptp.minus_811609699411566653omplex C2 A2)) (= (tptp.aa_complex_nat G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex C2 B3)) (= (tptp.aa_complex_nat H B2) tptp.zero_zero_nat))) (=> (= (tptp.groups5693394587270226106ex_nat G C2) (tptp.groups5693394587270226106ex_nat H C2)) (= (tptp.groups5693394587270226106ex_nat G A2) (tptp.groups5693394587270226106ex_nat H B3))))))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_int) (H tptp.fun_real_int)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_int G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_int H B2) tptp.zero_zero_int))) (=> (= (tptp.groups1932886352136224148al_int G C2) (tptp.groups1932886352136224148al_int H C2)) (= (tptp.groups1932886352136224148al_int G A2) (tptp.groups1932886352136224148al_int H B3))))))))) (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G tptp.fun_complex_int) (H tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex C2) (=> (tptp.ord_le211207098394363844omplex A2 C2) (=> (tptp.ord_le211207098394363844omplex B3 C2) (=> (forall ((A3 tptp.complex)) (=> (tptp.member_complex A3 (tptp.minus_811609699411566653omplex C2 A2)) (= (tptp.aa_complex_int G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex C2 B3)) (= (tptp.aa_complex_int H B2) tptp.zero_zero_int))) (=> (= (tptp.groups5690904116761175830ex_int G C2) (tptp.groups5690904116761175830ex_int H C2)) (= (tptp.groups5690904116761175830ex_int G A2) (tptp.groups5690904116761175830ex_int H B3))))))))) (forall ((C2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (let ((_let_1 (tptp.groups2073611262835488442omplex H))) (let ((_let_2 (tptp.groups2073611262835488442omplex G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) C2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) C2)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C2 A2))) (= (tptp.aa_nat_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B2) (tptp.minus_minus_set_nat C2 B3))) (= (tptp.aa_nat_complex H B2) tptp.zero_zero_complex))) (=> (= (tptp.aa_set_nat_complex _let_2 C2) (tptp.aa_set_nat_complex _let_1 C2)) (= (tptp.aa_set_nat_complex _let_2 A2) (tptp.aa_set_nat_complex _let_1 B3))))))))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_complex) (H tptp.fun_real_complex)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_complex H B2) tptp.zero_zero_complex))) (= (= (tptp.groups5754745047067104278omplex G A2) (tptp.groups5754745047067104278omplex H B3)) (= (tptp.groups5754745047067104278omplex G C2) (tptp.groups5754745047067104278omplex H C2))))))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_real) (H tptp.fun_real_real)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_real H B2) tptp.zero_zero_real))) (= (= (tptp.groups8097168146408367636l_real G A2) (tptp.groups8097168146408367636l_real H B3)) (= (tptp.groups8097168146408367636l_real G C2) (tptp.groups8097168146408367636l_real H C2))))))))) (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G tptp.fun_complex_real) (H tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex C2) (=> (tptp.ord_le211207098394363844omplex A2 C2) (=> (tptp.ord_le211207098394363844omplex B3 C2) (=> (forall ((A3 tptp.complex)) (=> (tptp.member_complex A3 (tptp.minus_811609699411566653omplex C2 A2)) (= (tptp.aa_complex_real G A3) tptp.zero_zero_real))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex C2 B3)) (= (tptp.aa_complex_real H B2) tptp.zero_zero_real))) (= (= (tptp.groups5808333547571424918x_real G A2) (tptp.groups5808333547571424918x_real H B3)) (= (tptp.groups5808333547571424918x_real G C2) (tptp.groups5808333547571424918x_real H C2))))))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_rat) (H tptp.fun_real_rat)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_rat H B2) tptp.zero_zero_rat))) (= (= (tptp.groups1300246762558778688al_rat G A2) (tptp.groups1300246762558778688al_rat H B3)) (= (tptp.groups1300246762558778688al_rat G C2) (tptp.groups1300246762558778688al_rat H C2))))))))) (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G tptp.fun_complex_rat) (H tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex C2) (=> (tptp.ord_le211207098394363844omplex A2 C2) (=> (tptp.ord_le211207098394363844omplex B3 C2) (=> (forall ((A3 tptp.complex)) (=> (tptp.member_complex A3 (tptp.minus_811609699411566653omplex C2 A2)) (= (tptp.aa_complex_rat G A3) tptp.zero_zero_rat))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex C2 B3)) (= (tptp.aa_complex_rat H B2) tptp.zero_zero_rat))) (= (= (tptp.groups5058264527183730370ex_rat G A2) (tptp.groups5058264527183730370ex_rat H B3)) (= (tptp.groups5058264527183730370ex_rat G C2) (tptp.groups5058264527183730370ex_rat H C2))))))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_nat) (H tptp.fun_real_nat)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_nat G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_nat H B2) tptp.zero_zero_nat))) (= (= (tptp.groups1935376822645274424al_nat G A2) (tptp.groups1935376822645274424al_nat H B3)) (= (tptp.groups1935376822645274424al_nat G C2) (tptp.groups1935376822645274424al_nat H C2))))))))) (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G tptp.fun_complex_nat) (H tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex C2) (=> (tptp.ord_le211207098394363844omplex A2 C2) (=> (tptp.ord_le211207098394363844omplex B3 C2) (=> (forall ((A3 tptp.complex)) (=> (tptp.member_complex A3 (tptp.minus_811609699411566653omplex C2 A2)) (= (tptp.aa_complex_nat G A3) tptp.zero_zero_nat))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex C2 B3)) (= (tptp.aa_complex_nat H B2) tptp.zero_zero_nat))) (= (= (tptp.groups5693394587270226106ex_nat G A2) (tptp.groups5693394587270226106ex_nat H B3)) (= (tptp.groups5693394587270226106ex_nat G C2) (tptp.groups5693394587270226106ex_nat H C2))))))))) (forall ((C2 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G tptp.fun_real_int) (H tptp.fun_real_int)) (=> (tptp.finite_finite_real C2) (=> (tptp.ord_less_eq_set_real A2 C2) (=> (tptp.ord_less_eq_set_real B3 C2) (=> (forall ((A3 tptp.real)) (=> (tptp.member_real A3 (tptp.minus_minus_set_real C2 A2)) (= (tptp.aa_real_int G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real C2 B3)) (= (tptp.aa_real_int H B2) tptp.zero_zero_int))) (= (= (tptp.groups1932886352136224148al_int G A2) (tptp.groups1932886352136224148al_int H B3)) (= (tptp.groups1932886352136224148al_int G C2) (tptp.groups1932886352136224148al_int H C2))))))))) (forall ((C2 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G tptp.fun_complex_int) (H tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex C2) (=> (tptp.ord_le211207098394363844omplex A2 C2) (=> (tptp.ord_le211207098394363844omplex B3 C2) (=> (forall ((A3 tptp.complex)) (=> (tptp.member_complex A3 (tptp.minus_811609699411566653omplex C2 A2)) (= (tptp.aa_complex_int G A3) tptp.zero_zero_int))) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex C2 B3)) (= (tptp.aa_complex_int H B2) tptp.zero_zero_int))) (= (= (tptp.groups5690904116761175830ex_int G A2) (tptp.groups5690904116761175830ex_int H B3)) (= (tptp.groups5690904116761175830ex_int G C2) (tptp.groups5690904116761175830ex_int H C2))))))))) (forall ((C2 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (let ((_let_1 (tptp.groups2073611262835488442omplex H))) (let ((_let_2 (tptp.groups2073611262835488442omplex G))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat C2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) C2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) C2)) (=> (forall ((A3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat A3) (tptp.minus_minus_set_nat C2 A2))) (= (tptp.aa_nat_complex G A3) tptp.zero_zero_complex))) (=> (forall ((B2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B2) (tptp.minus_minus_set_nat C2 B3))) (= (tptp.aa_nat_complex H B2) tptp.zero_zero_complex))) (= (= (tptp.aa_set_nat_complex _let_2 A2) (tptp.aa_set_nat_complex _let_1 B3)) (= (tptp.aa_set_nat_complex _let_2 C2) (tptp.aa_set_nat_complex _let_1 C2))))))))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G tptp.fun_complex_real)) (=> (tptp.ord_le211207098394363844omplex B3 A2) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5808333547571424918x_real G A2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups5808333547571424918x_real G (tptp.minus_811609699411566653omplex A2 B3))) (tptp.groups5808333547571424918x_real G B3)))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G tptp.fun_complex_rat)) (=> (tptp.ord_le211207098394363844omplex B3 A2) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5058264527183730370ex_rat G A2) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups5058264527183730370ex_rat G (tptp.minus_811609699411566653omplex A2 B3))) (tptp.groups5058264527183730370ex_rat G B3)))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G tptp.fun_complex_nat)) (=> (tptp.ord_le211207098394363844omplex B3 A2) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5693394587270226106ex_nat G A2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups5693394587270226106ex_nat G (tptp.minus_811609699411566653omplex A2 B3))) (tptp.groups5693394587270226106ex_nat G B3)))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G tptp.fun_complex_int)) (=> (tptp.ord_le211207098394363844omplex B3 A2) (=> (tptp.finite3207457112153483333omplex A2) (= (tptp.groups5690904116761175830ex_int G A2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups5690904116761175830ex_int G (tptp.minus_811609699411566653omplex A2 B3))) (tptp.groups5690904116761175830ex_int G B3)))))) (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) A2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (tptp.groups2906978787729119204at_rat G A2) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.minus_minus_set_nat A2 B3))) (tptp.groups2906978787729119204at_rat G B3)))))) (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) A2)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (tptp.groups3539618377306564664at_int G A2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.minus_minus_set_nat A2 B3))) (tptp.groups3539618377306564664at_int G B3)))))) (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G tptp.fun_int_real)) (=> (tptp.ord_less_eq_set_int B3 A2) (=> (tptp.finite_finite_int A2) (= (tptp.groups8778361861064173332t_real G A2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.groups8778361861064173332t_real G (tptp.minus_minus_set_int A2 B3))) (tptp.groups8778361861064173332t_real G B3)))))) (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G tptp.fun_int_rat)) (=> (tptp.ord_less_eq_set_int B3 A2) (=> (tptp.finite_finite_int A2) (= (tptp.groups3906332499630173760nt_rat G A2) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups3906332499630173760nt_rat G (tptp.minus_minus_set_int A2 B3))) (tptp.groups3906332499630173760nt_rat G B3)))))) (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G tptp.fun_int_nat)) (=> (tptp.ord_less_eq_set_int B3 A2) (=> (tptp.finite_finite_int A2) (= (tptp.groups4541462559716669496nt_nat G A2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.groups4541462559716669496nt_nat G (tptp.minus_minus_set_int A2 B3))) (tptp.groups4541462559716669496nt_nat G B3)))))) (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G tptp.fun_int_int)) (=> (tptp.ord_less_eq_set_int B3 A2) (=> (tptp.finite_finite_int A2) (= (tptp.groups4538972089207619220nt_int G A2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups4538972089207619220nt_int G (tptp.minus_minus_set_int A2 B3))) (tptp.groups4538972089207619220nt_int G B3)))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex A2) (=> (tptp.ord_le211207098394363844omplex B3 A2) (= (tptp.groups5808333547571424918x_real F (tptp.minus_811609699411566653omplex A2 B3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups5808333547571424918x_real F A2)) (tptp.groups5808333547571424918x_real F B3)))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex A2) (=> (tptp.ord_le211207098394363844omplex B3 A2) (= (tptp.groups5058264527183730370ex_rat F (tptp.minus_811609699411566653omplex A2 B3)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups5058264527183730370ex_rat F A2)) (tptp.groups5058264527183730370ex_rat F B3)))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex A2) (=> (tptp.ord_le211207098394363844omplex B3 A2) (= (tptp.groups5690904116761175830ex_int F (tptp.minus_811609699411566653omplex A2 B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups5690904116761175830ex_int F A2)) (tptp.groups5690904116761175830ex_int F B3)))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) A2)) (= (tptp.groups2906978787729119204at_rat F (tptp.minus_minus_set_nat A2 B3)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat F A2)) (tptp.groups2906978787729119204at_rat F B3)))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) A2)) (= (tptp.groups3539618377306564664at_int F (tptp.minus_minus_set_nat A2 B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups3539618377306564664at_int F A2)) (tptp.groups3539618377306564664at_int F B3)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_real)) (=> (tptp.finite_finite_int A2) (=> (tptp.ord_less_eq_set_int B3 A2) (= (tptp.groups8778361861064173332t_real F (tptp.minus_minus_set_int A2 B3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups8778361861064173332t_real F A2)) (tptp.groups8778361861064173332t_real F B3)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_rat)) (=> (tptp.finite_finite_int A2) (=> (tptp.ord_less_eq_set_int B3 A2) (= (tptp.groups3906332499630173760nt_rat F (tptp.minus_minus_set_int A2 B3)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups3906332499630173760nt_rat F A2)) (tptp.groups3906332499630173760nt_rat F B3)))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F tptp.fun_int_int)) (=> (tptp.finite_finite_int A2) (=> (tptp.ord_less_eq_set_int B3 A2) (= (tptp.groups4538972089207619220nt_int F (tptp.minus_minus_set_int A2 B3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups4538972089207619220nt_int F A2)) (tptp.groups4538972089207619220nt_int F B3)))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F tptp.fun_complex_complex)) (=> (tptp.finite3207457112153483333omplex A2) (=> (tptp.ord_le211207098394363844omplex B3 A2) (= (tptp.groups7754918857620584856omplex F (tptp.minus_811609699411566653omplex A2 B3)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.groups7754918857620584856omplex F A2)) (tptp.groups7754918857620584856omplex F B3)))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F tptp.fun_nat_real)) (let ((_let_1 (tptp.groups6591440286371151544t_real F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) A2)) (= (tptp.aa_set_nat_real _let_1 (tptp.minus_minus_set_nat A2 B3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_set_nat_real _let_1 A2)) (tptp.aa_set_nat_real _let_1 B3))))))) (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 ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.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.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real tptp.uminus_uminus_real B)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)))))) (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.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.aa_rat_rat tptp.uminus_uminus_rat B))) (let ((_let_4 (tptp.aa_rat_rat (tptp.times_times_rat A) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool _let_1 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) A)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 A))))))))))))) (forall ((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.times_times_rat A) C))) (let ((_let_4 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))))))))))) (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (tptp.aa_rat_rat (tptp.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.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (tptp.aa_rat_rat (tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (tptp.aa_rat_rat (tptp.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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Z))) Y) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z))) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) (tptp.aa_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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) Z))) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat (tptp.times_times_rat B) Z))) Z))))))) (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex B) Z))) Z))))))) (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_rat_rat (tptp.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.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Z))) Y) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Z))) Y) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat X)) (tptp.aa_rat_rat (tptp.times_times_rat Y) Z))) Z)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int A))) (tptp.pp (tptp.aa_int_bool _let_1 A))))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_Code_integer_bool _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A))) (tptp.pp (tptp.aa_Code_integer_bool _let_1 A))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) (or (= X Y) (= X (tptp.aa_real_real tptp.uminus_uminus_real Y)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_com8181001469867462503omplex tptp.power_power_complex X) _let_1) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Y) _let_1)) (or (= X Y) (= X (tptp.aa_complex_complex 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.aa_rat_rat 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.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X Y) (= X (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Y)))))) (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A2) B3)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.uminus_uminus_int N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int B3) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A2) N2)))))) (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real B3) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real B3 A2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F B2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups8097168146408367636l_real F A2)) (tptp.groups8097168146408367636l_real F B3))))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex B3 A2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F B2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.groups5808333547571424918x_real F A2)) (tptp.groups5808333547571424918x_real F B3))))))) (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real B3) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real B3 A2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F B2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups1300246762558778688al_rat F A2)) (tptp.groups1300246762558778688al_rat F B3))))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex B3 A2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F B2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups5058264527183730370ex_rat F A2)) (tptp.groups5058264527183730370ex_rat F B3))))))) (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (=> (forall ((B2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B2) (tptp.minus_minus_set_nat B3 A2))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F B2))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F A2)) (tptp.groups2906978787729119204at_rat F B3))))))) (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F tptp.fun_real_nat)) (=> (tptp.finite_finite_real B3) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real B3 A2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F B2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups1935376822645274424al_nat F A2)) (tptp.groups1935376822645274424al_nat F B3))))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex B3 A2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F B2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.groups5693394587270226106ex_nat F A2)) (tptp.groups5693394587270226106ex_nat F B3))))))) (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F tptp.fun_real_int)) (=> (tptp.finite_finite_real B3) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (forall ((B2 tptp.real)) (=> (tptp.member_real B2 (tptp.minus_minus_set_real B3 A2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_real_int F B2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups1932886352136224148al_int F A2)) (tptp.groups1932886352136224148al_int F B3))))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (forall ((B2 tptp.complex)) (=> (tptp.member_complex B2 (tptp.minus_811609699411566653omplex B3 A2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_complex_int F B2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups5690904116761175830ex_int F A2)) (tptp.groups5690904116761175830ex_int F B3))))))) (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (=> (forall ((B2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B2) (tptp.minus_minus_set_nat B3 A2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F B2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F A2)) (tptp.groups3539618377306564664at_int F B3))))))) (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 ((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.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.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.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C)) (tptp.aa_real_real tptp.uminus_uminus_real B)))))) (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.times_times_rat A) C)) (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real 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.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) (tptp.aa_rat_rat (tptp.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.aa_rat_rat tptp.uminus_uminus_rat B))) (let ((_let_3 (tptp.aa_rat_rat (tptp.times_times_rat A) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) A)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_2) _let_3))) (=> (not _let_4) (and (=> _let_1 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) _let_2))) (=> (not _let_1) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))) (forall ((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.times_times_rat A) C))) (let ((_let_4 (tptp.aa_rat_rat tptp.uminus_uminus_rat B))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) _let_4))) (=> (not _let_5) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) _let_3))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool _let_1 tptp.zero_zero_rat))))))))))))) (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool _let_2 C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_4) B))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 _let_1))))))))))))) (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool _let_2 C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) _let_1)) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat B) _let_4))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_4) B))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 _let_1))))))))))))) (forall ((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.aa_int_fun_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.aa_com8181001469867462503omplex tptp.power_power_complex A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_complex) (or (= A tptp.one_one_complex) (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((A tptp.rat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))))) (forall ((A tptp.code_integer)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (or (= A tptp.one_one_Code_integer) (= A (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2))) (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)) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2))) (let ((_let_2 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int tptp.uminus_uminus_int _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex A) N2))) (let ((_let_2 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) N2))) (let ((_let_2 (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)))))))) (forall ((K tptp.nat) (N2 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) N2)) (= (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K)) (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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) N2)) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K)) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K)) (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K)) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K)) (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) 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)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) X))))))))) (forall ((N2 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_ri631733984087533419it_int N2) 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) K)))) (forall ((N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K)))) (forall ((K tptp.int) (N2 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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) 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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int K)) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int L) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int)) L))))) (forall ((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.aa_int_int (tptp.aa_int_fun_int_int 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 ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.finite_finite_real B3) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (tptp.member_real B (tptp.minus_minus_set_real B3 A2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F B))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 B3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups8097168146408367636l_real F A2)) (tptp.groups8097168146408367636l_real F B3))))))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F tptp.fun_complex_real)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (tptp.member_complex B (tptp.minus_811609699411566653omplex B3 A2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_complex_real F B))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 B3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real F X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.groups5808333547571424918x_real F A2)) (tptp.groups5808333547571424918x_real F B3))))))))) (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F tptp.fun_real_rat)) (=> (tptp.finite_finite_real B3) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (tptp.member_real B (tptp.minus_minus_set_real B3 A2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_real_rat F B))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 B3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups1300246762558778688al_rat F A2)) (tptp.groups1300246762558778688al_rat F B3))))))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F tptp.fun_complex_rat)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (tptp.member_complex B (tptp.minus_811609699411566653omplex B3 A2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F B))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 B3) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups5058264527183730370ex_rat F A2)) (tptp.groups5058264527183730370ex_rat F B3))))))))) (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.minus_minus_set_nat B3 A2))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F B))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat F X3))))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.groups2906978787729119204at_rat F A2)) (tptp.groups2906978787729119204at_rat F B3))))))))) (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F tptp.fun_real_nat)) (=> (tptp.finite_finite_real B3) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (tptp.member_real B (tptp.minus_minus_set_real B3 A2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_real_nat F B))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 B3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_real_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups1935376822645274424al_nat F A2)) (tptp.groups1935376822645274424al_nat F B3))))))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (tptp.member_complex B (tptp.minus_811609699411566653omplex B3 A2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F B))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 B3) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_complex_nat F X3))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.groups5693394587270226106ex_nat F A2)) (tptp.groups5693394587270226106ex_nat F B3))))))))) (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F tptp.fun_real_int)) (=> (tptp.finite_finite_real B3) (=> (tptp.ord_less_eq_set_real A2 B3) (=> (tptp.member_real B (tptp.minus_minus_set_real B3 A2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_real_int F B))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 B3) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_real_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups1932886352136224148al_int F A2)) (tptp.groups1932886352136224148al_int F B3))))))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F tptp.fun_complex_int)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex A2 B3) (=> (tptp.member_complex B (tptp.minus_811609699411566653omplex B3 A2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_complex_int F B))) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 B3) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_complex_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups5690904116761175830ex_int F A2)) (tptp.groups5690904116761175830ex_int F B3))))))))) (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat B) (tptp.minus_minus_set_nat B3 A2))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F B))) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) B3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F X3))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups3539618377306564664at_int F A2)) (tptp.groups3539618377306564664at_int F B3))))))))) (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.aa_int_int (tptp.aa_int_fun_int_int 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.aa_int_int (tptp.aa_int_fun_int_int 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 ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.if_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int R2) tptp.zero_zero_int)))) (let ((_let_2 (tptp.aa_int_int tptp.uminus_uminus_int Q2))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A B) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R2))) (=> (not (= B tptp.zero_zero_int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int (tptp.aa_int_int tptp.uminus_uminus_int A) B) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int _let_1 _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int))) (tptp.aa_int_int (tptp.aa_int_fun_int_int _let_1 tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) R2)))))))))) (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_real_bool _let_2 tptp.zero_zero_real))))))))))))) (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_4 (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C))) (let ((_let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat B) C))) (and (=> _let_5 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_4) B))) (=> (not _let_5) (and (=> _let_3 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_4))) (=> (not _let_3) (tptp.pp (tptp.aa_rat_bool _let_2 tptp.zero_zero_rat))))))))))))) (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.zero_zero_real)))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) C)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_3) B))) (=> (not _let_2) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)))))))))))) (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat C) tptp.zero_zero_rat)))) (let ((_let_3 (tptp.aa_rat_rat (tptp.times_times_rat _let_1) C))) (let ((_let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) C)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.divide_divide_rat B) C)) _let_1)) (and (=> _let_4 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat B) _let_3))) (=> (not _let_4) (and (=> _let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_3) B))) (=> (not _let_2) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1)))))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real))))) (forall ((X tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer))))) (forall ((X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) X)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat))))) (forall ((X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) X)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) tptp.one_one_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_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) (N2 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)) N2))) (= (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))) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_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))) N2))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) N2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) _let_1) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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))) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N2))) (= (tptp.aa_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))) N2))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((N2 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) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 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.aa_int_fun_nat_int tptp.power_power_int _let_1) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex _let_1) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2))) (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))) N2)))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) 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 ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K) K))))) (forall ((N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) _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 ((B tptp.complex) (A tptp.complex)) (= (= B (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))) (forall ((B tptp.real) (A tptp.real)) (= (= B (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (= B (tptp.aa_rat_rat (tptp.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 ((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.times_times_rat B))) (let ((_let_2 (tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D))) (not (= (tptp.aa_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.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 ((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.times_times_rat X))) (let ((_let_2 (tptp.times_times_rat W))) (= (= (tptp.aa_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.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 ((N2 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))) N2))) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (= (tptp.aa_nat_int (tptp.aa_int_fun_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))) N2))) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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))) N2))) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.power_power_rat _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) _let_1))) (forall ((P tptp.fun_int_bool) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (=> (forall ((K2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K2)) (=> (not (= K2 tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (=> (forall ((K2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool P K2)) (=> (not (= K2 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (tptp.pp (tptp.aa_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K2) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (tptp.pp (tptp.aa_int_bool P K))))))) (forall ((L tptp.num) (Qr tptp.product_prod_nat_nat)) (= (tptp.unique5026877609467782581ep_nat L Qr) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat (tptp.aTP_Lamm_ey L)) Qr))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X))))))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2)))) (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 N2)))) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K)))))) (forall ((L tptp.num) (Qr tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int L) Qr) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_ez L)) Qr))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.ln_ln_real _let_23)) tptp.one_one_real)) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.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_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 ((M tptp.num) (N2 tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_kj) (tptp.unique5052692396658037445od_int M N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique5055182867167087721od_nat (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_kk) (tptp.unique5055182867167087721od_nat M N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique3479559517661332726nteger (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.produc6916734918728496179nteger tptp.aTP_Lamm_kl (tptp.unique3479559517661332726nteger M N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.divmod_nat M N2))) (let ((_let_2 (or (= N2 tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2))))) (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_km) (tptp.divmod_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2) N2)))))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N2)) (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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) (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))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X))) X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))))))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit1 N2)) (= M N2))) (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.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer A))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((F tptp.fun_Co3748208068438171869l_bool) (A tptp.code_integer) (B tptp.bool)) (=> (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool F A) B)) (tptp.pp (tptp.aa_Pro6456355659118895914l_bool (tptp.produc2506095642196730057l_bool F) (tptp.produc5135875973608410785r_bool A B))))) (forall ((F tptp.fun_num_fun_num_bool) (A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool F A) B)) (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.produc8237051459014760373m_bool F) (tptp.product_Pair_num_num A B))))) (forall ((F tptp.fun_nat_fun_num_bool) (A tptp.nat) (B tptp.num)) (=> (tptp.pp (tptp.aa_num_bool (tptp.aa_nat_fun_num_bool F A) B)) (tptp.pp (tptp.aa_Pro5426739851356932296m_bool (tptp.produc3677492636715751295m_bool F) (tptp.product_Pair_nat_num A B))))) (forall ((F tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool F A) B)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.produc8955392012077580105t_bool F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B))))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B))))) (forall ((P2 tptp.produc7417142470700560111r_bool) (C tptp.fun_Co3748208068438171869l_bool)) (=> (forall ((A3 tptp.code_integer) (B2 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool A3 B2)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool C A3) B2)))) (tptp.pp (tptp.aa_Pro6456355659118895914l_bool (tptp.produc2506095642196730057l_bool C) P2)))) (forall ((P2 tptp.product_prod_num_num) (C tptp.fun_num_fun_num_bool)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num A3 B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool C A3) B2)))) (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.produc8237051459014760373m_bool C) P2)))) (forall ((P2 tptp.product_prod_nat_num) (C tptp.fun_nat_fun_num_bool)) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P2 (tptp.product_Pair_nat_num A3 B2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_nat_fun_num_bool C A3) B2)))) (tptp.pp (tptp.aa_Pro5426739851356932296m_bool (tptp.produc3677492636715751295m_bool C) P2)))) (forall ((P2 tptp.product_prod_nat_nat) (C tptp.fun_nat_fun_nat_bool)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= P2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A3) B2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool C A3) B2)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.produc8955392012077580105t_bool C) P2)))) (forall ((P2 tptp.product_prod_int_int) (C tptp.fun_int_fun_int_bool)) (=> (forall ((A3 tptp.int) (B2 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A3) B2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool C A3) B2)))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool C) P2)))) (forall ((Z tptp.complex) (C tptp.fun_Co3393511490457469770omplex) (A tptp.code_integer) (B tptp.bool)) (=> (tptp.member_complex Z (tptp.aa_bool_set_complex (tptp.aa_Cod7104299617959582899omplex C A) B)) (tptp.member_complex Z (tptp.produc4797875024747972146omplex C (tptp.produc5135875973608410785r_bool A B))))) (forall ((Z tptp.real) (C tptp.fun_Co2315910201472382152t_real) (A tptp.code_integer) (B tptp.bool)) (=> (tptp.member_real Z (tptp.aa_bool_set_real (tptp.aa_Cod7081859000793828145t_real C A) B)) (tptp.member_real Z (tptp.produc4532933866054709936t_real C (tptp.produc5135875973608410785r_bool A B))))) (forall ((Z tptp.nat) (C tptp.fun_Co3833597871255845228et_nat) (A tptp.code_integer) (B tptp.bool)) (let ((_let_1 (tptp.member_nat Z))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_bool_set_nat (tptp.aa_Cod5518294568803216341et_nat C A) B))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.produc9066999194162305620et_nat C (tptp.produc5135875973608410785r_bool A B))))))) (forall ((Z tptp.int) (C tptp.fun_Co8243421489322702280et_int) (A tptp.code_integer) (B tptp.bool)) (=> (tptp.member_int Z (tptp.aa_bool_set_int (tptp.aa_Cod3028211423871489585et_int C A) B)) (tptp.member_int Z (tptp.produc4889148174653108912et_int C (tptp.produc5135875973608410785r_bool A B))))) (forall ((Z tptp.complex) (C tptp.fun_nu9041852840018610706omplex) (A tptp.num) (B tptp.num)) (=> (tptp.member_complex Z (tptp.aa_num_set_complex (tptp.aa_num241437687621652691omplex C A) B)) (tptp.member_complex Z (tptp.produc2866383454006189126omplex C (tptp.product_Pair_num_num A B))))) (forall ((Z tptp.real) (C tptp.fun_nu4698968662094489488t_real) (A tptp.num) (B tptp.num)) (=> (tptp.member_real Z (tptp.aa_num_set_real (tptp.aa_num2469771427700027217t_real C A) B)) (tptp.member_real Z (tptp.produc8296048397933160132t_real C (tptp.product_Pair_num_num A B))))) (forall ((Z tptp.nat) (C tptp.fun_nu530747996811530292et_nat) (A tptp.num) (B tptp.num)) (let ((_let_1 (tptp.member_nat Z))) (=> (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.aa_num_set_nat (tptp.aa_num5617506412915843061et_nat C A) B))) (tptp.pp (tptp.aa_set_nat_bool _let_1 (tptp.produc1361121860356118632et_nat C (tptp.product_Pair_num_num A B))))))) (forall ((Z tptp.int) (C tptp.fun_nu4940571614878387344et_int) (A tptp.num) (B tptp.num)) (=> (tptp.member_int Z (tptp.aa_num_set_int (tptp.aa_num3127423267984116305et_int C A) B)) (tptp.member_int Z (tptp.produc6406642877701697732et_int C (tptp.product_Pair_num_num A B))))) (forall ((Z tptp.complex) (C tptp.fun_na3925014923085203400omplex) (A tptp.nat) (B tptp.num)) (=> (tptp.member_complex Z (tptp.aa_num_set_complex (tptp.aa_nat4347971807543021193omplex C A) B)) (tptp.member_complex Z (tptp.produc6231982587499038204omplex C (tptp.product_Pair_nat_num A B))))) (forall ((Z tptp.real) (C tptp.fun_na3666575854997362246t_real) (A tptp.nat) (B tptp.num)) (=> (tptp.member_real Z (tptp.aa_num_set_real (tptp.aa_nat1437378620602899975t_real C A) B)) (tptp.member_real Z (tptp.produc1435849484188172666t_real C (tptp.product_Pair_nat_num A B))))) (forall ((P2 tptp.produc7417142470700560111r_bool) (Z tptp.complex) (C tptp.fun_Co3393511490457469770omplex)) (=> (forall ((A3 tptp.code_integer) (B2 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool A3 B2)) (tptp.member_complex Z (tptp.aa_bool_set_complex (tptp.aa_Cod7104299617959582899omplex C A3) B2)))) (tptp.member_complex Z (tptp.produc4797875024747972146omplex C P2)))) (forall ((P2 tptp.produc7417142470700560111r_bool) (Z tptp.real) (C tptp.fun_Co2315910201472382152t_real)) (=> (forall ((A3 tptp.code_integer) (B2 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool A3 B2)) (tptp.member_real Z (tptp.aa_bool_set_real (tptp.aa_Cod7081859000793828145t_real C A3) B2)))) (tptp.member_real Z (tptp.produc4532933866054709936t_real C P2)))) (forall ((P2 tptp.produc7417142470700560111r_bool) (Z tptp.nat) (C tptp.fun_Co3833597871255845228et_nat)) (=> (forall ((A3 tptp.code_integer) (B2 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool A3 B2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_bool_set_nat (tptp.aa_Cod5518294568803216341et_nat C A3) B2))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc9066999194162305620et_nat C P2))))) (forall ((P2 tptp.produc7417142470700560111r_bool) (Z tptp.int) (C tptp.fun_Co8243421489322702280et_int)) (=> (forall ((A3 tptp.code_integer) (B2 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool A3 B2)) (tptp.member_int Z (tptp.aa_bool_set_int (tptp.aa_Cod3028211423871489585et_int C A3) B2)))) (tptp.member_int Z (tptp.produc4889148174653108912et_int C P2)))) (forall ((P2 tptp.product_prod_num_num) (Z tptp.complex) (C tptp.fun_nu9041852840018610706omplex)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num A3 B2)) (tptp.member_complex Z (tptp.aa_num_set_complex (tptp.aa_num241437687621652691omplex C A3) B2)))) (tptp.member_complex Z (tptp.produc2866383454006189126omplex C P2)))) (forall ((P2 tptp.product_prod_num_num) (Z tptp.real) (C tptp.fun_nu4698968662094489488t_real)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num A3 B2)) (tptp.member_real Z (tptp.aa_num_set_real (tptp.aa_num2469771427700027217t_real C A3) B2)))) (tptp.member_real Z (tptp.produc8296048397933160132t_real C P2)))) (forall ((P2 tptp.product_prod_num_num) (Z tptp.nat) (C tptp.fun_nu530747996811530292et_nat)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num A3 B2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_num_set_nat (tptp.aa_num5617506412915843061et_nat C A3) B2))))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc1361121860356118632et_nat C P2))))) (forall ((P2 tptp.product_prod_num_num) (Z tptp.int) (C tptp.fun_nu4940571614878387344et_int)) (=> (forall ((A3 tptp.num) (B2 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num A3 B2)) (tptp.member_int Z (tptp.aa_num_set_int (tptp.aa_num3127423267984116305et_int C A3) B2)))) (tptp.member_int Z (tptp.produc6406642877701697732et_int C P2)))) (forall ((P2 tptp.product_prod_nat_num) (Z tptp.complex) (C tptp.fun_na3925014923085203400omplex)) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P2 (tptp.product_Pair_nat_num A3 B2)) (tptp.member_complex Z (tptp.aa_num_set_complex (tptp.aa_nat4347971807543021193omplex C A3) B2)))) (tptp.member_complex Z (tptp.produc6231982587499038204omplex C P2)))) (forall ((P2 tptp.product_prod_nat_num) (Z tptp.real) (C tptp.fun_na3666575854997362246t_real)) (=> (forall ((A3 tptp.nat) (B2 tptp.num)) (=> (= P2 (tptp.product_Pair_nat_num A3 B2)) (tptp.member_real Z (tptp.aa_num_set_real (tptp.aa_nat1437378620602899975t_real C A3) B2)))) (tptp.member_real Z (tptp.produc1435849484188172666t_real C P2)))) (forall ((P2 tptp.product_prod_nat_nat) (C tptp.fun_na4786964484885125043t_bool) (X tptp.product_prod_nat_nat)) (=> (forall ((A3 tptp.nat) (B2 tptp.nat)) (=> (= (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A3) B2) P2) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool C A3) B2) X)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool C) P2) X)))) (= (tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) (= (tptp.aa_complex_complex tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (tptp.aa_real_real tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real) (= (tptp.aa_rat_rat tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (= (tptp.aa_int_int tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int) (forall ((M tptp.num) (N2 tptp.num)) (not (= (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 M) (tptp.aa_num_num tptp.bit1 N2)))) (forall ((M tptp.num)) (not (= (tptp.aa_num_num tptp.bit1 M) tptp.one))) (forall ((N2 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit1 N2)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N2))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer A))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) A)))) (forall ((A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) A)))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_1) _let_1) (tptp.aa_rat_rat (tptp.times_times_rat A) A)))) (forall ((A tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int A))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B)))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B)))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B)))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B)))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) _let_86 (= (tptp.aa_complex_complex tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex) _let_85 _let_84 _let_83 (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.aa_complex_complex tptp.abs_abs_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.abs_abs_complex A)) (tptp.aa_complex_complex tptp.abs_abs_complex B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B)))) (forall ((A tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.abs_abs_real A))) (forall ((A tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.abs_abs_int A))) (forall ((A tptp.complex)) (= (tptp.aa_complex_complex tptp.abs_abs_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) (tptp.aa_complex_complex tptp.abs_abs_complex A))) (forall ((A tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat A))) (forall ((A tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.abs_abs_Code_integer A))) (forall ((M tptp.real) (K tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_real_real tptp.abs_abs_real M)) K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real M) K)))) (forall ((M tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int tptp.abs_abs_int M)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int M) K)))) (forall ((M tptp.rat) (K tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat tptp.abs_abs_rat M)) K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat M) K)))) (forall ((M tptp.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.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.rat) (K tptp.rat)) (let ((_let_1 (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat M))) (= (tptp.pp (tptp.aa_rat_bool _let_1 (tptp.aa_rat_rat tptp.abs_abs_rat K))) (tptp.pp (tptp.aa_rat_bool _let_1 K))))) (forall ((M tptp.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 ((P tptp.bool)) (let ((_let_1 (tptp.zero_n3304061248610475627l_real P))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.zero_n2052037380579107095ol_rat P))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int P))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((P tptp.bool)) (let ((_let_1 (tptp.zero_n356916108424825756nteger P))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tanh_real X)) (tptp.aa_real_real tptp.tanh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((F tptp.fun_int_int) (A2 tptp.set_int)) (let ((_let_1 (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_kn F) A2))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((F tptp.fun_nat_real) (A2 tptp.set_nat)) (let ((_let_1 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_ko F)) A2))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger)) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) tptp.zero_zero_real)) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) tptp.zero_zero_rat)) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) tptp.zero_zero_int)) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) A)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (= (tptp.aa_real_real tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.abs_abs_Code_integer A))) (not (= A tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.abs_abs_real A))) (not (= A tptp.zero_zero_real)))) (forall ((A tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.abs_abs_rat A))) (not (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int tptp.abs_abs_int A))) (not (= A tptp.zero_zero_int)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N2))) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) _let_1))) (= (tptp.aa_real_real tptp.abs_abs_real _let_53) tptp.one_one_real) (= (tptp.aa_int_int tptp.abs_abs_int _let_79) tptp.one_one_int) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_78) tptp.one_one_rat) (= (tptp.abs_abs_Code_integer _let_77) tptp.one_one_Code_integer) (forall ((A tptp.real) (N2 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)) N2)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int A)) N2)) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) N2)) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.abs_abs_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) N2)) (tptp.abs_abs_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit0 M)) _let_1) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) _let_1))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit1 M)))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num _let_1 N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((N2 tptp.num)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num tptp.one) (tptp.aa_num_num tptp.bit1 N2)))) (forall ((M tptp.num)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) tptp.one)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.tanh_real X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tanh_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((F tptp.fun_int_int) (A2 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.groups4538972089207619220nt_int F A2))) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_kn F) A2)))) (forall ((F tptp.fun_nat_real) (A2 tptp.set_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_ko F)) A2)))) (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.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_rat_rat tptp.abs_abs_rat B)))) (or (tptp.pp (tptp.aa_rat_bool _let_1 A)) (= B tptp.zero_zero_rat))))) (forall ((A tptp.real) (B tptp.real)) (= (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.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_rat_rat tptp.abs_abs_rat B))) tptp.zero_zero_rat)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (= B tptp.zero_zero_rat)))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.abs_abs_real A) (tptp.aa_real_real tptp.uminus_uminus_real A)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (= (tptp.abs_abs_Code_integer A) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int)) (= (tptp.aa_int_int tptp.abs_abs_int A) (tptp.aa_int_int tptp.uminus_uminus_int A)))) (forall ((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 ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)) tptp.one)))) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit1 M)) tptp.one) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) tptp.one)))) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bit0 M)) tptp.one) (tptp.aa_num_num tptp.bit1 M))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_num tptp.bit1 N2))) (forall ((F tptp.fun_int_int) (A2 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_kn F) A2)))) (forall ((F tptp.fun_nat_real) (A2 tptp.set_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_ko F)) A2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num M) N2)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num M) N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 N2))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.num) (N2 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 N2))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Pro6799258434465214121nt_int tptp.adjust_div (tptp.unique5052692396658037445od_int M N2))))) (forall ((M tptp.num) (N2 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 N2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Pro6799258434465214121nt_int tptp.adjust_div (tptp.unique5052692396658037445od_int M N2))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) N2))) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N2))) (or (not (= A tptp.zero_zero_real)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N2))) (or (not (= A tptp.zero_zero_rat)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N2))) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.power_power_rat A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((A tptp.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.aa_int_fun_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.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1)))) (forall ((A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((A tptp.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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_1)))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_complex)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups2073611262835488442omplex G))) (let ((_let_3 (tptp.aa_set_nat_complex _let_2 (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_4 (= _let_3 tptp.zero_zero_complex)) (=> (not _let_4) (= _let_3 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_set_nat_complex _let_2 (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_nat_complex G _let_1)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_nat_rat G _let_1))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_nat_int G _let_1))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_4 (= _let_3 tptp.zero_zero_nat)) (=> (not _let_4) (= _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_nat_nat G _let_1)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups6591440286371151544t_real G))) (let ((_let_3 (tptp.aa_set_nat_real _let_2 (tptp.set_or1269000886237332187st_nat M _let_1)))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) M)))) (and (=> _let_4 (= _let_3 tptp.zero_zero_real)) (=> (not _let_4) (= _let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real _let_2 (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_nat_real G _let_1)))))))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool tptp.unique6319869463603278526ux_int (tptp.unique5052692396658037445od_int N2 M))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool tptp.unique6322359934112328802ux_nat (tptp.unique5055182867167087721od_nat N2 M))))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (tptp.unique5706413561485394159nteger (tptp.unique3479559517661332726nteger N2 M)))) (forall ((M tptp.num)) (= (tptp.unique5052692396658037445od_int M tptp.one) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int M)) tptp.zero_zero_int))) (forall ((M tptp.num)) (= (tptp.unique5055182867167087721od_nat M tptp.one) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))) (forall ((M tptp.num)) (= (tptp.unique3479559517661332726nteger M tptp.one) (tptp.produc1086072967326762835nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) tptp.zero_z3403309356797280102nteger))) (forall ((A2 tptp.set_nat) (C tptp.fun_nat_complex)) (let ((_let_1 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_kp C)) A2))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2))))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_complex C tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((A2 tptp.set_nat) (C tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_kq C) A2))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2))))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_rat C tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((A2 tptp.set_nat) (C tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_kr C)) A2))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2))))) (and (=> _let_2 (= _let_1 (tptp.aa_nat_real C tptp.zero_zero_nat))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((W tptp.num) (A tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) _let_1) (tptp.aa_nat_rat (tptp.power_power_rat A) _let_1))))) (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) _let_1) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) _let_1))))) (forall ((W tptp.num) (A tptp.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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) _let_1) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) _let_1))))) (forall ((M tptp.nat) (N2 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 N2)))) (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))) N2))))) (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 ((N2 tptp.num)) (= (tptp.unique5052692396658037445od_int tptp.one (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.unique5055182867167087721od_nat tptp.one (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.unique3479559517661332726nteger tptp.one (tptp.aa_num_num tptp.bit0 N2)) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)))) (forall ((M tptp.nat) (N2 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 N2)))) (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))) N2))))) (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 ((N2 tptp.num)) (= (tptp.unique5052692396658037445od_int tptp.one (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.unique5055182867167087721od_nat tptp.one (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)))) (forall ((N2 tptp.num)) (= (tptp.unique3479559517661332726nteger tptp.one (tptp.aa_num_num tptp.bit1 N2)) (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one)))) (forall ((A2 tptp.set_nat) (C tptp.fun_nat_complex) (D tptp.fun_nat_complex)) (let ((_let_1 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ks C) D)) A2))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2))))) (and (=> _let_2 (= _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex C tptp.zero_zero_nat)) (tptp.aa_nat_complex D tptp.zero_zero_nat)))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((A2 tptp.set_nat) (C tptp.fun_nat_rat) (D tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_kt C) D) A2))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2))))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat C tptp.zero_zero_nat)) (tptp.aa_nat_rat D tptp.zero_zero_nat)))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((A2 tptp.set_nat) (C tptp.fun_nat_real) (D tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ku C) D)) A2))) (let ((_let_2 (and (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2))))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real C tptp.zero_zero_nat)) (tptp.aa_nat_real D tptp.zero_zero_nat)))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N2 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 N2))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Pro6799258434465214121nt_int tptp.adjust_div (tptp.unique5052692396658037445od_int tptp.one N2))))) (forall ((N2 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 N2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Pro6799258434465214121nt_int tptp.adjust_div (tptp.unique5052692396658037445od_int tptp.one N2))))) (forall ((V tptp.num) (W tptp.num)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 V))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_num_int tptp.numeral_numeral_int W)))) tptp.one_one_int))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 M))) (let ((_let_3 (tptp.unique5055182867167087721od_nat _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique5026877609467782581ep_nat _let_1 (tptp.unique5055182867167087721od_nat _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 M))) (let ((_let_3 (tptp.unique5052692396658037445od_int _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int _let_2)))) (=> (not _let_4) (= _let_3 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int _let_1) (tptp.unique5052692396658037445od_int _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 M))) (let ((_let_3 (tptp.unique3479559517661332726nteger _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique4921790084139445826nteger _let_1 (tptp.unique3479559517661332726nteger _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 M))) (let ((_let_3 (tptp.unique5055182867167087721od_nat _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique5026877609467782581ep_nat _let_1 (tptp.unique5055182867167087721od_nat _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 M))) (let ((_let_3 (tptp.unique5052692396658037445od_int _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int _let_2)))) (=> (not _let_4) (= _let_3 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int _let_1) (tptp.unique5052692396658037445od_int _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N2))) (let ((_let_2 (tptp.aa_num_num tptp.bit0 M))) (let ((_let_3 (tptp.unique3479559517661332726nteger _let_2 _let_1))) (let ((_let_4 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num M) N2)))) (and (=> _let_4 (= _let_3 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_4) (= _let_3 (tptp.unique4921790084139445826nteger _let_1 (tptp.unique3479559517661332726nteger _let_2 (tptp.aa_num_num tptp.bit0 _let_1))))))))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_nat_nat tptp.suc N2)) (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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_kv) (tptp.unique5052692396658037445od_int M N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique5055182867167087721od_nat (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_kw) (tptp.unique5055182867167087721od_nat M N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.unique3479559517661332726nteger (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.produc6916734918728496179nteger tptp.aTP_Lamm_kx (tptp.unique3479559517661332726nteger M N2)))) (forall ((P tptp.fun_Pr803113274115125473t_bool)) (= (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_ky P)) (tptp.uminus6221592323253981072nt_int (tptp.collec213857154873943460nt_int P)))) (forall ((P tptp.fun_complex_bool)) (= (tptp.collect_complex (tptp.aTP_Lamm_kz P)) (tptp.uminus8566677241136511917omplex (tptp.collect_complex P)))) (forall ((P tptp.fun_set_nat_bool)) (= (tptp.collect_set_nat (tptp.aTP_Lamm_la P)) (tptp.uminus613421341184616069et_nat (tptp.collect_set_nat P)))) (forall ((P tptp.fun_nat_bool)) (= (tptp.collect_nat (tptp.aTP_Lamm_lb P)) (tptp.uminus5710092332889474511et_nat (tptp.collect_nat P)))) (forall ((P tptp.fun_int_bool)) (= (tptp.collect_int (tptp.aTP_Lamm_lc P)) (tptp.uminus1532241313380277803et_int (tptp.collect_int P)))) (forall ((A2 tptp.set_real)) (= (tptp.uminus612125837232591019t_real A2) (tptp.collect_real (tptp.aTP_Lamm_ld A2)))) (forall ((A2 tptp.set_Pr958786334691620121nt_int)) (= (tptp.uminus6221592323253981072nt_int A2) (tptp.collec213857154873943460nt_int (tptp.aTP_Lamm_le A2)))) (forall ((A2 tptp.set_complex)) (= (tptp.uminus8566677241136511917omplex A2) (tptp.collect_complex (tptp.aTP_Lamm_lf A2)))) (forall ((A2 tptp.set_set_nat)) (= (tptp.uminus613421341184616069et_nat A2) (tptp.collect_set_nat (tptp.aTP_Lamm_lg A2)))) (forall ((A2 tptp.set_nat)) (= (tptp.uminus5710092332889474511et_nat A2) (tptp.collect_nat (tptp.aTP_Lamm_lh A2)))) (forall ((A2 tptp.set_int)) (= (tptp.uminus1532241313380277803et_int A2) (tptp.collect_int (tptp.aTP_Lamm_li A2)))) (forall ((A2 tptp.set_real)) (= (tptp.uminus612125837232591019t_real A2) (tptp.collect_real (tptp.uminus4638318004487240379l_bool (tptp.aTP_Lamm_a A2))))) (forall ((A2 tptp.set_Pr958786334691620121nt_int)) (= (tptp.uminus6221592323253981072nt_int A2) (tptp.collec213857154873943460nt_int (tptp.uminus8539327787930509866t_bool (tptp.aTP_Lamm_aa A2))))) (forall ((A2 tptp.set_complex)) (= (tptp.uminus8566677241136511917omplex A2) (tptp.collect_complex (tptp.uminus8337675090112669241x_bool (tptp.aTP_Lamm_ab A2))))) (forall ((A2 tptp.set_set_nat)) (= (tptp.uminus613421341184616069et_nat A2) (tptp.collect_set_nat (tptp.uminus6226608070181861729t_bool (tptp.aTP_Lamm_ac A2))))) (forall ((A2 tptp.set_nat)) (= (tptp.uminus5710092332889474511et_nat A2) (tptp.collect_nat (tptp.uminus1995910650241132439t_bool (tptp.aTP_Lamm_ad A2))))) (forall ((A2 tptp.set_int)) (= (tptp.uminus1532241313380277803et_int A2) (tptp.collect_int (tptp.uminus8094991720627284027t_bool (tptp.aTP_Lamm_ae A2))))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger A) (tptp.abs_abs_Code_integer A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_int_int tptp.abs_abs_int A)))) (forall ((A tptp.real) (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.aa_rat_rat tptp.abs_abs_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)))) (forall ((A tptp.code_integer)) (= (= (tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (= (tptp.aa_complex_complex tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (= (tptp.aa_real_real tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (tptp.aa_rat_rat tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger A) B)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.abs_abs_Code_integer A)) (tptp.abs_abs_Code_integer B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B)))) _let_86 _let_85 _let_84 _let_83 (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B)) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger B A)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B)) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B) A)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B)) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N2))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (tptp.abs_abs_Code_integer (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) N2))) (forall ((A tptp.real) (N2 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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N2))) (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.aa_rat_rat tptp.abs_abs_rat X) (tptp.aa_rat_rat tptp.abs_abs_rat Y)) (or (= X Y) (= X (tptp.aa_rat_rat tptp.uminus_uminus_rat Y))))) (forall ((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 ((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.rat) (K tptp.rat)) (=> (= (tptp.aa_rat_rat tptp.abs_abs_rat L) (tptp.aa_rat_rat tptp.abs_abs_rat K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat L) K)))) (forall ((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 ((Z tptp.complex) (C tptp.fun_Co3393511490457469770omplex) (P2 tptp.produc7417142470700560111r_bool)) (=> (tptp.member_complex Z (tptp.produc4797875024747972146omplex C P2)) (not (forall ((X3 tptp.code_integer) (Y4 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool X3 Y4)) (not (tptp.member_complex Z (tptp.aa_bool_set_complex (tptp.aa_Cod7104299617959582899omplex C X3) Y4)))))))) (forall ((Z tptp.real) (C tptp.fun_Co2315910201472382152t_real) (P2 tptp.produc7417142470700560111r_bool)) (=> (tptp.member_real Z (tptp.produc4532933866054709936t_real C P2)) (not (forall ((X3 tptp.code_integer) (Y4 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool X3 Y4)) (not (tptp.member_real Z (tptp.aa_bool_set_real (tptp.aa_Cod7081859000793828145t_real C X3) Y4)))))))) (forall ((Z tptp.nat) (C tptp.fun_Co3833597871255845228et_nat) (P2 tptp.produc7417142470700560111r_bool)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc9066999194162305620et_nat C P2))) (not (forall ((X3 tptp.code_integer) (Y4 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool X3 Y4)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_bool_set_nat (tptp.aa_Cod5518294568803216341et_nat C X3) Y4))))))))) (forall ((Z tptp.int) (C tptp.fun_Co8243421489322702280et_int) (P2 tptp.produc7417142470700560111r_bool)) (=> (tptp.member_int Z (tptp.produc4889148174653108912et_int C P2)) (not (forall ((X3 tptp.code_integer) (Y4 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool X3 Y4)) (not (tptp.member_int Z (tptp.aa_bool_set_int (tptp.aa_Cod3028211423871489585et_int C X3) Y4)))))))) (forall ((Z tptp.complex) (C tptp.fun_nu9041852840018610706omplex) (P2 tptp.product_prod_num_num)) (=> (tptp.member_complex Z (tptp.produc2866383454006189126omplex C P2)) (not (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num X3 Y4)) (not (tptp.member_complex Z (tptp.aa_num_set_complex (tptp.aa_num241437687621652691omplex C X3) Y4)))))))) (forall ((Z tptp.real) (C tptp.fun_nu4698968662094489488t_real) (P2 tptp.product_prod_num_num)) (=> (tptp.member_real Z (tptp.produc8296048397933160132t_real C P2)) (not (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num X3 Y4)) (not (tptp.member_real Z (tptp.aa_num_set_real (tptp.aa_num2469771427700027217t_real C X3) Y4)))))))) (forall ((Z tptp.nat) (C tptp.fun_nu530747996811530292et_nat) (P2 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.produc1361121860356118632et_nat C P2))) (not (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num X3 Y4)) (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Z) (tptp.aa_num_set_nat (tptp.aa_num5617506412915843061et_nat C X3) Y4))))))))) (forall ((Z tptp.int) (C tptp.fun_nu4940571614878387344et_int) (P2 tptp.product_prod_num_num)) (=> (tptp.member_int Z (tptp.produc6406642877701697732et_int C P2)) (not (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num X3 Y4)) (not (tptp.member_int Z (tptp.aa_num_set_int (tptp.aa_num3127423267984116305et_int C X3) Y4)))))))) (forall ((Z tptp.complex) (C tptp.fun_na3925014923085203400omplex) (P2 tptp.product_prod_nat_num)) (=> (tptp.member_complex Z (tptp.produc6231982587499038204omplex C P2)) (not (forall ((X3 tptp.nat) (Y4 tptp.num)) (=> (= P2 (tptp.product_Pair_nat_num X3 Y4)) (not (tptp.member_complex Z (tptp.aa_num_set_complex (tptp.aa_nat4347971807543021193omplex C X3) Y4)))))))) (forall ((Z tptp.real) (C tptp.fun_na3666575854997362246t_real) (P2 tptp.product_prod_nat_num)) (=> (tptp.member_real Z (tptp.produc1435849484188172666t_real C P2)) (not (forall ((X3 tptp.nat) (Y4 tptp.num)) (=> (= P2 (tptp.product_Pair_nat_num X3 Y4)) (not (tptp.member_real Z (tptp.aa_num_set_real (tptp.aa_nat1437378620602899975t_real C X3) Y4)))))))) (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (tptp.aa_num_num tptp.bit0 X22) (tptp.aa_num_num tptp.bit1 X32)))) (forall ((X32 tptp.num)) (not (= tptp.one (tptp.aa_num_num tptp.bit1 X32)))) (forall ((C tptp.fun_Co3748208068438171869l_bool) (P2 tptp.produc7417142470700560111r_bool)) (=> (tptp.pp (tptp.aa_Pro6456355659118895914l_bool (tptp.produc2506095642196730057l_bool C) P2)) (not (forall ((X3 tptp.code_integer) (Y4 tptp.bool)) (=> (= P2 (tptp.produc5135875973608410785r_bool X3 Y4)) (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool C X3) Y4)))))))) (forall ((C tptp.fun_num_fun_num_bool) (P2 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.produc8237051459014760373m_bool C) P2)) (not (forall ((X3 tptp.num) (Y4 tptp.num)) (=> (= P2 (tptp.product_Pair_num_num X3 Y4)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool C X3) Y4)))))))) (forall ((C tptp.fun_nat_fun_num_bool) (P2 tptp.product_prod_nat_num)) (=> (tptp.pp (tptp.aa_Pro5426739851356932296m_bool (tptp.produc3677492636715751295m_bool C) P2)) (not (forall ((X3 tptp.nat) (Y4 tptp.num)) (=> (= P2 (tptp.product_Pair_nat_num X3 Y4)) (not (tptp.pp (tptp.aa_num_bool (tptp.aa_nat_fun_num_bool C X3) Y4)))))))) (forall ((C tptp.fun_nat_fun_nat_bool) (P2 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.produc8955392012077580105t_bool C) P2)) (not (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (= P2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y4)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool C X3) Y4)))))))) (forall ((C tptp.fun_int_fun_int_bool) (P2 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool C) P2)) (not (forall ((X3 tptp.int) (Y4 tptp.int)) (=> (= P2 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y4)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool C X3) Y4)))))))) (forall ((F tptp.fun_Co3748208068438171869l_bool) (A tptp.code_integer) (B tptp.bool)) (=> (tptp.pp (tptp.aa_Pro6456355659118895914l_bool (tptp.produc2506095642196730057l_bool F) (tptp.produc5135875973608410785r_bool A B))) (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool F A) B)))) (forall ((F tptp.fun_num_fun_num_bool) (A tptp.num) (B tptp.num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.produc8237051459014760373m_bool F) (tptp.product_Pair_num_num A B))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool F A) B)))) (forall ((F tptp.fun_nat_fun_num_bool) (A tptp.nat) (B tptp.num)) (=> (tptp.pp (tptp.aa_Pro5426739851356932296m_bool (tptp.produc3677492636715751295m_bool F) (tptp.product_Pair_nat_num A B))) (tptp.pp (tptp.aa_num_bool (tptp.aa_nat_fun_num_bool F A) B)))) (forall ((F tptp.fun_nat_fun_nat_bool) (A tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.produc8955392012077580105t_bool F) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool F A) B)))) (forall ((F tptp.fun_int_fun_int_bool) (A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool F) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool F A) B)))) (forall ((R tptp.fun_na4786964484885125043t_bool) (A tptp.nat) (B tptp.nat) (C tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool R) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A) B)) C)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool R A) B) C)))) (forall ((C tptp.fun_na4786964484885125043t_bool) (P2 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool C) P2) Z)) (not (forall ((X3 tptp.nat) (Y4 tptp.nat)) (=> (= P2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y4)) (not (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool C X3) Y4) Z)))))))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.abs_abs_Code_integer A)))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.abs_abs_int A)))) (forall ((A tptp.code_integer)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real A)) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int A)) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A)) (= (tptp.abs_abs_Code_integer A) A))) (forall ((A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.aa_real_real tptp.abs_abs_real A) A))) (forall ((A tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) A)) (= (tptp.aa_rat_rat tptp.abs_abs_rat A) A))) (forall ((A tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) A)) (= (tptp.aa_int_int tptp.abs_abs_int A) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.plus_p5714425477246183910nteger A B))) (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B))))) (forall ((A tptp.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.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B))) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer B))) (let ((_let_2 (tptp.abs_abs_Code_integer A))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_2) C)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger _let_1) D)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_2) _let_1)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger C) D)))))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real B))) (let ((_let_2 (tptp.aa_real_real tptp.abs_abs_real A))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_2) C)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) D)))))))) (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat B))) (let ((_let_2 (tptp.aa_rat_rat tptp.abs_abs_rat A))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_2) C)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_1) D)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.times_times_rat _let_2) _let_1)) (tptp.aa_rat_rat (tptp.times_times_rat C) D)))))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int B))) (let ((_let_2 (tptp.aa_int_int tptp.abs_abs_int A))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_2) C)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int _let_1) D)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) D)))))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B))) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger 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.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B) A))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) A))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B)))) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B))))) (forall ((A tptp.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.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B)))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B)))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B))) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B))))) (forall ((A tptp.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.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.abs_abs_real A)) (tptp.aa_real_real tptp.abs_abs_real B))))) (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) (tptp.aa_real_real tptp.abs_abs_real A)))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) (tptp.abs_abs_Code_integer A)))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat A)))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) (tptp.aa_int_int tptp.abs_abs_int A)))) (forall ((A tptp.real) (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.aa_rat_rat tptp.abs_abs_rat A)) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B))))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real A)) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real A)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer A)) B)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger A)) B)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real 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.aa_rat_rat tptp.uminus_uminus_rat A)) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) B)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int A)) B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int A)) B))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.aa_rat_rat tptp.abs_abs_rat A)) B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (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 ((A2 tptp.set_nat) (F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat _let_1) A2)) (= (tptp.aa_nat_nat F _let_1) (tptp.aa_nat_nat G _let_1))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) A2))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) A2))) (=> (forall ((X3 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X3))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat _let_1) A2)) (= (tptp.aa_nat_real F _let_1) (tptp.aa_nat_real G _let_1))))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) A2))))) (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (tptp.aa_num_num tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y (tptp.aa_num_num tptp.bit1 X33)))))))) (forall ((X tptp.product_prod_num_num)) (=> (not (= X (tptp.product_Pair_num_num tptp.one tptp.one))) (=> (forall ((N tptp.num)) (not (= X (tptp.product_Pair_num_num tptp.one (tptp.aa_num_num tptp.bit0 N))))) (=> (forall ((N tptp.num)) (not (= X (tptp.product_Pair_num_num tptp.one (tptp.aa_num_num tptp.bit1 N))))) (=> (forall ((M2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) tptp.one)))) (=> (forall ((M2 tptp.num) (N tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) (tptp.aa_num_num tptp.bit0 N))))) (=> (forall ((M2 tptp.num) (N tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 M2) (tptp.aa_num_num tptp.bit1 N))))) (=> (forall ((M2 tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) tptp.one)))) (=> (forall ((M2 tptp.num) (N tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) (tptp.aa_num_num tptp.bit0 N))))) (not (forall ((M2 tptp.num) (N tptp.num)) (not (= X (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 M2) (tptp.aa_num_num tptp.bit1 N))))))))))))))) (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 ((A2 tptp.set_complex) (G tptp.fun_complex_nat) (F tptp.fun_complex_nat)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_complex_nat G X3)) (tptp.aa_complex_nat F X3))))) (= (tptp.groups5693394587270226106ex_nat (tptp.aa_fun2465681967280144180ex_nat (tptp.aTP_Lamm_lj G) F) A2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups5693394587270226106ex_nat F A2)) (tptp.groups5693394587270226106ex_nat G A2))))) (forall ((A2 tptp.set_real) (G tptp.fun_real_nat) (F tptp.fun_real_nat)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat G X3)) (tptp.aa_real_nat F X3))))) (= (tptp.groups1935376822645274424al_nat (tptp.aa_fun211602392931233840al_nat (tptp.aTP_Lamm_lk G) F) A2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups1935376822645274424al_nat F A2)) (tptp.groups1935376822645274424al_nat G A2))))) (forall ((A2 tptp.set_set_nat) (G tptp.fun_set_nat_nat) (F tptp.fun_set_nat_nat)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.member_set_nat X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat G X3)) (tptp.aa_set_nat_nat F X3))))) (= (tptp.groups8294997508430121362at_nat (tptp.aa_fun3386010016858254564at_nat (tptp.aTP_Lamm_ll G) F) A2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups8294997508430121362at_nat F A2)) (tptp.groups8294997508430121362at_nat G A2))))) (forall ((A2 tptp.set_int) (G tptp.fun_int_nat) (F tptp.fun_int_nat)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 A2) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat G X3)) (tptp.aa_int_nat F X3))))) (= (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_lm G) F) A2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups4541462559716669496nt_nat F A2)) (tptp.groups4541462559716669496nt_nat G A2))))) (forall ((A2 tptp.set_nat) (G tptp.fun_nat_nat) (F tptp.fun_nat_nat)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat G X3)) (tptp.aa_nat_nat F X3))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_ln G) F)) A2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) A2))))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_lo G)) (tptp.set_or1269000886237332187st_nat M N2)))) (forall ((G tptp.fun_nat_real) (M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_lp G)) (tptp.set_or1269000886237332187st_nat M N2)))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lq G) K)) (tptp.set_or1269000886237332187st_nat M N2)))) (forall ((G tptp.fun_nat_real) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) K))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr G) K)) (tptp.set_or1269000886237332187st_nat M N2)))) (forall ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) E2)))) (= X tptp.zero_zero_real))) (forall ((X tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) E2)))) (= X tptp.zero_zero_rat))) (forall ((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.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.times_times_rat A) B)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B)))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (tptp.pp (tptp.aa_int_bool _let_1 A)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) tptp.zero_zero_int))) (or (tptp.pp (tptp.aa_int_bool _let_1 B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) tptp.zero_zero_int)))) (= (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B)))))) (forall ((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.times_times_rat (tptp.aa_rat_rat tptp.abs_abs_rat Y)) X) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.times_times_rat Y) X))))) (forall ((X tptp.int) (Y tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.abs_abs_int Y)) X) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) X))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) N2)))) (forall ((A tptp.real) (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 (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N2)))) (forall ((A tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.abs_abs_real A))) tptp.zero_zero_real))) (forall ((A tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A))) tptp.zero_zero_rat))) (forall ((A tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.abs_abs_int A))) tptp.zero_zero_int))) (forall ((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.aa_rat_rat tptp.abs_abs_rat B)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) A)) (or (= B A) (= B (tptp.aa_rat_rat tptp.uminus_uminus_rat A)))))) (forall ((A tptp.int) (B tptp.int)) (= (= A (tptp.aa_int_int tptp.abs_abs_int B)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) A)) (or (= B A) (= B (tptp.aa_int_int tptp.uminus_uminus_int A)))))) (forall ((A tptp.real) (B tptp.real)) (= (= (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.aa_rat_rat tptp.abs_abs_rat A) B) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) B)) (or (= A B) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat B)))))) (forall ((A tptp.int) (B tptp.int)) (= (= (tptp.aa_int_int tptp.abs_abs_int A) B) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (or (= A B) (= A (tptp.aa_int_int tptp.uminus_uminus_int B)))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.abs_abs_real X)) Y) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y))))) (forall ((Y tptp.rat) (X tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) Y)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) Y) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.divide_divide_rat X) Y))))) (forall ((X2 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real X2))) (let ((_let_2 (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X2) tptp.zero_zero_real)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real X2))) (=> (not _let_2) (= _let_1 X2)))))) (forall ((X2 tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int X2))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X2) tptp.zero_zero_int)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int X2))) (=> (not _let_2) (= _let_1 X2)))))) (forall ((X2 tptp.rat)) (let ((_let_1 (tptp.aa_rat_rat tptp.abs_abs_rat X2))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X2) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat X2))) (=> (not _let_2) (= _let_1 X2)))))) (forall ((X2 tptp.code_integer)) (let ((_let_1 (tptp.abs_abs_Code_integer X2))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X2) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X2))) (=> (not _let_2) (= _let_1 X2)))))) (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.aa_rat_rat tptp.abs_abs_rat A))) (let ((_let_2 (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) tptp.zero_zero_rat)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat A))) (=> (not _let_2) (= _let_1 A)))))) (forall ((A tptp.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.aa_rat_rat tptp.abs_abs_rat A) (tptp.aa_rat_rat 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 ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.plus_p5714425477246183910nteger A B) (tptp.plus_p5714425477246183910nteger C D)))) (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A C)) (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger B D)))))) (forall ((A tptp.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.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) (tptp.aa_rat_rat (tptp.plus_plus_rat C) D)))) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) C))) (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B) D)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int C) D)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) C))) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int B) D)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger A B))) (tptp.plus_p5714425477246183910nteger (tptp.abs_abs_Code_integer A) (tptp.abs_abs_Code_integer B))))) (forall ((A tptp.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.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) B))) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))))) (forall ((A tptp.int) (B tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int A)) (tptp.aa_int_int tptp.abs_abs_int B))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger X A))) R2)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.minus_8373710615458151222nteger A R2)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) (tptp.plus_p5714425477246183910nteger A R2)))))) (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) A))) R2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) R2)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) R2)))))) (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) A))) R2)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) R2)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) (tptp.aa_rat_rat (tptp.plus_plus_rat A) R2)))))) (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) A))) R2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) R2)) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) R2)))))) (forall ((X tptp.code_integer) (A tptp.code_integer) (R2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger X A))) R2)) (and (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.minus_8373710615458151222nteger A R2)) X)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger X) (tptp.plus_p5714425477246183910nteger A R2)))))) (forall ((X tptp.real) (A tptp.real) (R2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) A))) R2)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) R2)) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) R2)))))) (forall ((X tptp.rat) (A tptp.rat) (R2 tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) A))) R2)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) R2)) X)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) (tptp.aa_rat_rat (tptp.plus_plus_rat A) R2)))))) (forall ((X tptp.int) (A tptp.int) (R2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) A))) R2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int A) R2)) X)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) R2)))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.finite_finite_int A2) (= (= (tptp.groups4541462559716669496nt_nat F A2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.int)) (and (tptp.member_int X4 A2) (= (tptp.aa_int_nat F X4) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (forall ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 A2) (=> (not (= X4 Xa4)) (= (tptp.aa_int_nat F Xa4) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex A2) (= (= (tptp.groups5693394587270226106ex_nat F A2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.complex)) (and (tptp.member_complex X4 A2) (= (tptp.aa_complex_nat F X4) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (forall ((Xa4 tptp.complex)) (=> (tptp.member_complex Xa4 A2) (=> (not (= X4 Xa4)) (= (tptp.aa_complex_nat F Xa4) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A2)) (= (tptp.aa_nat_nat F X4) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (forall ((Xa4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa4) A2)) (=> (not (= X4 Xa4)) (= (tptp.aa_nat_nat F Xa4) tptp.zero_zero_nat))))))))) (forall ((F tptp.fun_nat_nat) (A2 tptp.set_nat) (N2 tptp.nat)) (=> (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2) (tptp.aa_nat_nat tptp.suc N2)) (exists ((X3 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) A2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F X3))))))) (forall ((A2 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.finite_finite_int A2) (= (= (tptp.groups4541462559716669496nt_nat F A2) tptp.one_one_nat) (exists ((X4 tptp.int)) (and (tptp.member_int X4 A2) (= (tptp.aa_int_nat F X4) tptp.one_one_nat) (forall ((Xa4 tptp.int)) (=> (tptp.member_int Xa4 A2) (=> (not (= X4 Xa4)) (= (tptp.aa_int_nat F Xa4) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex A2) (= (= (tptp.groups5693394587270226106ex_nat F A2) tptp.one_one_nat) (exists ((X4 tptp.complex)) (and (tptp.member_complex X4 A2) (= (tptp.aa_complex_nat F X4) tptp.one_one_nat) (forall ((Xa4 tptp.complex)) (=> (tptp.member_complex Xa4 A2) (=> (not (= X4 Xa4)) (= (tptp.aa_complex_nat F Xa4) tptp.zero_zero_nat))))))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (= (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2) tptp.one_one_nat) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) A2)) (= (tptp.aa_nat_nat F X4) tptp.one_one_nat) (forall ((Xa4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Xa4) A2)) (=> (not (= X4 Xa4)) (= (tptp.aa_nat_nat F Xa4) tptp.zero_zero_nat))))))))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N2))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N2))) (= (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 N2)) (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 ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N2)) (tptp.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 ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N2)) (tptp.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 ((N2 tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N2))))) (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.aa_int_fun_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.aa_int_fun_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.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) _let_1) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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.aa_rat_rat tptp.uminus_uminus_rat X)) _let_1) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1))))) (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 K)))) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger X)) _let_1) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _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 N2)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int Q2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N2))) _let_2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 M)) _let_2) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N2)) _let_2)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2) _let_1)))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 N2)) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 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 N2))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M))) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N2))) _let_1))))) (forall ((M tptp.num) (Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N2)) _let_1))))) (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) B)) (exists ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((Y2 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) Y2))) D3)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Y2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y2) B)))))))))) (forall ((X tptp.complex) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_ls X) M)) I6) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_1) I6))))) (forall ((X tptp.rat) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (tptp.power_power_rat X))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_lt X) M) I6) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.groups2906978787729119204at_rat _let_1 I6))))) (forall ((X tptp.int) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (= (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_lu X) M) I6) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.groups3539618377306564664at_int _let_1 I6))))) (forall ((X tptp.real) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lv X) M)) I6) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_1) I6))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat N2 M))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_lw G) N2) M)) _let_1)))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat N2 M))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) _let_1) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_nat4085805313368488148t_real (tptp.aTP_Lamm_lx G) N2) M)) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N2))) (= (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real N2))) (= (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 N2)) (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 ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (= (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 N2)) (tptp.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 ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Z))) (let ((_let_2 (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_complex _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Z) _let_2)) _let_2))))) (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real Z))) (let ((_let_2 (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_real _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Z) _let_2)) _let_2))))) (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (tptp.power_power_rat Z))) (let ((_let_2 (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat Z) _let_2)) _let_2))))) (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Z))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Z) _let_2)) _let_2))))) (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int Z))) (let ((_let_2 (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat W)))) (= (tptp.aa_nat_int _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 W))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Z) _let_2)) _let_2))))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.one_one_nat) N2)) (= (tptp.groups7754918857620584856omplex tptp.aTP_Lamm_af (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool tptp.aTP_Lamm_cf N2))) tptp.zero_zero_complex))) (forall ((N2 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) N2)) (= (tptp.groups7754918857620584856omplex tptp.aTP_Lamm_af (tptp.collect_complex (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_de N2) C))) tptp.zero_zero_complex))) (forall ((X tptp.code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer (tptp.abs_abs_Code_integer X))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real tptp.abs_abs_real X))))) (forall ((X tptp.rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) (tptp.aa_rat_rat (tptp.plus_plus_rat tptp.one_one_rat) (tptp.aa_rat_rat tptp.abs_abs_rat X))))) (forall ((X tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_int_int tptp.abs_abs_int X))))) (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F tptp.fun_complex_nat)) (=> (tptp.finite3207457112153483333omplex B3) (=> (tptp.ord_le211207098394363844omplex B3 A2) (= (tptp.groups5693394587270226106ex_nat F (tptp.minus_811609699411566653omplex A2 B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups5693394587270226106ex_nat F A2)) (tptp.groups5693394587270226106ex_nat F B3)))))) (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F tptp.fun_int_nat)) (=> (tptp.finite_finite_int B3) (=> (tptp.ord_less_eq_set_int B3 A2) (= (tptp.groups4541462559716669496nt_nat F (tptp.minus_minus_set_int A2 B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups4541462559716669496nt_nat F A2)) (tptp.groups4541462559716669496nt_nat F B3)))))) (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat F))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat B3)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat B3) A2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.minus_minus_set_nat A2 B3)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat _let_1 A2)) (tptp.aa_set_nat_nat _let_1 B3))))))) (forall ((F tptp.fun_nat_complex) (K tptp.nat)) (let ((_let_1 (tptp.groups2073611262835488442omplex F))) (=> (= (tptp.aa_nat_complex F tptp.zero_zero_nat) tptp.zero_zero_complex) (= (tptp.aa_set_nat_complex _let_1 (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) K)) (tptp.aa_set_nat_complex _let_1 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K)))))) (forall ((F tptp.fun_nat_rat) (K tptp.nat)) (=> (= (tptp.aa_nat_rat F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (tptp.groups2906978787729119204at_rat F (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) K)) (tptp.groups2906978787729119204at_rat F (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K))))) (forall ((F tptp.fun_nat_int) (K tptp.nat)) (=> (= (tptp.aa_nat_int F tptp.zero_zero_nat) tptp.zero_zero_int) (= (tptp.groups3539618377306564664at_int F (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) K)) (tptp.groups3539618377306564664at_int F (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K))))) (forall ((F tptp.fun_nat_nat) (K tptp.nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat F))) (=> (= (tptp.aa_nat_nat F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) K)) (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K)))))) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (let ((_let_1 (tptp.groups6591440286371151544t_real F))) (=> (= (tptp.aa_nat_real F tptp.zero_zero_nat) tptp.zero_zero_real) (= (tptp.aa_set_nat_real _let_1 (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) K)) (tptp.aa_set_nat_real _let_1 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat K)))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_nat_rat G _let_1))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_nat_int G _let_1))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (= (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_nat_nat G _let_1)))))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups6591440286371151544t_real G))) (= (tptp.aa_set_nat_real _let_2 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real _let_2 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_nat_real G _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat G M)) (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G M)) (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.groups6591440286371151544t_real G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_real _let_1 (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G M)) (tptp.aa_set_nat_real _let_1 (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M _let_1)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat G _let_1)) (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G _let_1)) (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_2)) (= (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G _let_2)) (tptp.aa_set_nat_nat _let_1 (tptp.set_or1269000886237332187st_nat M N2)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.groups6591440286371151544t_real G))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_2)) (= (tptp.aa_set_nat_real _let_1 (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G _let_2)) (tptp.aa_set_nat_real _let_1 (tptp.set_or1269000886237332187st_nat M N2)))))))) (forall ((N2 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 N2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (forall ((N2 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 N2))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_int tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N2)))))) (forall ((N2 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 N2)))))) (forall ((N2 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 N2)))))) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.times_times_rat (tptp.aa_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.aa_int_fun_nat_int tptp.power_power_int A) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 tptp.one))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) A)) A))) (forall ((N2 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 N2))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_zero_nat))) (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N2))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_zero_int))) (forall ((N2 tptp.num) (Q2 tptp.num)) (not (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))) (= (tptp.aa_num_nat tptp.numeral_numeral_nat _let_54) (tptp.aa_nat_nat tptp.suc _let_39)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.suc N2))) (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))) N2))) (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 ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((Y2 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) Y2))) D3)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Y2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y2) B)))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G _let_1)) (tptp.aa_nat_rat G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat G M)) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ly G) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G _let_1)) (tptp.aa_nat_int G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G M)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_lz G) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1)) (tptp.aa_nat_nat G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G M)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_lo G)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_real)) (let ((_let_1 (tptp.set_or1269000886237332187st_nat M N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) _let_1)) (tptp.aa_nat_real G (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G M)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_lp G)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ma F) (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F _let_1)) (tptp.aa_nat_rat F M)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_mb F) (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F _let_1)) (tptp.aa_nat_int F M)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_mc F)) (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F _let_1)) (tptp.aa_nat_real F M)))))) (forall ((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 ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer X)) (tptp.abs_abs_Code_integer Y))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) (tptp.aa_rat_rat tptp.abs_abs_rat Y))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)))))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int X)) (tptp.aa_int_int tptp.abs_abs_int Y))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1)))))) (forall ((X tptp.code_integer)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (tptp.abs_abs_Code_integer X) tptp.one_one_Code_integer))) (forall ((X tptp.rat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_rat) (= (tptp.aa_rat_rat tptp.abs_abs_rat X) tptp.one_one_rat))) (forall ((X tptp.real)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_real) (= (tptp.aa_real_real tptp.abs_abs_real X) tptp.one_one_real))) (forall ((X tptp.int)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_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 ((X32 tptp.num)) (= (tptp.aa_num_nat tptp.size_size_num (tptp.aa_num_num tptp.bit1 X32)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_size_num X32)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) N2) (tptp.aa_nat_rat (tptp.power_power_rat A) N2)))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.abs_abs_Code_integer A)) N2) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real A)) N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2)))) (forall ((N2 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))) N2)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.abs_abs_int A)) N2) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int A) N2)))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_rat) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat M N2))) (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat _let_3 _let_2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_int) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat M N2))) (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat _let_3 _let_2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_nat) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups3542108847815614940at_nat G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_nat _let_4 (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_4 (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_set_nat_nat _let_4 (tptp.set_or1269000886237332187st_nat _let_3 _let_2)))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G tptp.fun_nat_real) (P2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 P2))) (let ((_let_3 (tptp.aa_nat_nat _let_1 tptp.one_one_nat))) (let ((_let_4 (tptp.groups6591440286371151544t_real G))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_3)) (= (tptp.aa_set_nat_real _let_4 (tptp.set_or1269000886237332187st_nat M _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real _let_4 (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_set_nat_real _let_4 (tptp.set_or1269000886237332187st_nat _let_3 _let_2)))))))))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit1 M))) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat M)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 M))) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) _let_1)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_num_int tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))) (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 M)) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one) _let_1)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))) (forall ((Q2 tptp.num) (N2 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 N2))) _let_1)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))) (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int tptp.one)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 N2))) _let_1)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int N2)) (tptp.aa_num_int tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))) (forall ((Q2 tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 Q2)))) (= (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger tptp.one) _let_1) (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit1 N2)) _let_1)) (= (tptp.modulo364778990260209775nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))) (forall ((M tptp.nat) (N2 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)))) N2) (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)) N2))) (forall ((M tptp.nat) (N2 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)))) N2) (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)) N2))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.unique5052692396658037445od_int M N2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int _let_2) _let_1)))))) (forall ((Qr tptp.product_prod_int_int)) (= (tptp.aa_Pro6799258434465214121nt_int tptp.adjust_div Qr) (tptp.aa_Pro6799258434465214121nt_int (tptp.produc8211389475949308722nt_int tptp.aTP_Lamm_md) Qr))) (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.aa_nat_Code_integer (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.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((P tptp.fun_re1255401033344146673l_bool) (X tptp.real)) (=> (forall ((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.aa_rat_rat tptp.abs_abs_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((P tptp.fun_int_fun_int_bool) (X tptp.int)) (=> (forall ((X3 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X3)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P X3) (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_int_fun_nat_int tptp.power_power_int X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((Y tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) _let_1)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Y) _let_1))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer X)) Y)))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) Y)))))) (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) Y)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) Y)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_nat_Code_integer (tptp.power_8256067586552552935nteger X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)))) (forall ((X tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_rat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat tptp.abs_abs_rat X)) tptp.one_one_rat)))) (forall ((X tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_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 ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.unique5052692396658037445od_int M N2) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int _let_2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.unique5055182867167087721od_nat M N2) (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) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (= (tptp.unique3479559517661332726nteger M N2) (tptp.produc1086072967326762835nteger (tptp.divide6298287555418463151nteger _let_2 _let_1) (tptp.modulo364778990260209775nteger _let_2 _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.unique5055182867167087721od_nat M N2) (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 ((N2 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))) N2)) (=> (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.aa_nat_Code_integer (tptp.power_8256067586552552935nteger A) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger B) N2)))))) (forall ((N2 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))) N2)) (=> (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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real B) N2)))))) (forall ((N2 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))) N2)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat A)) (tptp.aa_rat_rat tptp.abs_abs_rat B))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat A) N2)) (tptp.aa_nat_rat (tptp.power_power_rat B) N2)))))) (forall ((N2 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))) N2)) (=> (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.aa_int_fun_nat_int tptp.power_power_int A) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int B) N2)))))) (forall ((I6 tptp.set_complex) (X tptp.fun_co8153928105989009288nteger) (A tptp.fun_co8153928105989009288nteger) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_com4217951221296830281nteger X I3))))) (=> (= (tptp.groups6621422865394947399nteger X I6) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.aa_com4217951221296830281nteger A I3) B))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.groups6621422865394947399nteger (tptp.aa_fun5267417455630836558nteger (tptp.aTP_Lamm_me X) A) I6) B))) Delta)))))) (forall ((I6 tptp.set_real) (X tptp.fun_re6978948838062957830nteger) (A tptp.fun_re6978948838062957830nteger) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_real_Code_integer X I3))))) (=> (= (tptp.groups7713935264441627589nteger X I6) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.aa_real_Code_integer A I3) B))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.groups7713935264441627589nteger (tptp.aa_fun7923231501384339402nteger (tptp.aTP_Lamm_mf X) A) I6) B))) Delta)))))) (forall ((I6 tptp.set_nat) (X tptp.fun_nat_Code_integer) (A tptp.fun_nat_Code_integer) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer X I3))))) (=> (= (tptp.groups7501900531339628137nteger X I6) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer A I3) B))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.groups7501900531339628137nteger (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_mg X) A) I6) B))) Delta)))))) (forall ((I6 tptp.set_int) (X tptp.fun_int_Code_integer) (A tptp.fun_int_Code_integer) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_int_Code_integer X I3))))) (=> (= (tptp.groups7873554091576472773nteger X I6) tptp.one_one_Code_integer) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.aa_int_Code_integer A I3) B))) Delta)))) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.abs_abs_Code_integer (tptp.minus_8373710615458151222nteger (tptp.groups7873554091576472773nteger (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_mh X) A) I6) B))) Delta)))))) (forall ((I6 tptp.set_complex) (X tptp.fun_complex_real) (A tptp.fun_complex_real) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real X I3))))) (=> (= (tptp.groups5808333547571424918x_real X I6) tptp.one_one_real) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real A I3)) B))) Delta)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups5808333547571424918x_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_mi X) A) I6)) B))) Delta)))))) (forall ((I6 tptp.set_real) (X tptp.fun_real_real) (A tptp.fun_real_real) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real X I3))))) (=> (= (tptp.groups8097168146408367636l_real X I6) tptp.one_one_real) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real A I3)) B))) Delta)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups8097168146408367636l_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_mj X) A) I6)) B))) Delta)))))) (forall ((I6 tptp.set_int) (X tptp.fun_int_real) (A tptp.fun_int_real) (B tptp.real) (Delta tptp.real)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_int_real X I3))))) (=> (= (tptp.groups8778361861064173332t_real X I6) tptp.one_one_real) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_int_real A I3)) B))) Delta)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.groups8778361861064173332t_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_mk X) A) I6)) B))) Delta)))))) (forall ((I6 tptp.set_complex) (X tptp.fun_complex_rat) (A tptp.fun_complex_rat) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_complex_rat X I3))))) (=> (= (tptp.groups5058264527183730370ex_rat X I6) tptp.one_one_rat) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_complex_rat A I3)) B))) Delta)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups5058264527183730370ex_rat (tptp.aa_fun7622890401989837636ex_rat (tptp.aTP_Lamm_ml X) A) I6)) B))) Delta)))))) (forall ((I6 tptp.set_real) (X tptp.fun_real_rat) (A tptp.fun_real_rat) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_real_rat X I3))))) (=> (= (tptp.groups1300246762558778688al_rat X I6) tptp.one_one_rat) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_real_rat A I3)) B))) Delta)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups1300246762558778688al_rat (tptp.aa_fun2468082234287226944al_rat (tptp.aTP_Lamm_mm X) A) I6)) B))) Delta)))))) (forall ((I6 tptp.set_nat) (X tptp.fun_nat_rat) (A tptp.fun_nat_rat) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) (tptp.aa_nat_rat X I3))))) (=> (= (tptp.groups2906978787729119204at_rat X I6) tptp.one_one_rat) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat A I3)) B))) Delta)))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat tptp.abs_abs_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_mn X) A) I6)) B))) Delta)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_complex)) (let ((_let_1 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_mo F)) (tptp.set_or1269000886237332187st_nat M N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex F M)) (tptp.aa_nat_complex F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_rat)) (let ((_let_1 (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_mp F) (tptp.set_or1269000886237332187st_nat M N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F M)) (tptp.aa_nat_rat F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_mq F) (tptp.set_or1269000886237332187st_nat M N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F M)) (tptp.aa_nat_int F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_mr F)) (tptp.set_or1269000886237332187st_nat M N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F M)) (tptp.aa_nat_real F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ms F) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N2)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F N2)) (tptp.aa_nat_rat F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_mt F) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F N2)) (tptp.aa_nat_int F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_mu F)) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F N2)) (tptp.aa_nat_real F M))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.divmod_nat M N2) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_1 N2)) tptp.one_one_int) (tptp.groups3539618377306564664at_int _let_1 (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_ca N2)))))) (forall ((N2 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 N2)) tptp.one_one_nat) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat _let_1) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_ca N2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) X)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_1) (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.power_power_rat X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.one_one_rat) X)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int) X)) (tptp.groups3539618377306564664at_int _let_1 (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_1 M)) (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) X)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_1) (tptp.set_or1269000886237332187st_nat M N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((G tptp.fun_nat_rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups2906978787729119204at_rat G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_mv G) (tptp.set_or1269000886237332187st_nat M N2))))) (forall ((G tptp.fun_nat_int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.groups3539618377306564664at_int G (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_mw G) (tptp.set_or1269000886237332187st_nat M N2))))) (forall ((G tptp.fun_nat_nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_mx G)) (tptp.set_or1269000886237332187st_nat M N2))))) (forall ((G tptp.fun_nat_real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat _let_1 M) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat _let_1 N2)))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_my G)) (tptp.set_or1269000886237332187st_nat M N2))))) (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 ((N2 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 N2)) (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_ca N2)))))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_ai) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (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 N2) (tptp.aa_nat_nat tptp.suc N2))) (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.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 ((A tptp.nat) (D tptp.nat) (N2 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_mz A) D)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (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 N2)) (tptp.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 N2) D)))) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_ai) (tptp.set_or1269000886237332187st_nat M N2)) (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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) 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 ((N2 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 N2) (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 N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) _let_2)))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.unique5055182867167087721od_nat M N2))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) (tptp.aa_num_nat tptp.numeral_numeral_nat M)))) (=> (not _let_2) (= _let_1 (tptp.unique5026877609467782581ep_nat N2 (tptp.unique5055182867167087721od_nat M (tptp.aa_num_num tptp.bit0 N2))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.unique5052692396658037445od_int M N2))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) (tptp.aa_num_int tptp.numeral_numeral_int M)))) (=> (not _let_2) (= _let_1 (tptp.aa_Pro6970504127699319548nt_int (tptp.unique5024387138958732305ep_int N2) (tptp.unique5052692396658037445od_int M (tptp.aa_num_num tptp.bit0 N2))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.unique3479559517661332726nteger M N2))) (let ((_let_2 (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (and (=> _let_2 (= _let_1 (tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M)))) (=> (not _let_2) (= _let_1 (tptp.unique4921790084139445826nteger N2 (tptp.unique3479559517661332726nteger M (tptp.aa_num_num tptp.bit0 N2))))))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real _let_53) (tptp.aa_real_real tptp.uminus_uminus_real _let_55)) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int _let_79) (tptp.aa_int_int tptp.uminus_uminus_int _let_80)) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex _let_50) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_82)) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat _let_78) (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_81)) (= (tptp.neg_nu7757733837767384882nteger _let_77) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_54))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (= (tptp.aa_real_real _let_2 (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_2 X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) _let_82) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real tptp.one_one_real) _let_55) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) _let_81) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) _let_80) (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (let ((_let_2 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_1) (tptp.set_or1269000886237332187st_nat M N2)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_or1269000886237332187st_nat M N2)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 M)) (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_rat_rat (tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_1) (tptp.set_or1269000886237332187st_nat M N2)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) X)))))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (= M N2))) (forall ((P tptp.bool) (Q tptp.fun_int_fun_int_bool) (X2 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_na P) Q)) X2)) (and (tptp.pp P) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool Q) X2))))) (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 ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (= (tptp.aa_rat_rat tptp.abs_abs_rat _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.aa_int_int tptp.abs_abs_int _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (= (tptp.aa_real_real tptp.abs_abs_real _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N2 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 N2))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M) tptp.zero_z3403309356797280102nteger) (= M tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_z3403309356797280102nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (= tptp.zero_zero_nat N2))) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger tptp.zero_zero_nat) tptp.zero_z3403309356797280102nteger) (forall ((N2 tptp.num)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.numera6690914467698888265omplex N2))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_rat tptp.numeral_numeral_rat N2))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_int tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_real tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.plus_p5714425477246183910nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat M) N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))) (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex X) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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_int tptp.semiri1314217659103216013at_int X) (tptp.aa_nat_int (tptp.aa_int_fun_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 ((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_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_Code_integer tptp.semiri4939895301339042750nteger X) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger 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.aa_com8181001469867462503omplex 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_int (tptp.aa_int_fun_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 ((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_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_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger B)) W) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat B) W) X))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat M) N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) N2))) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat) _let_76 (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger tptp.one_one_nat) tptp.one_one_Code_integer) (forall ((N2 tptp.nat)) (= (= tptp.one_one_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_Code_integer (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2) tptp.one_one_rat) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2) tptp.one_one_real) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2) tptp.one_one_Code_integer) (= N2 tptp.one_one_nat))) (forall ((N2 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 N2)))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (= (tptp.aa_num_nat tptp.pred_numeral tptp.one) tptp.zero_zero_nat) (forall ((K tptp.num) (N2 tptp.nat)) (= (= (tptp.aa_num_nat tptp.numeral_numeral_nat K) (tptp.aa_nat_nat tptp.suc N2)) (= (tptp.aa_num_nat tptp.pred_numeral K) N2))) (forall ((N2 tptp.nat) (K tptp.num)) (= (= (tptp.aa_nat_nat tptp.suc N2) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (= N2 (tptp.aa_num_nat tptp.pred_numeral K)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.arctan X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arctan X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int) (forall ((P tptp.bool)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n3304061248610475627l_real 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.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_bool_nat tptp.zero_n2687167440665602831ol_nat P)) (tptp.zero_n356916108424825756nteger P))) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real _let_53) _let_53) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int _let_79) _let_79) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex _let_50) _let_50) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat _let_78) _let_78) (= (tptp.neg_nu5831290666863070958nteger _let_77) _let_77) (forall ((K tptp.num)) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex (tptp.numera6690914467698888265omplex K)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit1 K)))) (forall ((K tptp.num)) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real (tptp.aa_num_real tptp.numeral_numeral_real K)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 K)))) (forall ((K tptp.num)) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit1 K)))) (forall ((K tptp.num)) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (forall ((F tptp.fun_int_nat) (A2 tptp.set_int)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.groups4541462559716669496nt_nat F A2)) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_nb F) A2))) (forall ((F tptp.fun_complex_nat) (A2 tptp.set_complex)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.groups5693394587270226106ex_nat F A2)) (tptp.groups7754918857620584856omplex (tptp.aTP_Lamm_nc F) A2))) (forall ((F tptp.fun_nat_nat) (A2 tptp.set_nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_nd F) A2))) (forall ((F tptp.fun_nat_nat) (A2 tptp.set_nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_ne F) A2))) (forall ((F tptp.fun_nat_nat) (A2 tptp.set_nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_nf F)) A2))) (forall ((F tptp.fun_nat_nat) (A2 tptp.set_nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_ng F)) A2))) (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_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int)) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex tptp.one_one_complex) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_rat_rat (tptp.plus_plus_rat tptp.one_one_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat tptp.suc M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat tptp.one_one_nat) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)))) (forall ((M tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat tptp.suc M)) (tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)))) (forall ((W tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_num_real tptp.numeral_numeral_real W)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (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)) N2)))) (forall ((N2 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 N2)) (tptp.aa_num_real tptp.numeral_numeral_real W))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat W))))) (forall ((N2 tptp.num) (M tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real N2)) (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 N2)) M)))) (forall ((K tptp.num) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat tptp.pred_numeral K)) N2)))) (forall ((N2 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 N2)) (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 N2) (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.pred_numeral (tptp.aa_num_num tptp.bit1 K)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 K)))) (forall ((K tptp.num) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.pred_numeral K)) N2)))) (forall ((N2 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 N2)) (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 N2) (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((N2 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 N2)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_num_nat tptp.pred_numeral K)))) (forall ((K tptp.num) (N2 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 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_num_nat tptp.pred_numeral K)) N2))) (forall ((N2 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 N2)) (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 N2) (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num) (N2 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 N2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_num_nat tptp.pred_numeral K)) N2)))) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) _let_53) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) _let_79) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) _let_50) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) _let_78) (= (tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) _let_77) (forall ((N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 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 N2))) (tptp.pp (tptp.aa_nat_bool _let_1 N2))))) (forall ((N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real K))) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int K))) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex K))) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (= (tptp.neg_nu7757733837767384882nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.neg_nu5831290666863070958nteger _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real K))) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int K))) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex K))) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex _let_1)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat _let_1)) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K))) (= (tptp.neg_nu5831290666863070958nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger _let_1)) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.neg_nu7757733837767384882nteger _let_1))))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Y) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N2)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2)))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Y) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N2)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2)))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2)))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Y) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real X)) N2)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2)))) (forall ((Y tptp.nat) (X tptp.num) (N2 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)) N2))) (= (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.nat) (X tptp.num) (N2 tptp.nat)) (= (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Y) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) N2)) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2)))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.numera6690914467698888265omplex X)) N2) (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)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat X)) N2) (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)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2) (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)) N2) Y))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real X)) N2) (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)) N2) Y))) (forall ((X tptp.num) (N2 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)) N2))) (= (= _let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))) (forall ((X tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger X)) N2) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Y)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat X)) N2) Y))) (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_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.aa_int_fun_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 ((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_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_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger 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_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_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int (tptp.aa_int_fun_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 ((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_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_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger B)) W)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger 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_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_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger 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.aa_int_fun_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 ((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_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger B)) W)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger 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.aa_int_fun_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) (N2 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)) N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X)) N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (N2 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)) N2))) (or (tptp.pp (tptp.aa_nat_bool _let_1 X)) (= N2 tptp.zero_zero_nat))))) (forall ((X tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) N2))) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) X)) (= N2 tptp.zero_zero_nat)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I2)) N2))) (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 I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I2)) N2))) (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 I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real I2)) N2))) (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 I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 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 I2)) N2))) (= (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) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger I2)) N2))) (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 I2)) N2))))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I2)) N2)) (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 I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I2)) N2)) (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 I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real I2)) N2)) (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 I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 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 I2)) N2)))) (= (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 ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger I2)) N2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger 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 I2)) N2)) X)))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real I2)) N2))) (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 I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger I2)) N2))) (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 I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I2)) N2))) (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 I2)) N2))))) (forall ((X tptp.nat) (I2 tptp.num) (N2 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 I2)) N2))) (= (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) (I2 tptp.num) (N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I2)) N2))) (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 I2)) N2))))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real I2)) N2)) (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 I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger I2)) N2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger 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 I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X tptp.nat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat I2)) N2)) (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 I2)) N2)) X)))) (forall ((I2 tptp.num) (N2 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 I2)) N2)))) (= (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 ((I2 tptp.num) (N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int I2)) N2)) (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 I2)) N2)) X)))) (forall ((N2 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 N2))) (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))))) (forall ((N2 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 N2))) (tptp.pp (tptp.aa_nat_bool _let_1 N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (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))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A2 tptp.fun_int_fun_int_bool) (B3 tptp.fun_int_fun_int_bool)) (=> (tptp.ord_le4546832483993983377t_bool A2 B3) (tptp.ord_le2843351958646193337nt_int (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool A2)) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool B3))))) (forall ((Prod tptp.product_prod_int_int)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool tptp.aTP_Lamm_nh) Prod))) (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat X))) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_1) Y) (tptp.aa_rat_rat (tptp.times_times_rat Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) Y) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) Y) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Y) _let_1)))) (forall ((X tptp.nat) (Y tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) Y) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger 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 X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((Z tptp.int)) (not (forall ((M2 tptp.nat) (N 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 N))))))) (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 tptp.semiri5074537144036343181t_real N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))) (forall ((N2 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 N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) tptp.zero_z3403309356797280102nteger)))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_real))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat tptp.suc N2)) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (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 ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (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.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M))) (= (tptp.divide6298287555418463151nteger A (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_2) _let_1)) (tptp.divide6298287555418463151nteger (tptp.divide6298287555418463151nteger A _let_2) _let_1))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real I2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) J)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger I2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) 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 I2)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) 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 I2)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) 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 I2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int J))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) (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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) (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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) (tptp.divide6298287555418463151nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)))) (forall ((M tptp.nat) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_num_nat tptp.numeral_numeral_nat N2)) (tptp.aa_num_int tptp.numeral_numeral_int N2))) (forall ((M tptp.int) (N2 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) N2)) tptp.one_one_int) (= (tptp.aa_int_int tptp.abs_abs_int M) tptp.one_one_int))) (forall ((Z tptp.int)) (=> (forall ((N tptp.nat)) (not (= Z (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (not (forall ((N 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 N))))))))) (forall ((P tptp.fun_int_bool) (Z tptp.int)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool P (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (=> (forall ((N 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 N)))))) (tptp.pp (tptp.aa_int_bool P Z))))) (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) (N2 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 N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (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 ((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 ((N tptp.nat)) (not (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))))) (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 ((N tptp.nat)) (= K (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.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 ((N2 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 N2) M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (forall ((M tptp.nat) (N2 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 N2)) 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) N2))) Z))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2)) (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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2)) (tptp.modulo364778990260209775nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))) (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_76 (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 ((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 ((F tptp.fun_int_nat) (A2 tptp.set_int)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.groups4541462559716669496nt_nat F A2)) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_nb F) A2))) (forall ((F tptp.fun_nat_nat) (A2 tptp.set_nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_nd F) A2))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat K) (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.pred_numeral K)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.semiri4216267220026989637d_enat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_Ext7969882492699152700d_enat (tptp.aa_Ext3475206891998675565d_enat tptp.ord_ma741700101516333627d_enat (tptp.semiri4216267220026989637d_enat X)) (tptp.semiri4216267220026989637d_enat Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_int_int (tptp.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)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.ord_max_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat X)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.ord_max_nat X) Y)) (tptp.ord_max_Code_integer (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger X) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Y)))) (forall ((X2 tptp.nat) (Xa tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X2) Xa)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((X2 tptp.nat) (Xa tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X2) Xa)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (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 N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (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 N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (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 N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (forall ((Y2 tptp.real)) (exists ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N)) X))))))) (forall ((M tptp.int)) (=> (forall ((N tptp.nat)) (not (= M (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))) (not (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 (= M (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))))))) (forall ((N2 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 N2) X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X))))) (forall ((I2 tptp.int) (D tptp.int)) (=> (not (= I2 tptp.zero_zero_int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int D) I2)) (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 I2)))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))) (forall ((A tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z)) (exists ((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 ((N2 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 N2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (and (= N2 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))) (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L))) (tptp.aa_int_int tptp.abs_abs_int L))))) (forall ((D tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat D) N2)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) D)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real D))))) (forall ((N2 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 N2))) 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 ((N tptp.nat)) (not (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))))))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.pred_numeral K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) tptp.one_one_nat))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.modulo_modulo_int A))) (let ((_let_3 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.times_times_int _let_1))) (= (tptp.aa_int_int _let_2 (tptp.aa_int_int _let_4 _let_3)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int A) _let_1)) _let_3))) (tptp.aa_int_int _let_2 _let_1)))))))) (forall ((A tptp.nat) (M tptp.nat) (N2 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 N2))) (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.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (let ((_let_3 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1))) (= (tptp.modulo364778990260209775nteger A (tptp.aa_Cod1783974652533396728nteger _let_3 _let_2)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_3 (tptp.modulo364778990260209775nteger (tptp.divide6298287555418463151nteger A _let_1) _let_2)) (tptp.modulo364778990260209775nteger A _let_1))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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) N2)))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat M) N2)))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2)) (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) N2)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real 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 ((N tptp.nat)) (=> (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) 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 ((N tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)) (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)))))) (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N tptp.nat)) (=> (= K (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))) (not (forall ((N tptp.nat)) (=> (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N))))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) 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 N2)) tptp.one_one_real)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (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 ((I2 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 I2) 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 I2)) (tptp.aa_int_int _let_1 J))))))) (forall ((M tptp.int) (N2 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) N2)) M)) (= (tptp.aa_int_int tptp.abs_abs_int N2) tptp.one_one_int)))) (forall ((N2 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 N2))))))) (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 ((N tptp.nat)) (= X (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat tptp.suc N))))))) (forall ((N2 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 N2)))) tptp.zero_zero_int))) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex tptp.neg_nu8557863876264182079omplex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) X)) tptp.one_one_complex))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.neg_nu8295874005876285629c_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) X)) tptp.one_one_real))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat tptp.neg_nu5219082963157363817nc_rat X) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) X)) tptp.one_one_rat))) (forall ((X tptp.int)) (= (tptp.aa_int_int tptp.neg_nu5851722552734809277nc_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) X)) tptp.one_one_int))) (forall ((A tptp.nat) (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 ((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 ((N2 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 N2)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((N2 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 N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((N2 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 N2) M)) (=> (not (= N2 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 N2)))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.divide_divide_rat tptp.one_one_rat))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (=> (not (= N2 tptp.zero_zero_nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M))) (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int tptp.abs_abs_int K)) L))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) L)))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.plus_plus_int K))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int _let_1 (tptp.aa_int_int tptp.abs_abs_int L)))) (tptp.pp (tptp.aa_int_bool _let_2 (tptp.aa_int_int _let_1 L))))))) (forall ((X tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 C)) (=> (forall ((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 ((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 ((N tptp.nat)) (=> (= K (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N)))))))) (forall ((P tptp.fun_int_bool) (X tptp.nat) (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 ((N2 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 N2)) (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 N2) X)))))) (forall ((N2 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 N2)) (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 N2) X)))) tptp.one_one_real))) (forall ((X tptp.real) (N2 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) N2)) (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.ln_ln_real X))))) (forall ((M tptp.nat) (N2 tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc I3))) (tptp.aa_nat_int F I3)))) tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (=> (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 N2))) (exists ((I3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) I3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) N2)) (= (tptp.aa_nat_int F I3) K)))))))) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex tptp.neg_nu6511756317524482435omplex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) X)) tptp.one_one_complex))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.neg_nu6075765906172075777c_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) X)) tptp.one_one_real))) (forall ((X tptp.rat)) (= (tptp.aa_rat_rat tptp.neg_nu3179335615603231917ec_rat X) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat X) X)) tptp.one_one_rat))) (forall ((X tptp.int)) (= (tptp.aa_int_int tptp.neg_nu3811975205180677377ec_int X) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) X)) tptp.one_one_int))) (forall ((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 ((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 ((X tptp.real) (N2 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 N2)) 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)) N2))))) (forall ((X tptp.real) (N2 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 N2)) X))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) N2)))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc I3))) (tptp.aa_nat_int F I3)))) tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_nat_int F N2))) (exists ((I3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) N2)) (= (tptp.aa_nat_int F I3) K))))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_int) (K tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I3) tptp.one_one_nat))) (tptp.aa_nat_int F I3)))) tptp.one_one_int)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F tptp.zero_zero_nat)) K)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int K) (tptp.aa_nat_int F N2))) (exists ((I3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) N2)) (= (tptp.aa_nat_int F I3) K))))))) (forall ((A tptp.complex) (D tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) (let ((_let_2 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_complex_complex _let_2 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ni A) D)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex _let_2 A)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) D))))))) (forall ((A tptp.rat) (D tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (let ((_let_2 (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_rat_rat _let_2 (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_nj A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat _let_2 A)) (tptp.aa_rat_rat (tptp.times_times_rat _let_1) D))))))) (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_int_int _let_2 (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_nk A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int _let_2 A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) D))))))) (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_Cod1783974652533396728nteger _let_2 (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_nl A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger _let_2 A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) D))))))) (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_nat_nat _let_2 (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_nm A) D)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) D))))))) (forall ((A tptp.real) (D tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real _let_2 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_nn A) D)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_2 A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) D))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_rat_rat (tptp.times_times_rat _let_1) (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.arctan X)) (tptp.aa_real_real tptp.arctan Y)) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)))))))) (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_nk A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (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.aa_int_fun_int_int tptp.plus_plus_int _let_2) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) A)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) D)))) _let_1))))) (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_nl A) D) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger _let_2 tptp.one_one_Code_integer)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) A) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_2) D))) _let_1))))) (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_nm A) D)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) A)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_2) D)))) _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (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_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2))) (tptp.aa_rat_rat (tptp.times_times_rat _let_1) (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((X tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (let ((_let_3 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_2) (tptp.set_or1269000886237332187st_nat M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_2 M)) (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex _let_2 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.aa_complex_complex _let_1 X)))))))))) (forall ((X tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.power_power_rat X))) (let ((_let_3 (tptp.groups2906978787729119204at_rat _let_2 (tptp.set_or1269000886237332187st_nat M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_2 M)) (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat _let_2 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.aa_rat_rat _let_1 X)))))))))) (forall ((X tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_3 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_2) (tptp.set_or1269000886237332187st_nat M (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_2 M)) (tptp.aa_real_real _let_1 (tptp.aa_nat_real _let_2 (tptp.aa_nat_nat tptp.suc N2))))) (tptp.aa_real_real _let_1 X)))))))))) (forall ((N2 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))) N2)) (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 N2)) X))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real _let_1 X)) N2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (= (tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2)) (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_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (= (tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2)) (tptp.divide6298287555418463151nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer)) (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 (tptp.produc1917071388513777916omplex tptp.aTP_Lamm_no (tptp.divmod_nat N2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 (tptp.produc6207742614233964070at_rat tptp.aTP_Lamm_np (tptp.divmod_nat N2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 (tptp.produc6840382203811409530at_int tptp.aTP_Lamm_nq (tptp.divmod_nat N2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.aa_Pro6168199777849092593t_real (tptp.produc1703576794950452218t_real tptp.aTP_Lamm_nr) (tptp.divmod_nat N2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_Pro4243173770044397973at_nat (tptp.produc6842872674320459806at_nat tptp.aTP_Lamm_ns) (tptp.divmod_nat N2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 (tptp.produc1830744345554046123nteger tptp.aTP_Lamm_nt (tptp.divmod_nat N2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((E tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) E)) (not (forall ((N tptp.nat)) (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat tptp.suc N)))) E))))))) (forall ((E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (not (forall ((N 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 N)))) E))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.topolo6980174941875973593q_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nu X)))) (forall ((H tptp.real) (Z tptp.real) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2))) (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 N2)))) (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) N2)) (tptp.aa_nat_real _let_4 N2))) 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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2))) (let ((_let_2 (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Z))) (let ((_let_4 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Z) H))) (=> (not (= H tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) K5)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex _let_4)) K5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex _let_4) N2)) (tptp.aa_nat_complex _let_3 N2))) H)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2)) (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 N2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real K5) (tptp.aa_nat_nat _let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex H)))))))))))) (forall ((X tptp.rat) (Y tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) X)) (exists ((N tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Y) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N)) X)))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (exists ((N 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 N)) X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nv X)))))) (forall ((F tptp.fun_nat_complex)) (= (tptp.suminf_complex (tptp.aTP_Lamm_kp F)) (tptp.aa_nat_complex F tptp.zero_zero_nat))) (forall ((F tptp.fun_nat_real)) (= (tptp.suminf_real (tptp.aTP_Lamm_kr F)) (tptp.aa_nat_real F tptp.zero_zero_nat))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_1)))) (forall ((B tptp.complex) (A tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex B) A))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.topolo6980174941875973593q_real (tptp.aa_real_fun_nat_real tptp.power_power_real X))))) (forall ((X tptp.real)) (exists ((N 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 N))))) (forall ((X tptp.rat)) (exists ((N 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 N))))) (forall ((X tptp.rat)) (exists ((N 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 N))))) (forall ((X tptp.real)) (exists ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N))))) (forall ((P tptp.fun_nat_bool)) (=> (not (tptp.pp (tptp.aa_nat_bool P tptp.zero_zero_nat))) (=> (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_13))) (exists ((N tptp.nat)) (and (not (tptp.pp (tptp.aa_nat_bool P N))) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_nat_nat tptp.suc 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.aa_real_real tptp.arctan X) (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nw X))))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) _let_1)))) (forall ((A tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_num_real tptp.numeral_numeral_real W)))) (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real W)))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.real_V7735802525324610683m_real A))))) (forall ((W tptp.num) (A tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex W)) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real W)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) _let_1)))) (forall ((A tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_num_real tptp.numeral_numeral_real W)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((W tptp.num)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) (tptp.aa_num_real tptp.numeral_numeral_real W))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real)) (= X tptp.zero_zero_real))) (forall ((X tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real)) (= X tptp.zero_zero_complex))) (forall ((C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real C)) tptp.one_one_real)) (= (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.power_power_real C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) C))))) (forall ((C tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)) tptp.one_one_real)) (= (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) C))))) (= (tptp.suminf_complex tptp.aTP_Lamm_nx) tptp.zero_zero_complex) (= (tptp.suminf_real tptp.aTP_Lamm_fb) tptp.zero_zero_real) (= (tptp.suminf_nat tptp.aTP_Lamm_bl) tptp.zero_zero_nat) (= (tptp.suminf_int tptp.aTP_Lamm_ny) tptp.zero_zero_int) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real W))) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real _let_1) _let_1))) (forall ((W tptp.num)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.numera6690914467698888265omplex W)) (tptp.aa_num_real tptp.numeral_numeral_real W))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex B) A)))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B)))) (forall ((S3 tptp.set_real) (F tptp.fun_real_complex) (G tptp.fun_real_real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_real_complex F X3))) (tptp.aa_real_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups5754745047067104278omplex F S3))) (tptp.groups8097168146408367636l_real G S3))))) (forall ((S3 tptp.set_set_nat) (F tptp.fun_set_nat_complex) (G tptp.fun_set_nat_real)) (=> (forall ((X3 tptp.set_nat)) (=> (tptp.member_set_nat X3 S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_set_nat_complex F X3))) (tptp.aa_set_nat_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups8255218700646806128omplex F S3))) (tptp.groups5107569545109728110t_real G S3))))) (forall ((S3 tptp.set_int) (F tptp.fun_int_complex) (G tptp.fun_int_real)) (=> (forall ((X3 tptp.int)) (=> (tptp.member_int X3 S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_int_complex F X3))) (tptp.aa_int_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups3049146728041665814omplex F S3))) (tptp.groups8778361861064173332t_real G S3))))) (forall ((S3 tptp.set_nat) (F tptp.fun_nat_complex) (G tptp.fun_nat_real)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F X3))) (tptp.aa_nat_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) S3))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) S3))))) (forall ((S3 tptp.set_complex) (F tptp.fun_complex_complex) (G tptp.fun_complex_real)) (=> (forall ((X3 tptp.complex)) (=> (tptp.member_complex X3 S3) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex F X3))) (tptp.aa_complex_real G X3))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups7754918857620584856omplex F S3))) (tptp.groups5808333547571424918x_real G S3))))) (forall ((S3 tptp.set_nat) (F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X3) S3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F X3))) (tptp.aa_nat_real G X3))))) (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_set_nat_real (tptp.groups6591440286371151544t_real F) S3))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) S3))))) (forall ((X tptp.real) (N2 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) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) N2))) (forall ((X tptp.complex) (N2 tptp.nat)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) N2))) (forall ((F tptp.fun_nat_complex) (A2 tptp.set_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) A2))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_nz F)) A2)))) (forall ((F tptp.fun_complex_complex) (A2 tptp.set_complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.groups7754918857620584856omplex F A2))) (tptp.groups5808333547571424918x_real (tptp.aTP_Lamm_oa F) A2)))) (forall ((F tptp.fun_nat_real) (A2 tptp.set_nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_ob F)) A2)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.uminus_uminus_real X)) Y)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) Y)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B))))) (forall ((W tptp.real) (N2 tptp.nat) (Z tptp.real)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real W) N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Z) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real W) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z))))) (forall ((W tptp.complex) (N2 tptp.nat) (Z tptp.complex)) (=> (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex W) N2) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Z) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex W) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))))) (forall ((X tptp.real) (R2 tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) S2)))))) (forall ((X tptp.complex) (R2 tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) S2)))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) E)))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y))) E)))) (forall ((X tptp.real) (R2 tptp.real) (Y tptp.real) (S2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R2) S2)))))) (forall ((X tptp.complex) (R2 tptp.real) (Y tptp.complex) (S2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R2) S2)))))) (forall ((X tptp.real) (N2 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) N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) N2)))) (forall ((X tptp.complex) (N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) N2)))) (forall ((A tptp.real) (R2 tptp.real) (B tptp.real) (S2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real B)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R2) S2)))))) (forall ((A tptp.complex) (R2 tptp.real) (B tptp.complex) (S2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R2) S2)))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))) E)))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B))) C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) C))))) (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B))))) (forall ((A tptp.complex) (B tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B))))) (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex _let_1 Y))) E1)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex Y) Z))) E22)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex _let_1 Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real E1) E22))))))) (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y))) E)))) (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) E)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y))) E)))) (forall ((A tptp.real) (B tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B))))) (forall ((A tptp.complex) (B tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B))))) (forall ((A tptp.real) (B tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))))) (forall ((A tptp.complex) (B tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B))))) (forall ((N3 tptp.set_nat) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (=> (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) N3))) (= (tptp.aa_nat_complex F N) tptp.zero_zero_complex))) (= (tptp.suminf_complex F) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) N3))))) (forall ((N3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (=> (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) N3))) (= (tptp.aa_nat_int F N) tptp.zero_zero_int))) (= (tptp.suminf_int F) (tptp.groups3539618377306564664at_int F N3))))) (forall ((N3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (=> (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) N3))) (= (tptp.aa_nat_nat F N) tptp.zero_zero_nat))) (= (tptp.suminf_nat F) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) N3))))) (forall ((N3 tptp.set_nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (=> (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) N3))) (= (tptp.aa_nat_real F N) tptp.zero_zero_real))) (= (tptp.suminf_real F) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) N3))))) (forall ((W tptp.real) (N2 tptp.nat)) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real W) N2) tptp.one_one_real) (or (= (tptp.aa_real_real tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))) (forall ((W tptp.complex) (N2 tptp.nat)) (=> (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex W) N2) tptp.one_one_complex) (or (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N2 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.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex C) D)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) C))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex B) D)))))) (forall ((A tptp.real) (B tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real A)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real B)))) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B))))) (forall ((A tptp.complex) (B tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex A)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B)))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B))))) (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.aa_com8181001469867462503omplex tptp.power_power_complex X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.one_one_complex) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X) tptp.one_one_real))) (forall ((Z tptp.real) (W tptp.real) (M tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real W)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Z) M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real W) M)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z) W)))))))) (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex W)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Z) M)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex W) M)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex Z) W)))))))) (= _let_63 (tptp.suminf_real tptp.aTP_Lamm_oc)) (forall ((H tptp.complex) (Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Z))) (=> (not (= H tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Z) H)) N2)) (tptp.aa_nat_complex _let_2 N2))) H)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2)) (tptp.aa_nat_complex _let_2 _let_1))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex H) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_oe H) Z) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H tptp.rat) (Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (tptp.power_power_rat Z))) (=> (not (= H tptp.zero_zero_rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Z) H)) N2)) (tptp.aa_nat_rat _let_2 N2))) H)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (tptp.aa_nat_rat _let_2 _let_1))) (tptp.aa_rat_rat (tptp.times_times_rat H) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_og H) Z) N2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H tptp.real) (Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real Z))) (=> (not (= H tptp.zero_zero_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) H)) N2)) (tptp.aa_nat_real _let_2 N2))) H)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_nat_real _let_2 _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real H) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_oi H) Z) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.summable_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nw X)))) (forall ((R tptp.set_Pr9123050470547338789r_bool) (S3 tptp.set_Pr9123050470547338789r_bool)) (= (tptp.ord_le3056413707720749373l_bool (tptp.aTP_Lamm_oj R) (tptp.aTP_Lamm_oj S3)) (tptp.ord_le5008643164228425349r_bool R S3))) (forall ((R tptp.set_Pr8218934625190621173um_num) (S3 tptp.set_Pr8218934625190621173um_num)) (= (tptp.ord_le2278887450727035829m_bool (tptp.aTP_Lamm_ok R) (tptp.aTP_Lamm_ok S3)) (tptp.ord_le880128212290418581um_num R S3))) (forall ((R tptp.set_Pr6200539531224447659at_num) (S3 tptp.set_Pr6200539531224447659at_num)) (= (tptp.ord_le8094096262961209215m_bool (tptp.aTP_Lamm_ol R) (tptp.aTP_Lamm_ol S3)) (tptp.ord_le8085105155179020875at_num R S3))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (tptp.ord_le4899916226251588169t_bool (tptp.aTP_Lamm_om R) (tptp.aTP_Lamm_om S3)) (tptp.ord_le3146513528884898305at_nat R S3))) (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (tptp.ord_le4546832483993983377t_bool (tptp.aTP_Lamm_on R) (tptp.aTP_Lamm_on S3)) (tptp.ord_le2843351958646193337nt_int R S3))) (forall ((S3 tptp.set_int)) (= (not (tptp.finite_finite_int S3)) (forall ((M6 tptp.int)) (exists ((N5 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int M6) (tptp.aa_int_int tptp.abs_abs_int N5))) (tptp.member_int N5 S3)))))) (forall ((R1 tptp.fun_Pr5837708615769641901m_bool) (R22 tptp.fun_Pr5837708615769641901m_bool)) (=> (tptp.ord_le7676714441581034317m_bool R1 R22) (tptp.ord_le998981803562422117m_bool (tptp.accp_P3113834385874906142um_num R22) (tptp.accp_P3113834385874906142um_num R1)))) (forall ((R1 tptp.fun_Pr248683899324676269t_bool) (R22 tptp.fun_Pr248683899324676269t_bool)) (=> (tptp.ord_le2087689725136068685t_bool R1 R22) (tptp.pp (tptp.aa_fun8663595511526100224l_bool (tptp.ord_le2468614981408567801t_bool (tptp.accp_P4275260045618599050at_nat R22)) (tptp.accp_P4275260045618599050at_nat R1))))) (forall ((R1 tptp.fun_Pr3099820731930151597t_bool) (R22 tptp.fun_Pr3099820731930151597t_bool)) (=> (tptp.ord_le4938826557741544013t_bool R1 R22) (tptp.ord_le4737936599360737601t_bool (tptp.accp_P1096762738010456898nt_int R22) (tptp.accp_P1096762738010456898nt_int R1)))) (forall ((R1 tptp.fun_li8598321315282354825t_bool) (R22 tptp.fun_li8598321315282354825t_bool)) (=> (tptp.ord_le4434192926011882025t_bool R1 R22) (tptp.ord_le2936377143570524336t_bool (tptp.accp_list_nat R22) (tptp.accp_list_nat R1)))) (forall ((R1 tptp.fun_nat_fun_nat_bool) (R22 tptp.fun_nat_fun_nat_bool)) (=> (tptp.ord_le4899916226251588169t_bool R1 R22) (tptp.ord_le8840051076831633728t_bool (tptp.accp_nat R22) (tptp.accp_nat R1)))) (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (tptp.member_set_nat I2 (tptp.set_or890127255671739683et_nat K)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat I2) K)))) (forall ((I2 tptp.rat) (K tptp.rat)) (= (tptp.member_rat I2 (tptp.set_ord_lessThan_rat K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat I2) K)))) (forall ((I2 tptp.num) (K tptp.num)) (= (tptp.member_num I2 (tptp.set_ord_lessThan_num K)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num I2) K)))) (forall ((I2 tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I2) K)))) (forall ((I2 tptp.int) (K tptp.int)) (= (tptp.member_int I2 (tptp.aa_int_set_int tptp.set_ord_lessThan_int K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int I2) K)))) (forall ((I2 tptp.real) (K tptp.real)) (= (tptp.member_real I2 (tptp.set_or5984915006950818249n_real K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real I2) K)))) (forall ((I2 tptp.bool) (K tptp.bool)) (= (tptp.member_bool I2 (tptp.aa_bool_set_bool tptp.set_or4454636193642143162n_bool K)) (tptp.pp (tptp.aa_bool_bool (tptp.ord_less_bool I2) K)))) (forall ((I2 tptp.nat) (F tptp.fun_nat_complex)) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_fn I2) F))) (forall ((I2 tptp.nat) (F tptp.fun_nat_real)) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_oo I2) F))) (forall ((I2 tptp.nat) (F tptp.fun_nat_nat)) (tptp.summable_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_op I2) F))) (forall ((I2 tptp.nat) (F tptp.fun_nat_int)) (tptp.summable_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_oq I2) F))) (tptp.summable_complex tptp.aTP_Lamm_nx) (tptp.summable_real tptp.aTP_Lamm_fb) (tptp.summable_nat tptp.aTP_Lamm_bl) (tptp.summable_int tptp.aTP_Lamm_ny) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (= (tptp.summable_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr F) K)) (tptp.summable_real F))) (forall ((F tptp.fun_nat_complex) (K tptp.nat)) (= (tptp.summable_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_or F) K)) (tptp.summable_complex F))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_ord_lessThan_rat X) (tptp.set_ord_lessThan_rat Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_ord_lessThan_num X) (tptp.set_ord_lessThan_num Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.ord_less_eq_set_int (tptp.aa_int_set_int tptp.set_ord_lessThan_int X) (tptp.aa_int_set_int tptp.set_ord_lessThan_int Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.ord_less_eq_set_real (tptp.set_or5984915006950818249n_real X) (tptp.set_or5984915006950818249n_real Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.bool) (Y tptp.bool)) (= (tptp.ord_less_eq_set_bool (tptp.aa_bool_set_bool tptp.set_or4454636193642143162n_bool X) (tptp.aa_bool_set_bool tptp.set_or4454636193642143162n_bool Y)) (tptp.pp (tptp.aa_bool_bool (tptp.ord_less_eq_bool X) Y)))) (forall ((C tptp.complex) (F tptp.fun_nat_complex)) (= (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_os C) F)) (or (= C tptp.zero_zero_complex) (tptp.summable_complex F)))) (forall ((C tptp.real) (F tptp.fun_nat_real)) (= (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hk C) F)) (or (= C tptp.zero_zero_real) (tptp.summable_real F)))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (= (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ot F) C)) (or (= C tptp.zero_zero_complex) (tptp.summable_complex F)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (= (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ht F) C)) (or (= C tptp.zero_zero_real) (tptp.summable_real F)))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ou P) F)))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ov P) F)))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.summable_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_ow P) F)))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat (tptp.collect_nat P))) (tptp.summable_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_ox P) F)))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_oy A2) F)))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_oz A2) F)))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.summable_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_pa A2) F)))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.summable_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_pb A2) F)))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_nat_rat G N2)))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_nat_int G N2)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat G))) (= (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_nat_nat G N2))))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat)) (let ((_let_1 (tptp.groups6591440286371151544t_real G))) (= (tptp.aa_set_nat_real _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_nat_real G N2))))) (forall ((C tptp.real)) (= (tptp.summable_real (tptp.aa_real_fun_nat_real tptp.power_power_real C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real C)) tptp.one_one_real)))) (forall ((C tptp.complex)) (= (tptp.summable_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex C)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)) tptp.one_one_real)))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aTP_Lamm_ob F)) (tptp.summable_real F))) (forall ((F tptp.fun_nat_complex)) (=> (tptp.summable_real (tptp.aTP_Lamm_nz F)) (tptp.summable_complex F))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F N))) (tptp.aa_nat_real G N)))))) (=> (tptp.summable_real G) (tptp.summable_real F)))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_real)) (=> (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F N))) (tptp.aa_nat_real G N)))))) (=> (tptp.summable_real G) (tptp.summable_complex F)))) (forall ((G tptp.fun_nat_real) (N3 tptp.nat) (F tptp.fun_nat_real)) (=> (tptp.summable_real G) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F N))) (tptp.aa_nat_real G N))))) (tptp.summable_real F)))) (forall ((G tptp.fun_nat_real) (N3 tptp.nat) (F tptp.fun_nat_complex)) (=> (tptp.summable_real G) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F N))) (tptp.aa_nat_real G N))))) (tptp.summable_complex F)))) (forall ((C tptp.complex)) (= (tptp.summable_complex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_pc C)) (= C tptp.zero_zero_complex))) (forall ((C tptp.real)) (= (tptp.summable_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_pd C)) (= C tptp.zero_zero_real))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (=> (tptp.summable_complex F) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_pe F) C)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_hg F) C)))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (=> (tptp.summable_complex F) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_pf F) C)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_pg F) C)))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (=> (tptp.summable_complex G) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ph F) G))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ho F) G))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (tptp.summable_nat G) (tptp.summable_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hn F) G))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (tptp.summable_int G) (tptp.summable_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_pi F) G))))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (=> (tptp.summable_complex G) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_pj F) G))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hr F) G))))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (=> (tptp.summable_complex F) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ot F) C)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ht F) C)))) (forall ((F tptp.fun_nat_real)) (= (tptp.summable_real (tptp.aTP_Lamm_lp F)) (tptp.summable_real F))) (forall ((F tptp.fun_nat_complex)) (= (tptp.summable_complex (tptp.aTP_Lamm_pk F)) (tptp.summable_complex F))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (tptp.summable_real (tptp.aTP_Lamm_fy F)))) (forall ((F tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (tptp.summable_complex (tptp.aTP_Lamm_pl F)))) (forall ((F tptp.fun_nat_real)) (= (tptp.summable_real (tptp.aTP_Lamm_fy F)) (tptp.summable_real F))) (forall ((F tptp.fun_nat_complex)) (= (tptp.summable_complex (tptp.aTP_Lamm_pl F)) (tptp.summable_complex F))) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (=> (tptp.summable_real F) (tptp.summable_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr F) K)))) (forall ((F tptp.fun_nat_complex) (K tptp.nat)) (=> (tptp.summable_complex F) (tptp.summable_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_or F) K)))) (forall ((I6 tptp.set_complex) (F tptp.fun_co8378349014452122532t_real)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.summable_real (tptp.aa_com20334259897932645t_real F I3)))) (tptp.summable_real (tptp.aa_fun471735231769099483t_real (tptp.aTP_Lamm_pn I6) F)))) (forall ((I6 tptp.set_real) (F tptp.fun_re4238438383274954274t_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.summable_real (tptp.aa_real_fun_nat_real F I3)))) (tptp.summable_real (tptp.aa_fun628238740774635481t_real (tptp.aTP_Lamm_po I6) F)))) (forall ((I6 tptp.set_int) (F tptp.fun_int_fun_nat_real)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.summable_real (tptp.aa_int_fun_nat_real F I3)))) (tptp.summable_real (tptp.aa_fun2842512154077127769t_real (tptp.aTP_Lamm_pq I6) F)))) (forall ((I6 tptp.set_real) (F tptp.fun_re2084383175013312036omplex)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.summable_complex (tptp.aa_rea1531280491672885477omplex F I3)))) (tptp.summable_complex (tptp.aa_fun7632768522510439005omplex (tptp.aTP_Lamm_ps I6) F)))) (forall ((I6 tptp.set_nat) (F tptp.fun_na1142814060743658952omplex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.summable_complex (tptp.aa_nat6454746962644518025omplex F I3)))) (tptp.summable_complex (tptp.aa_fun4886358607025424513omplex (tptp.aTP_Lamm_pu I6) F)))) (forall ((I6 tptp.set_int) (F tptp.fun_in8056368165505483812omplex)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.summable_complex (tptp.aa_int4144929030551567077omplex F I3)))) (tptp.summable_complex (tptp.aa_fun3543561798013398749omplex (tptp.aTP_Lamm_pw I6) F)))) (forall ((I6 tptp.set_int) (F tptp.fun_int_fun_nat_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.summable_int (tptp.aa_int_fun_nat_int F I3)))) (tptp.summable_int (tptp.aa_fun8710705519803144921at_int (tptp.aTP_Lamm_py I6) F)))) (forall ((I6 tptp.set_complex) (F tptp.fun_co3258106519541737638omplex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex F I3)))) (tptp.summable_complex (tptp.aa_fun5003373910569599327omplex (tptp.aTP_Lamm_qa I6) F)))) (forall ((I6 tptp.set_nat) (F tptp.fun_nat_fun_nat_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.summable_nat (tptp.aa_nat_fun_nat_nat F I3)))) (tptp.summable_nat (tptp.aa_fun8466562714962205125at_nat (tptp.aTP_Lamm_qb I6) F)))) (forall ((I6 tptp.set_nat) (F tptp.fun_nat_fun_nat_real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.summable_real (tptp.aa_nat_fun_nat_real F I3)))) (tptp.summable_real (tptp.aa_fun7039663905532832253t_real (tptp.aTP_Lamm_qc I6) F)))) (forall ((F tptp.fun_nat_int) (X tptp.int)) (=> (tptp.summable_int F) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N))) X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.suminf_int F)) X))))) (forall ((F tptp.fun_nat_nat) (X tptp.nat)) (=> (tptp.summable_nat F) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N))) X))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.suminf_nat F)) X))))) (forall ((F tptp.fun_nat_real) (X tptp.real)) (=> (tptp.summable_real F) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N))) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.suminf_real F)) X))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aTP_Lamm_ko F)) (tptp.summable_real F))) (forall ((U tptp.set_nat)) (= (tptp.set_or890127255671739683et_nat U) (tptp.collect_set_nat (tptp.aTP_Lamm_qd U)))) (forall ((U tptp.rat)) (= (tptp.set_ord_lessThan_rat U) (tptp.collect_rat (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_qe U)))) (forall ((U tptp.num)) (= (tptp.set_ord_lessThan_num U) (tptp.collect_num (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_qf U)))) (forall ((U tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat U) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_ca U)))) (forall ((U tptp.int)) (= (tptp.aa_int_set_int tptp.set_ord_lessThan_int U) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_qg U)))) (forall ((U tptp.real)) (= (tptp.set_or5984915006950818249n_real U) (tptp.collect_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_qh U)))) (forall ((U tptp.bool)) (= (tptp.aa_bool_set_bool tptp.set_or4454636193642143162n_bool U) (tptp.collect_bool (tptp.aTP_Lamm_qi U)))) (forall ((F tptp.fun_nat_int) (X tptp.int)) (=> (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 F N)))) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N))) X))) (tptp.summable_int F)))) (forall ((F tptp.fun_nat_nat) (X tptp.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) (tptp.aa_nat_nat F N)))) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N))) X))) (tptp.summable_nat F)))) (forall ((F tptp.fun_nat_real) (X tptp.real)) (=> (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 F N)))) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N))) X))) (tptp.summable_real F)))) (forall ((S3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (exists ((K3 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K3)))))) (forall ((S3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (exists ((K2 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K2)))))) (forall ((F tptp.fun_nat_real) (X tptp.real) (Z tptp.real)) (=> (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj F) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real X))) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qk F) Z))))) (forall ((F tptp.fun_nat_complex) (X tptp.complex) (Z tptp.complex)) (=> (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql F) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))) (tptp.summable_real (tptp.aa_com20334259897932645t_real (tptp.aTP_Lamm_qm F) Z))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N)) (tptp.aa_nat_real G N)))) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.suminf_real F)) (tptp.suminf_real G))))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (forall ((N tptp.nat)) (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 G N)))) (=> (tptp.summable_nat F) (=> (tptp.summable_nat G) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.suminf_nat F)) (tptp.suminf_nat G))))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (forall ((N tptp.nat)) (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 G N)))) (=> (tptp.summable_int F) (=> (tptp.summable_int G) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.suminf_int F)) (tptp.suminf_int G))))))) (forall ((F tptp.fun_nat_complex) (K tptp.nat)) (=> (tptp.summable_complex F) (= (tptp.suminf_complex F) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.suminf_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_or F) K))) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K)))))) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (=> (tptp.summable_real F) (= (tptp.suminf_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.suminf_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr F) K))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K)))))) (forall ((F tptp.fun_nat_complex) (K tptp.nat)) (=> (tptp.summable_complex F) (= (tptp.suminf_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_or F) K)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.suminf_complex F)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K)))))) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (=> (tptp.summable_real F) (= (tptp.suminf_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr F) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.suminf_real F)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K)))))) (forall ((M tptp.rat) (N2 tptp.rat)) (= (tptp.ord_less_set_rat (tptp.set_ord_lessThan_rat M) (tptp.set_ord_lessThan_rat N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.ord_less_set_num (tptp.set_ord_lessThan_num M) (tptp.set_ord_lessThan_num N2)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((M tptp.int) (N2 tptp.int)) (= (tptp.ord_less_set_int (tptp.aa_int_set_int tptp.set_ord_lessThan_int M) (tptp.aa_int_set_int tptp.set_ord_lessThan_int N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int M) N2)))) (forall ((M tptp.real) (N2 tptp.real)) (= (tptp.ord_less_set_real (tptp.set_or5984915006950818249n_real M) (tptp.set_or5984915006950818249n_real N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real M) N2)))) (forall ((M tptp.bool) (N2 tptp.bool)) (= (tptp.ord_less_set_bool (tptp.aa_bool_set_bool tptp.set_or4454636193642143162n_bool M) (tptp.aa_bool_set_bool tptp.set_or4454636193642143162n_bool N2)) (tptp.pp (tptp.aa_bool_bool (tptp.ord_less_bool M) N2)))) (forall ((C tptp.complex) (F tptp.fun_nat_complex)) (=> (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_os C) F)) (=> (not (= C tptp.zero_zero_complex)) (tptp.summable_complex F)))) (forall ((C tptp.real) (F tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hk C) F)) (=> (not (= C tptp.zero_zero_real)) (tptp.summable_real F)))) (tptp.summable_real _let_75) (tptp.summable_int _let_74) (tptp.summable_complex _let_73) (tptp.pp (tptp.aa_real_bool _let_71 tptp.pi)) (forall ((F tptp.fun_nat_int) (N2 tptp.nat)) (=> (tptp.summable_int F) (=> (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F M2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups3539618377306564664at_int F (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.suminf_int F)))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat)) (=> (tptp.summable_nat F) (=> (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F M2))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.suminf_nat F)))))) (forall ((F tptp.fun_nat_real) (N2 tptp.nat)) (=> (tptp.summable_real F) (=> (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real F M2))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.suminf_real F)))))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (=> (tptp.summable_complex F) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.suminf_complex F)) C) (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_pe F) C))))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real F)) C) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_hg F) C))))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (=> (tptp.summable_complex F) (= (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_pf F) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C) (tptp.suminf_complex F))))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (= (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_pg F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) (tptp.suminf_real F))))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (=> (tptp.summable_complex G) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.suminf_complex F)) (tptp.suminf_complex G)) (tptp.suminf_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ph F) G)))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.suminf_real F)) (tptp.suminf_real G)) (tptp.suminf_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ho F) G)))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (tptp.summable_nat G) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.suminf_nat F)) (tptp.suminf_nat G)) (tptp.suminf_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hn F) G)))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (tptp.summable_int G) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.suminf_int F)) (tptp.suminf_int G)) (tptp.suminf_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_pi F) G)))))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (=> (tptp.summable_complex G) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.suminf_complex F)) (tptp.suminf_complex G)) (tptp.suminf_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_pj F) G)))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (tptp.summable_real G) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.suminf_real F)) (tptp.suminf_real G)) (tptp.suminf_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hr F) G)))))) (forall ((F tptp.fun_nat_complex) (C tptp.complex)) (=> (tptp.summable_complex F) (= (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ot F) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.suminf_complex F)) C)))) (forall ((F tptp.fun_nat_real) (C tptp.real)) (=> (tptp.summable_real F) (= (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ht F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.suminf_real F)) C)))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (= (tptp.suminf_real (tptp.aTP_Lamm_fy F)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.suminf_real F))))) (forall ((F tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (= (tptp.suminf_complex (tptp.aTP_Lamm_pl F)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.suminf_complex F))))) (forall ((I6 tptp.set_complex) (F tptp.fun_co8378349014452122532t_real)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.summable_real (tptp.aa_com20334259897932645t_real F I3)))) (= (tptp.suminf_real (tptp.aa_fun471735231769099483t_real (tptp.aTP_Lamm_pn I6) F)) (tptp.groups5808333547571424918x_real (tptp.aTP_Lamm_qn F) I6)))) (forall ((I6 tptp.set_real) (F tptp.fun_re4238438383274954274t_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.summable_real (tptp.aa_real_fun_nat_real F I3)))) (= (tptp.suminf_real (tptp.aa_fun628238740774635481t_real (tptp.aTP_Lamm_po I6) F)) (tptp.groups8097168146408367636l_real (tptp.aTP_Lamm_qo F) I6)))) (forall ((I6 tptp.set_int) (F tptp.fun_int_fun_nat_real)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.summable_real (tptp.aa_int_fun_nat_real F I3)))) (= (tptp.suminf_real (tptp.aa_fun2842512154077127769t_real (tptp.aTP_Lamm_pq I6) F)) (tptp.groups8778361861064173332t_real (tptp.aTP_Lamm_qp F) I6)))) (forall ((I6 tptp.set_real) (F tptp.fun_re2084383175013312036omplex)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.summable_complex (tptp.aa_rea1531280491672885477omplex F I3)))) (= (tptp.suminf_complex (tptp.aa_fun7632768522510439005omplex (tptp.aTP_Lamm_ps I6) F)) (tptp.groups5754745047067104278omplex (tptp.aTP_Lamm_qq F) I6)))) (forall ((I6 tptp.set_nat) (F tptp.fun_na1142814060743658952omplex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.summable_complex (tptp.aa_nat6454746962644518025omplex F I3)))) (= (tptp.suminf_complex (tptp.aa_fun4886358607025424513omplex (tptp.aTP_Lamm_pu I6) F)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_qr F)) I6)))) (forall ((I6 tptp.set_int) (F tptp.fun_in8056368165505483812omplex)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.summable_complex (tptp.aa_int4144929030551567077omplex F I3)))) (= (tptp.suminf_complex (tptp.aa_fun3543561798013398749omplex (tptp.aTP_Lamm_pw I6) F)) (tptp.groups3049146728041665814omplex (tptp.aTP_Lamm_qs F) I6)))) (forall ((I6 tptp.set_int) (F tptp.fun_int_fun_nat_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.summable_int (tptp.aa_int_fun_nat_int F I3)))) (= (tptp.suminf_int (tptp.aa_fun8710705519803144921at_int (tptp.aTP_Lamm_py I6) F)) (tptp.groups4538972089207619220nt_int (tptp.aTP_Lamm_qt F) I6)))) (forall ((I6 tptp.set_complex) (F tptp.fun_co3258106519541737638omplex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex F I3)))) (= (tptp.suminf_complex (tptp.aa_fun5003373910569599327omplex (tptp.aTP_Lamm_qa I6) F)) (tptp.groups7754918857620584856omplex (tptp.aTP_Lamm_qu F) I6)))) (forall ((I6 tptp.set_nat) (F tptp.fun_nat_fun_nat_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.summable_nat (tptp.aa_nat_fun_nat_nat F I3)))) (= (tptp.suminf_nat (tptp.aa_fun8466562714962205125at_nat (tptp.aTP_Lamm_qb I6) F)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_qv F)) I6)))) (forall ((I6 tptp.set_nat) (F tptp.fun_nat_fun_nat_real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.summable_real (tptp.aa_nat_fun_nat_real F I3)))) (= (tptp.suminf_real (tptp.aa_fun7039663905532832253t_real (tptp.aTP_Lamm_qc I6) F)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_qw F)) I6)))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (I2 tptp.nat)) (=> (tptp.summable_int F) (=> (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F M2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) I2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F I2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.groups3539618377306564664at_int F (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.suminf_int F)))))))) (forall ((F tptp.fun_nat_nat) (N2 tptp.nat) (I2 tptp.nat)) (=> (tptp.summable_nat F) (=> (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F M2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) I2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F I2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.suminf_nat F)))))))) (forall ((F tptp.fun_nat_real) (N2 tptp.nat) (I2 tptp.nat)) (=> (tptp.summable_real F) (=> (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F M2))))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) I2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real F I2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.suminf_real F)))))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (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 F N)))) (= (= (tptp.suminf_real F) tptp.zero_zero_real) (forall ((N5 tptp.nat)) (= (tptp.aa_nat_real F N5) tptp.zero_zero_real)))))) (forall ((F tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (forall ((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 F N)))) (= (= (tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N5 tptp.nat)) (= (tptp.aa_nat_nat F N5) tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (forall ((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 F N)))) (= (= (tptp.suminf_int F) tptp.zero_zero_int) (forall ((N5 tptp.nat)) (= (tptp.aa_nat_int F N5) tptp.zero_zero_int)))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (forall ((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 F N)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.suminf_real F)))))) (forall ((F tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (forall ((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 F N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.suminf_nat F)))))) (forall ((F tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (forall ((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 F N)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.suminf_int F)))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (forall ((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 F N)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.suminf_real F)))))) (forall ((F tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (forall ((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 F N)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.suminf_nat F)))))) (forall ((F tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (forall ((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 F N)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.suminf_int F)))))) (forall ((F tptp.fun_nat_complex)) (tptp.summable_complex (tptp.aTP_Lamm_kp F))) (forall ((F tptp.fun_nat_real)) (tptp.summable_real (tptp.aTP_Lamm_kr F))) (forall ((F tptp.fun_nat_complex)) (tptp.summable_complex (tptp.aTP_Lamm_kp F))) (forall ((F tptp.fun_nat_real)) (tptp.summable_real (tptp.aTP_Lamm_kr F))) (forall ((F tptp.fun_nat_int)) (tptp.summable_int (tptp.aTP_Lamm_qx F))) (forall ((F tptp.fun_nat_complex) (Z tptp.complex)) (=> (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql F) Z)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_qy F) Z)))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (=> (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj F) Z)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qz F) Z)))) (forall ((F tptp.fun_nat_complex) (Z tptp.complex)) (= (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_qy F) Z)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql F) Z)))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (= (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qz F) Z)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj F) Z)))) (forall ((F tptp.fun_nat_complex) (M tptp.nat) (Z tptp.complex)) (= (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_ra F) M) Z)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql F) Z)))) (forall ((F tptp.fun_nat_real) (M tptp.nat) (Z tptp.real)) (= (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_rb F) M) Z)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj F) Z)))) (forall ((F tptp.fun_nat_complex) (G tptp.fun_nat_real)) (=> (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F N))) (tptp.aa_nat_real G N)))))) (=> (tptp.summable_real G) (tptp.summable_real (tptp.aTP_Lamm_nz F))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real F N))) (tptp.aa_nat_real G N)))))) (=> (tptp.summable_real G) (tptp.summable_real (tptp.aTP_Lamm_ko F))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_rc G) N2)) _let_1) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) _let_1)))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_rd G) N2)) _let_1) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) _let_1)))) (forall ((F tptp.fun_nat_real)) (let ((_let_1 (tptp.aTP_Lamm_ko F))) (=> (tptp.summable_real _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.suminf_real F))) (tptp.suminf_real _let_1)))))) (forall ((Q tptp.fun_int_nat) (P tptp.fun_int_nat) (N2 tptp.int)) (let ((_let_1 (tptp.aa_int_set_int tptp.set_ord_lessThan_int N2))) (=> (forall ((X3 tptp.int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat Q X3)) (tptp.aa_int_nat P X3)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups4541462559716669496nt_nat P _let_1)) (tptp.groups4541462559716669496nt_nat Q _let_1)) (tptp.groups4541462559716669496nt_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_lm Q) P) _let_1))))) (forall ((Q tptp.fun_real_nat) (P tptp.fun_real_nat) (N2 tptp.real)) (let ((_let_1 (tptp.set_or5984915006950818249n_real N2))) (=> (forall ((X3 tptp.real)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_real_nat Q X3)) (tptp.aa_real_nat P X3)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups1935376822645274424al_nat P _let_1)) (tptp.groups1935376822645274424al_nat Q _let_1)) (tptp.groups1935376822645274424al_nat (tptp.aa_fun211602392931233840al_nat (tptp.aTP_Lamm_lk Q) P) _let_1))))) (forall ((Q tptp.fun_bool_nat) (P tptp.fun_bool_nat) (N2 tptp.bool)) (let ((_let_1 (tptp.aa_bool_set_bool tptp.set_or4454636193642143162n_bool N2))) (=> (forall ((X3 tptp.bool)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_bool_nat Q X3)) (tptp.aa_bool_nat P X3)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.groups5768501273728744877ol_nat P _let_1)) (tptp.groups5768501273728744877ol_nat Q _let_1)) (tptp.groups5768501273728744877ol_nat (tptp.aa_fun9101744387563128124ol_nat (tptp.aTP_Lamm_re Q) P) _let_1))))) (forall ((Q tptp.fun_nat_nat) (P tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (=> (forall ((X3 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat Q X3)) (tptp.aa_nat_nat P X3)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat P) _let_1)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat Q) _let_1)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_ln Q) P)) _let_1))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (=> (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 F N)))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.suminf_real F))) (exists ((I5 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real F I5)))))))) (forall ((F tptp.fun_nat_nat)) (=> (tptp.summable_nat F) (=> (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 F N)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.suminf_nat F))) (exists ((I5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F I5)))))))) (forall ((F tptp.fun_nat_int)) (=> (tptp.summable_int F) (=> (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 F N)))) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.suminf_int F))) (exists ((I5 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int F I5)))))))) (forall ((F tptp.fun_nat_real) (I2 tptp.nat)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.summable_real F) (=> (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 F N)))) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_nat_real F I2))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.suminf_real F)))))))) (forall ((F tptp.fun_nat_nat) (I2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat))) (=> (tptp.summable_nat F) (=> (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 F N)))) (=> (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.aa_nat_nat F I2))) (tptp.pp (tptp.aa_nat_bool _let_1 (tptp.suminf_nat F)))))))) (forall ((F tptp.fun_nat_int) (I2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int))) (=> (tptp.summable_int F) (=> (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 F N)))) (=> (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_nat_int F I2))) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.suminf_int F)))))))) (forall ((F tptp.fun_nat_real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aTP_Lamm_qj F))) (=> (tptp.summable_real (tptp.aa_real_fun_nat_real _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) (tptp.aa_real_real tptp.real_V7735802525324610683m_real X))) (tptp.summable_real (tptp.aa_real_fun_nat_real _let_1 Z)))))) (forall ((F tptp.fun_nat_complex) (X tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.aTP_Lamm_ql F))) (=> (tptp.summable_complex (tptp.aa_com8181001469867462503omplex _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex _let_1 Z)))))) (forall ((C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real C)) tptp.one_one_real)) (tptp.summable_real (tptp.aa_real_fun_nat_real tptp.power_power_real C)))) (forall ((C tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)) tptp.one_one_real)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex C)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) tptp.one_one_real)) (tptp.summable_real (tptp.aa_real_fun_nat_real tptp.power_power_real X)))) (forall ((X tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) tptp.one_one_real)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X)))) (forall ((F tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (= (tptp.suminf_complex (tptp.aTP_Lamm_pk F)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.suminf_complex F)) (tptp.aa_nat_complex F tptp.zero_zero_nat))))) (forall ((F tptp.fun_nat_real)) (=> (tptp.summable_real F) (= (tptp.suminf_real (tptp.aTP_Lamm_lp F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.suminf_real F)) (tptp.aa_nat_real F tptp.zero_zero_nat))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.pi) _let_62)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_23) tptp.pi)) (not (= _let_25 _let_23)) (forall ((F tptp.fun_nat_real) (K tptp.nat)) (=> (tptp.summable_real F) (=> (forall ((D3 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))) D3))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real F (tptp.aa_nat_nat _let_2 _let_1))) (tptp.aa_nat_real F (tptp.aa_nat_nat _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat K))) (tptp.suminf_real F)))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ly G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_lz G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_lo G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G tptp.zero_zero_nat)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_lp G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((F tptp.fun_nat_rat) (M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_rf F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F tptp.zero_zero_nat)) (tptp.aa_nat_rat F M)))) (forall ((F tptp.fun_nat_int) (M tptp.nat)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_rg F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F tptp.zero_zero_nat)) (tptp.aa_nat_int F M)))) (forall ((F tptp.fun_nat_real) (M tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_rh F)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F tptp.zero_zero_nat)) (tptp.aa_nat_real F M)))) (forall ((F tptp.fun_nat_rat) (M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ma F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F M)) (tptp.aa_nat_rat F tptp.zero_zero_nat)))) (forall ((F tptp.fun_nat_int) (M tptp.nat)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_mb F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F M)) (tptp.aa_nat_int F tptp.zero_zero_nat)))) (forall ((F tptp.fun_nat_real) (M tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_mc F)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F M)) (tptp.aa_nat_real F tptp.zero_zero_nat)))) (forall ((F tptp.fun_nat_rat) (N2 tptp.nat) (R2 tptp.rat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat F _let_1)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) R2)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_ri F) R2) _let_1)))) (forall ((F tptp.fun_nat_int) (N2 tptp.nat) (R2 tptp.int)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups3539618377306564664at_int F _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) R2)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_rj F) R2) _let_1)))) (forall ((F tptp.fun_nat_Code_integer) (N2 tptp.nat) (R2 tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.minus_8373710615458151222nteger (tptp.groups7501900531339628137nteger F _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) R2)) (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_rk F) R2) _let_1)))) (forall ((F tptp.fun_nat_real) (N2 tptp.nat) (R2 tptp.real)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) R2)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_rl F) R2)) _let_1)))) (forall ((F tptp.fun_nat_real)) (let ((_let_1 (tptp.aTP_Lamm_ob F))) (=> (tptp.summable_real _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.suminf_real F))) (tptp.suminf_real _let_1)))))) (forall ((F tptp.fun_nat_complex)) (let ((_let_1 (tptp.aTP_Lamm_nz F))) (=> (tptp.summable_real _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.suminf_complex F))) (tptp.suminf_real _let_1)))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_lo G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_lp G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((F tptp.fun_nat_int) (I6 tptp.set_nat)) (=> (tptp.summable_int F) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I6)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) (tptp.uminus5710092332889474511et_nat I6))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int F N))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F I6)) (tptp.suminf_int F))))))) (forall ((F tptp.fun_nat_nat) (I6 tptp.set_nat)) (=> (tptp.summable_nat F) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I6)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) (tptp.uminus5710092332889474511et_nat I6))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat F N))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) I6)) (tptp.suminf_nat F))))))) (forall ((F tptp.fun_nat_real) (I6 tptp.set_nat)) (=> (tptp.summable_real F) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat I6)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) (tptp.uminus5710092332889474511et_nat I6))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F N))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) I6)) (tptp.suminf_real F))))))) (forall ((R tptp.set_Pr9123050470547338789r_bool) (S3 tptp.set_Pr9123050470547338789r_bool)) (= (forall ((X4 tptp.code_integer) (Xa4 tptp.bool)) (let ((_let_1 (tptp.produc5135875973608410785r_bool X4 Xa4))) (= (tptp.member7941544277139469958r_bool _let_1 R) (tptp.member7941544277139469958r_bool _let_1 S3)))) (= R S3))) (forall ((R tptp.set_Pr8218934625190621173um_num) (S3 tptp.set_Pr8218934625190621173um_num)) (= (forall ((X4 tptp.num) (Xa4 tptp.num)) (let ((_let_1 (tptp.product_Pair_num_num X4 Xa4))) (= (tptp.member7279096912039735102um_num _let_1 R) (tptp.member7279096912039735102um_num _let_1 S3)))) (= R S3))) (forall ((R tptp.set_Pr6200539531224447659at_num) (S3 tptp.set_Pr6200539531224447659at_num)) (= (forall ((X4 tptp.nat) (Xa4 tptp.num)) (let ((_let_1 (tptp.product_Pair_nat_num X4 Xa4))) (= (tptp.member9148766508732265716at_num _let_1 R) (tptp.member9148766508732265716at_num _let_1 S3)))) (= R S3))) (forall ((R tptp.set_Pr1261947904930325089at_nat) (S3 tptp.set_Pr1261947904930325089at_nat)) (= (forall ((X4 tptp.nat) (Xa4 tptp.nat)) (let ((_let_1 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X4) Xa4))) (= (tptp.member8440522571783428010at_nat _let_1 R) (tptp.member8440522571783428010at_nat _let_1 S3)))) (= R S3))) (forall ((R tptp.set_Pr958786334691620121nt_int) (S3 tptp.set_Pr958786334691620121nt_int)) (= (forall ((X4 tptp.int) (Xa4 tptp.int)) (let ((_let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X4) Xa4))) (= (tptp.member5262025264175285858nt_int _let_1 R) (tptp.member5262025264175285858nt_int _let_1 S3)))) (= R S3))) (forall ((X2 tptp.code_integer) (Xa tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool tptp.bot_bo8679169850809196913l_bool X2) Xa)) (tptp.member7941544277139469958r_bool (tptp.produc5135875973608410785r_bool X2 Xa) tptp.bot_bo3208612889749783737r_bool))) (forall ((X2 tptp.num) (Xa tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.bot_bo3939865688069203585m_bool X2) Xa)) (tptp.member7279096912039735102um_num (tptp.product_Pair_num_num X2 Xa) tptp.bot_bo9056780473022590049um_num))) (forall ((X2 tptp.nat) (Xa tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_nat_fun_num_bool tptp.bot_bo531702463448601163m_bool X2) Xa)) (tptp.member9148766508732265716at_num (tptp.product_Pair_nat_num X2 Xa) tptp.bot_bo7038385379056416535at_num))) (forall ((X2 tptp.nat) (Xa tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.bot_bo6560894463593755925t_bool X2) Xa)) (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X2) Xa) tptp.bot_bo2099793752762293965at_nat))) (forall ((X2 tptp.int) (Xa tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.bot_bo6207810721336151133t_bool X2) Xa)) (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X2) Xa) tptp.bot_bo1796632182523588997nt_int))) (not (= _let_25 tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_25) _let_23)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_25) _let_23)) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (let ((_let_2 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex))) (= (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex _let_1 N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex _let_2 X)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.minus_minus_rat tptp.one_one_rat))) (= (tptp.aa_rat_rat _let_2 (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat _let_2 X)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (= (tptp.aa_int_int _let_2 (tptp.aa_nat_int _let_1 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_2 X)) (tptp.groups3539618377306564664at_int _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (= (tptp.aa_real_real _let_2 (tptp.aa_nat_real _let_1 N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_2 X)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex _let_1 N2)) tptp.one_one_complex) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) tptp.one_one_complex)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 N2)) tptp.one_one_rat) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) tptp.one_one_rat)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int _let_1 N2)) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) tptp.one_one_int)) (tptp.groups3539618377306564664at_int _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real _let_1 N2)) tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (=> (not (= X tptp.one_one_complex)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex _let_1 N2)) tptp.one_one_complex)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) tptp.one_one_complex)))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (=> (not (= X tptp.one_one_rat)) (= (tptp.groups2906978787729119204at_rat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat _let_1 N2)) tptp.one_one_rat)) (tptp.aa_rat_rat (tptp.minus_minus_rat X) tptp.one_one_rat)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (=> (not (= X tptp.one_one_real)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_1) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real _let_1 N2)) tptp.one_one_real)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) tptp.one_one_real)))))) (forall ((F tptp.fun_nat_complex) (Z tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql F) Z))) (=> (tptp.summable_complex _let_1) (= (tptp.suminf_complex _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex F tptp.zero_zero_nat)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_qy F) Z))) Z)))))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj F) Z))) (=> (tptp.summable_real _let_1) (= (tptp.suminf_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real F tptp.zero_zero_nat)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qz F) Z))) Z)))))) (forall ((F tptp.fun_nat_complex) (Z tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql F) Z))) (=> (tptp.summable_complex _let_1) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_qy F) Z))) Z) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.suminf_complex _let_1)) (tptp.aa_nat_complex F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj F) Z))) (=> (tptp.summable_real _let_1) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qz F) Z))) Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.suminf_real _let_1)) (tptp.aa_nat_real F tptp.zero_zero_nat)))))) (forall ((R2 tptp.real) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (=> (tptp.summable_real F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) N8)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.suminf_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr F) N8)))) R2)))))))) (forall ((R2 tptp.real) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R2)) (=> (tptp.summable_complex F) (exists ((N7 tptp.nat)) (forall ((N8 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) N8)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.suminf_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_or F) N8)))) R2)))))))) (forall ((F tptp.fun_nat_complex) (E tptp.real)) (=> (tptp.summable_complex F) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (not (forall ((N7 tptp.nat)) (not (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) M3)) (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) (tptp.set_or1269000886237332187st_nat M3 N8)))) E))))))))))) (forall ((F tptp.fun_nat_real) (E tptp.real)) (=> (tptp.summable_real F) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (not (forall ((N7 tptp.nat)) (not (forall ((M3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N7) M3)) (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.set_or1269000886237332187st_nat M3 N8)))) E))))))))))) (forall ((F tptp.fun_nat_real) (Z tptp.real)) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F I3)) tptp.one_one_real))) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real F I3)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Z)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z) tptp.one_one_real)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj F) Z))))))) (forall ((R2 tptp.real) (R0 tptp.real) (A tptp.fun_nat_complex) (M7 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) R2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real R2) R0)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex A N))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real R0) N))) M7))) (tptp.summable_real (tptp.aa_fun7054779078796324018t_real (tptp.aTP_Lamm_rm R2) A)))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (let ((_let_3 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex _let_2 N2))) (tptp.aa_complex_complex _let_1 X)))))))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.power_power_rat X))) (let ((_let_3 (tptp.groups2906978787729119204at_rat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat _let_2 N2))) (tptp.aa_rat_rat _let_1 X)))))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_3 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real _let_2 N2))) (tptp.aa_real_real _let_1 X)))))))))) (forall ((Z tptp.complex) (H tptp.complex) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_rn Z) H) M)) _let_1) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_ro Z) H) M)) _let_1)))) (forall ((Z tptp.rat) (H tptp.rat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_rp Z) H) M) _let_1) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_rq Z) H) M) _let_1)))) (forall ((Z tptp.int) (H tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M))) (= (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_rr Z) H) M) _let_1) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_rs Z) H) M) _let_1)))) (forall ((Z tptp.real) (H tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat M))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_rt Z) H) M)) _let_1) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_ru Z) H) M)) _let_1)))) (tptp.pp (tptp.aa_real_bool _let_72 _let_25)) (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) _let_1)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Y) _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_rv X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) _let_1)) (tptp.aa_nat_rat (tptp.power_power_rat Y) _let_1)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_rw X) N2) Y) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) _let_1)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_rx X) N2) Y) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_ry X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Y) N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_rz X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((X tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat X) N2)) (tptp.aa_nat_rat (tptp.power_power_rat Y) N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_sa X) N2) Y) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Y) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_sb X) N2) Y) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((X tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_sc X) N2) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (tptp.pp (tptp.aa_real_bool _let_71 _let_25)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_51)) tptp.pi)) (forall ((C tptp.real) (N3 tptp.nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.one_one_real)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real F N))))))) (tptp.summable_real F)))) (forall ((C tptp.real) (N3 tptp.nat) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) tptp.one_one_real)) (=> (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N3) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F (tptp.aa_nat_nat tptp.suc N)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex F N))))))) (tptp.summable_complex F)))) (forall ((Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arctan Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (= (tptp.aa_real_real tptp.arctan tptp.one_one_real) _let_63) (forall ((N2 tptp.nat) (F tptp.fun_nat_Code_integer) (K5 tptp.code_integer) (K tptp.nat)) (=> (forall ((P4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat P4) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer F P4)) K5)))) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) K5)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.groups7501900531339628137nteger F (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) K5)))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_rat) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat P4) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat F P4)) K5)))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat tptp.zero_zero_rat) K5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.groups2906978787729119204at_rat F (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) K5)))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_int) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat P4) N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int F P4)) K5)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int F (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) K5)))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_nat) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat P4) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat F P4)) K5)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) K5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)) K5)))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_real) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat P4) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F P4)) K5)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) K5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) K5)))))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex _let_1 X)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_sd X) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat tptp.one_one_rat))) (= (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat (tptp.power_power_rat X) N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat _let_1 X)) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_se X) N2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (= (tptp.aa_int_int _let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int X) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_1 X)) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_sf X) N2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (= (tptp.aa_real_real _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 X)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_sg X) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))) (forall ((R2 tptp.set_Pr9123050470547338789r_bool) (S2 tptp.set_Pr9123050470547338789r_bool)) (=> (forall ((X3 tptp.code_integer) (Y4 tptp.bool)) (let ((_let_1 (tptp.produc5135875973608410785r_bool X3 Y4))) (=> (tptp.member7941544277139469958r_bool _let_1 R2) (tptp.member7941544277139469958r_bool _let_1 S2)))) (tptp.ord_le5008643164228425349r_bool R2 S2))) (forall ((R2 tptp.set_Pr8218934625190621173um_num) (S2 tptp.set_Pr8218934625190621173um_num)) (=> (forall ((X3 tptp.num) (Y4 tptp.num)) (let ((_let_1 (tptp.product_Pair_num_num X3 Y4))) (=> (tptp.member7279096912039735102um_num _let_1 R2) (tptp.member7279096912039735102um_num _let_1 S2)))) (tptp.ord_le880128212290418581um_num R2 S2))) (forall ((R2 tptp.set_Pr6200539531224447659at_num) (S2 tptp.set_Pr6200539531224447659at_num)) (=> (forall ((X3 tptp.nat) (Y4 tptp.num)) (let ((_let_1 (tptp.product_Pair_nat_num X3 Y4))) (=> (tptp.member9148766508732265716at_num _let_1 R2) (tptp.member9148766508732265716at_num _let_1 S2)))) (tptp.ord_le8085105155179020875at_num R2 S2))) (forall ((R2 tptp.set_Pr1261947904930325089at_nat) (S2 tptp.set_Pr1261947904930325089at_nat)) (=> (forall ((X3 tptp.nat) (Y4 tptp.nat)) (let ((_let_1 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y4))) (=> (tptp.member8440522571783428010at_nat _let_1 R2) (tptp.member8440522571783428010at_nat _let_1 S2)))) (tptp.ord_le3146513528884898305at_nat R2 S2))) (forall ((R2 tptp.set_Pr958786334691620121nt_int) (S2 tptp.set_Pr958786334691620121nt_int)) (=> (forall ((X3 tptp.int) (Y4 tptp.int)) (let ((_let_1 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X3) Y4))) (=> (tptp.member5262025264175285858nt_int _let_1 R2) (tptp.member5262025264175285858nt_int _let_1 S2)))) (tptp.ord_le2843351958646193337nt_int R2 S2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_28) 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.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_real_real tptp.arctan Y))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_2) _let_1)))))) (forall ((Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_real_real tptp.arctan Y)))) (forall ((S3 tptp.set_nat)) (= (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3))) (forall ((M6 tptp.nat)) (exists ((N5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M6) N5)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N5) S3))))))) (forall ((K tptp.nat) (S3 tptp.set_nat)) (=> (forall ((M2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K) M2)) (exists ((N8 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N8)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N8) S3)))))) (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3))))) (forall ((S3 tptp.set_nat)) (= (not (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3))) (forall ((M6 tptp.nat)) (exists ((N5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N5) S3))))))) (forall ((D2 tptp.fun_Pr6287530515171585797m_bool) (R tptp.fun_Pr5837708615769641901m_bool) (X tptp.product_prod_num_num) (P tptp.fun_Pr6287530515171585797m_bool)) (=> (tptp.ord_le998981803562422117m_bool D2 (tptp.accp_P3113834385874906142um_num R)) (=> (forall ((X3 tptp.product_prod_num_num) (Z3 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool D2 X3)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.aa_Pro2164613399825298270m_bool R Z3) X3)) (tptp.pp (tptp.aa_Pro762926636801165566m_bool D2 Z3))))) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool D2 X)) (=> (forall ((X3 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool D2 X3)) (=> (forall ((Z4 tptp.product_prod_num_num)) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.aa_Pro2164613399825298270m_bool R Z4) X3)) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P Z4)))) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P X3))))) (tptp.pp (tptp.aa_Pro762926636801165566m_bool P X))))))) (forall ((D2 tptp.fun_Pr7757163693017731481t_bool) (R tptp.fun_Pr248683899324676269t_bool) (X tptp.product_prod_nat_nat) (P tptp.fun_Pr7757163693017731481t_bool)) (=> (tptp.pp (tptp.aa_fun8663595511526100224l_bool (tptp.ord_le2468614981408567801t_bool D2) (tptp.accp_P4275260045618599050at_nat R))) (=> (forall ((X3 tptp.product_prod_nat_nat) (Z3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D2 X3)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool R Z3) X3)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D2 Z3))))) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D2 X)) (=> (forall ((X3 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool D2 X3)) (=> (forall ((Z4 tptp.product_prod_nat_nat)) (=> (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool R Z4) X3)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P Z4)))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X3))))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P X))))))) (forall ((D2 tptp.fun_Pr803113274115125473t_bool) (R tptp.fun_Pr3099820731930151597t_bool) (X tptp.product_prod_int_int) (P tptp.fun_Pr803113274115125473t_bool)) (=> (tptp.ord_le4737936599360737601t_bool D2 (tptp.accp_P1096762738010456898nt_int R)) (=> (forall ((X3 tptp.product_prod_int_int) (Z3 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D2 X3)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool R Z3) X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D2 Z3))))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D2 X)) (=> (forall ((X3 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool D2 X3)) (=> (forall ((Z4 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_Pro1534211998248933470t_bool R Z4) X3)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P Z4)))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X3))))) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool P X))))))) (forall ((D2 tptp.fun_list_nat_bool) (R tptp.fun_li8598321315282354825t_bool) (X tptp.list_nat) (P tptp.fun_list_nat_bool)) (=> (tptp.ord_le2936377143570524336t_bool D2 (tptp.accp_list_nat R)) (=> (forall ((X3 tptp.list_nat) (Z3 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool D2 X3)) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_lis4768068104879709938t_bool R Z3) X3)) (tptp.pp (tptp.aa_list_nat_bool D2 Z3))))) (=> (tptp.pp (tptp.aa_list_nat_bool D2 X)) (=> (forall ((X3 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool D2 X3)) (=> (forall ((Z4 tptp.list_nat)) (=> (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_lis4768068104879709938t_bool R Z4) X3)) (tptp.pp (tptp.aa_list_nat_bool P Z4)))) (tptp.pp (tptp.aa_list_nat_bool P X3))))) (tptp.pp (tptp.aa_list_nat_bool P X))))))) (forall ((D2 tptp.fun_nat_bool) (R tptp.fun_nat_fun_nat_bool) (X tptp.nat) (P tptp.fun_nat_bool)) (=> (tptp.ord_le8840051076831633728t_bool D2 (tptp.accp_nat R)) (=> (forall ((X3 tptp.nat) (Z3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool D2 X3)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R Z3) X3)) (tptp.pp (tptp.aa_nat_bool D2 Z3))))) (=> (tptp.pp (tptp.aa_nat_bool D2 X)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool D2 X3)) (=> (forall ((Z4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool R Z4) X3)) (tptp.pp (tptp.aa_nat_bool P Z4)))) (tptp.pp (tptp.aa_nat_bool P X3))))) (tptp.pp (tptp.aa_nat_bool P X))))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_sh 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))) N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_si F)) _let_1)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_sj G)) _let_1))))) (forall ((R tptp.set_complex) (S3 tptp.set_complex)) (= (tptp.ord_le4633831435867229666x_bool (tptp.aTP_Lamm_ab R) (tptp.aTP_Lamm_ab S3)) (tptp.ord_le211207098394363844omplex R S3))) (forall ((R tptp.set_real) (S3 tptp.set_real)) (= (tptp.ord_le5573776112191778788l_bool (tptp.aTP_Lamm_a R) (tptp.aTP_Lamm_a S3)) (tptp.ord_less_eq_set_real R S3))) (forall ((R tptp.set_set_nat) (S3 tptp.set_set_nat)) (= (tptp.ord_le1461730252015488778t_bool (tptp.aTP_Lamm_ac R) (tptp.aTP_Lamm_ac S3)) (tptp.ord_le6893508408891458716et_nat R S3))) (forall ((R tptp.set_nat) (S3 tptp.set_nat)) (= (tptp.ord_le8840051076831633728t_bool (tptp.aTP_Lamm_ad R) (tptp.aTP_Lamm_ad S3)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat R) S3)))) (forall ((R tptp.set_int) (S3 tptp.set_int)) (= (tptp.ord_le5715760110363009508t_bool (tptp.aTP_Lamm_ae R) (tptp.aTP_Lamm_ae S3)) (tptp.ord_less_eq_set_int R S3))) (= (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_70) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_57 (tptp.aa_num_real tptp.numeral_numeral_real _let_69))))) (tptp.aa_real_real _let_43 (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_67 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 _let_30))))))))) _let_63) (= _let_63 (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_62) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_57 _let_70)))) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real _let_57 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 _let_69)))))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_mint X) Y) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (let ((_let_2 (tptp.pp B2))) (let ((_let_3 (tptp.pp A3))) (=> (= X _let_1) (=> (and (=> _let_3 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_2) (= Y tptp.none_nat))))) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2))) (=> (= X _let_1) (=> (= Y (tptp.some_nat Mi2)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1))))))))))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (tptp.vEBT_vebt_maxt X) Y) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X)) (=> (forall ((A3 tptp.bool) (B2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf A3 B2))) (let ((_let_2 (tptp.pp A3))) (let ((_let_3 (tptp.pp B2))) (=> (= X _let_1) (=> (and (=> _let_3 (= Y (tptp.some_nat tptp.one_one_nat))) (=> (not _let_3) (and (=> _let_2 (= Y (tptp.some_nat tptp.zero_zero_nat))) (=> (not _let_2) (= Y tptp.none_nat))))) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uu2 Uv2 Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Mi2) Ma2)) Ux2 Uy2 Uz2))) (=> (= X _let_1) (=> (= Y (tptp.some_nat Ma2)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1))))))))))))) (forall ((F tptp.fun_nat_nat) (Mm tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_lo F)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Mm)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat Mm)))) (forall ((F tptp.fun_nat_real) (Mm tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_lp F)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Mm)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat Mm)))) (forall ((A0 tptp.fun_nat_fun_num_num) (A1 tptp.nat) (A22 tptp.nat) (A32 tptp.num) (P tptp.fun_fu2950424802767353155m_bool)) (=> (tptp.accp_P3591886921626383704at_num tptp.set_fo256927282339908995el_num (tptp.produc460779904311030791at_num A0 (tptp.produc1195630363706982562at_num A1 (tptp.product_Pair_nat_num A22 A32)))) (=> (forall ((F2 tptp.fun_nat_fun_num_num) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.num)) (let ((_let_1 (tptp.aa_fun7437090807486079916m_bool P F2))) (=> (tptp.accp_P3591886921626383704at_num tptp.set_fo256927282339908995el_num (tptp.produc460779904311030791at_num F2 (tptp.produc1195630363706982562at_num A3 (tptp.product_Pair_nat_num B2 Acc)))) (=> (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A3))) (tptp.pp (tptp.aa_num_bool (tptp.aa_nat_fun_num_bool (tptp.aa_nat2608338788294301521m_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A3) tptp.one_one_nat)) B2) (tptp.aa_num_num (tptp.aa_nat_fun_num_num F2 A3) Acc)))) (tptp.pp (tptp.aa_num_bool (tptp.aa_nat_fun_num_bool (tptp.aa_nat2608338788294301521m_bool _let_1 A3) B2) Acc)))))) (tptp.pp (tptp.aa_num_bool (tptp.aa_nat_fun_num_bool (tptp.aa_nat2608338788294301521m_bool (tptp.aa_fun7437090807486079916m_bool P A0) A1) A22) A32))))) (forall ((A0 tptp.fun_nat_fun_nat_nat) (A1 tptp.nat) (A22 tptp.nat) (A32 tptp.nat) (P tptp.fun_fu7164412255009898145t_bool)) (=> (tptp.accp_P4694664897847628410at_nat tptp.set_fo3699595496184130361el_nat (tptp.produc2818902965508115497at_nat A0 (tptp.produc487386426758144856at_nat A1 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat A22) A32)))) (=> (forall ((F2 tptp.fun_nat_fun_nat_nat) (A3 tptp.nat) (B2 tptp.nat) (Acc tptp.nat)) (let ((_let_1 (tptp.aa_fun2305595801590362634t_bool P F2))) (=> (tptp.accp_P4694664897847628410at_nat tptp.set_fo3699595496184130361el_nat (tptp.produc2818902965508115497at_nat F2 (tptp.produc487386426758144856at_nat A3 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat B2) Acc)))) (=> (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B2) A3))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_nat8637530788439456283t_bool _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A3) tptp.one_one_nat)) B2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat F2 A3) Acc)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_nat8637530788439456283t_bool _let_1 A3) B2) Acc)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aa_fun2305595801590362634t_bool P A0) A1) A22) A32))))) (forall ((X tptp.fun_Pr2477239776880934807at_nat) (Xa2 tptp.option4927543243414619207at_nat) (Xb tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (=> (= (tptp.vEBT_V1502963449132264192at_nat X Xa2 Xb) Y) (=> (tptp.accp_P4760198183577772864at_nat tptp.vEBT_V7235779383477046023at_nat (tptp.produc7814092408141220007at_nat X (tptp.produc488173922507101015at_nat Xa2 Xb))) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) (=> (= Y tptp.none_P5556105721700978146at_nat) (not (tptp.accp_P4760198183577772864at_nat tptp.vEBT_V7235779383477046023at_nat (tptp.produc7814092408141220007at_nat X (tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat Xb)))))) (=> (forall ((V2 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.some_P7363390416028606310at_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb tptp.none_P5556105721700978146at_nat) (=> (= Y tptp.none_P5556105721700978146at_nat) (not (tptp.accp_P4760198183577772864at_nat tptp.vEBT_V7235779383477046023at_nat (tptp.produc7814092408141220007at_nat X (tptp.produc488173922507101015at_nat _let_1 tptp.none_P5556105721700978146at_nat))))))))) (not (forall ((A3 tptp.product_prod_nat_nat)) (=> (= Xa2 (tptp.some_P7363390416028606310at_nat A3)) (forall ((B2 tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.some_P7363390416028606310at_nat B2))) (=> (= Xb _let_1) (=> (= Y (tptp.some_P7363390416028606310at_nat (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat X A3) B2))) (not (tptp.accp_P4760198183577772864at_nat tptp.vEBT_V7235779383477046023at_nat (tptp.produc7814092408141220007at_nat X (tptp.produc488173922507101015at_nat (tptp.some_P7363390416028606310at_nat A3) _let_1)))))))))))))))) (forall ((X tptp.fun_num_fun_num_num) (Xa2 tptp.option_num) (Xb tptp.option_num) (Y tptp.option_num)) (=> (= (tptp.vEBT_V819420779217536731ft_num X Xa2 Xb) Y) (=> (tptp.accp_P1225658569124232473on_num tptp.vEBT_V452583751252753300el_num (tptp.produc6360833703471310868on_num X (tptp.produc8585076106096196333on_num Xa2 Xb))) (=> (=> (= Xa2 tptp.none_num) (=> (= Y tptp.none_num) (not (tptp.accp_P1225658569124232473on_num tptp.vEBT_V452583751252753300el_num (tptp.produc6360833703471310868on_num X (tptp.produc8585076106096196333on_num tptp.none_num Xb)))))) (=> (forall ((V2 tptp.num)) (let ((_let_1 (tptp.some_num V2))) (=> (= Xa2 _let_1) (=> (= Xb tptp.none_num) (=> (= Y tptp.none_num) (not (tptp.accp_P1225658569124232473on_num tptp.vEBT_V452583751252753300el_num (tptp.produc6360833703471310868on_num X (tptp.produc8585076106096196333on_num _let_1 tptp.none_num))))))))) (not (forall ((A3 tptp.num)) (=> (= Xa2 (tptp.some_num A3)) (forall ((B2 tptp.num)) (let ((_let_1 (tptp.some_num B2))) (=> (= Xb _let_1) (=> (= Y (tptp.some_num (tptp.aa_num_num (tptp.aa_num_fun_num_num X A3) B2))) (not (tptp.accp_P1225658569124232473on_num tptp.vEBT_V452583751252753300el_num (tptp.produc6360833703471310868on_num X (tptp.produc8585076106096196333on_num (tptp.some_num A3) _let_1)))))))))))))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 tptp.option_nat) (Xb tptp.option_nat) (Y tptp.option_nat)) (=> (= (tptp.aa_opt1882420858203594238on_nat (tptp.aa_opt7711074727033721499on_nat (tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb) Y) (=> (tptp.accp_P5526603486790338531on_nat tptp.vEBT_V3895251965096974666el_nat (tptp.produc6699827698519632094on_nat X (tptp.produc5098337634421038937on_nat Xa2 Xb))) (=> (=> (= Xa2 tptp.none_nat) (=> (= Y tptp.none_nat) (not (tptp.accp_P5526603486790338531on_nat tptp.vEBT_V3895251965096974666el_nat (tptp.produc6699827698519632094on_nat X (tptp.produc5098337634421038937on_nat tptp.none_nat Xb)))))) (=> (forall ((V2 tptp.nat)) (let ((_let_1 (tptp.some_nat V2))) (=> (= Xa2 _let_1) (=> (= Xb tptp.none_nat) (=> (= Y tptp.none_nat) (not (tptp.accp_P5526603486790338531on_nat tptp.vEBT_V3895251965096974666el_nat (tptp.produc6699827698519632094on_nat X (tptp.produc5098337634421038937on_nat _let_1 tptp.none_nat))))))))) (not (forall ((A3 tptp.nat)) (=> (= Xa2 (tptp.some_nat A3)) (forall ((B2 tptp.nat)) (let ((_let_1 (tptp.some_nat B2))) (=> (= Xb _let_1) (=> (= Y (tptp.some_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X A3) B2))) (not (tptp.accp_P5526603486790338531on_nat tptp.vEBT_V3895251965096974666el_nat (tptp.produc6699827698519632094on_nat X (tptp.produc5098337634421038937on_nat (tptp.some_nat A3) _let_1)))))))))))))))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real tptp.aTP_Lamm_sk) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2))) tptp.one_one_real)) (forall ((X tptp.fun_nat_fun_num_num) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.accp_P3591886921626383704at_num tptp.set_fo256927282339908995el_num (tptp.produc460779904311030791at_num X (tptp.produc1195630363706982562at_num Xa2 (tptp.product_Pair_nat_num Xb Xc)))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xb) Xa2)))) (=> (= (tptp.aa_num_num (tptp.aa_nat_fun_num_num (tptp.set_fo8365102181078989356at_num X Xa2) Xb) Xc) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (tptp.aa_num_num (tptp.aa_nat_fun_num_num (tptp.set_fo8365102181078989356at_num X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (tptp.aa_num_num (tptp.aa_nat_fun_num_num X Xa2) Xc))))) (not _let_1)))))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.accp_P4694664897847628410at_nat tptp.set_fo3699595496184130361el_nat (tptp.produc2818902965508115497at_nat X (tptp.produc487386426758144856at_nat Xa2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xb) Xc)))))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Xb) Xa2)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X Xa2) Xb) Xc) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Xa2) tptp.one_one_nat)) Xb) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X Xa2) Xc))))) (not _let_1)))))))) (forall ((F tptp.fun_nat_fun_num_num) (A tptp.nat) (B tptp.nat) (Acc2 tptp.num)) (let ((_let_1 (tptp.aa_num_num (tptp.aa_nat_fun_num_num (tptp.set_fo8365102181078989356at_num F A) B) Acc2))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)))) (=> (tptp.accp_P3591886921626383704at_num tptp.set_fo256927282339908995el_num (tptp.produc460779904311030791at_num F (tptp.produc1195630363706982562at_num A (tptp.product_Pair_nat_num B Acc2)))) (and (=> _let_2 (= _let_1 Acc2)) (=> (not _let_2) (= _let_1 (tptp.aa_num_num (tptp.aa_nat_fun_num_num (tptp.set_fo8365102181078989356at_num F (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) tptp.one_one_nat)) B) (tptp.aa_num_num (tptp.aa_nat_fun_num_num F A) Acc2))))))))) (forall ((F tptp.fun_nat_fun_nat_nat) (A tptp.nat) (B tptp.nat) (Acc2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F A) B) Acc2))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat B) A)))) (=> (tptp.accp_P4694664897847628410at_nat tptp.set_fo3699595496184130361el_nat (tptp.produc2818902965508115497at_nat F (tptp.produc487386426758144856at_nat A (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat B) Acc2)))) (and (=> _let_2 (= _let_1 Acc2)) (=> (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) Acc2))))))))) (forall ((N2 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)) N2)))) tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) N2)))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.pi) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) M))))) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))) (= (tptp.aa_complex_complex 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))) (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 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.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.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.aa_complex_complex tptp.sin_complex X))) (let ((_let_2 (tptp.aa_complex_complex tptp.cos_complex X))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_2) _let_2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sin_real X))) (let ((_let_2 (tptp.aa_real_real tptp.cos_real X))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N2 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 N2)) tptp.pi)) tptp.zero_zero_real)) (forall ((N2 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 N2))) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.cos_real _let_25) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_51) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_25) tptp.one_one_real) (= (tptp.aa_real_real tptp.cos_real _let_51) tptp.one_one_real) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.cos_real X))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.sin_real X))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) X)) (tptp.aa_real_real tptp.cos_real X))) (forall ((N2 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 N2)) 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)) N2))) (forall ((N2 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 N2))) (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)) N2))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_1)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_1)) tptp.one_one_complex))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_1)) tptp.one_one_real))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_1)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_1)) tptp.one_one_complex))) (forall ((N2 tptp.nat)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.zero_zero_real)) (forall ((N2 tptp.nat)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.one_one_real)) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sin_real X)))) (= (tptp.aa_real_real tptp.cos_real _let_68) tptp.zero_zero_real) (= (tptp.aa_real_real tptp.sin_real _let_68) _let_53) (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.aa_complex_complex tptp.cos_complex X) tptp.one_one_complex) (= (tptp.aa_complex_complex tptp.sin_complex X) tptp.zero_zero_complex))) (forall ((X tptp.real)) (=> (= (tptp.aa_real_real tptp.cos_real X) tptp.one_one_real) (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real))) (forall ((X tptp.real) (Y tptp.real)) (exists ((R3 tptp.real) (A3 tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R3))) (and (= X (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.cos_real A3))) (= Y (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.sin_real A3))))))) (forall ((X tptp.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.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) (Y tptp.real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex _let_1 X)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex tptp.sin_complex X))) (tptp.aa_complex_complex tptp.cos_complex X))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.sin_real X))) (tptp.aa_real_real tptp.cos_real X))))) (forall ((X tptp.real)) (exists ((Y4 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) Y4)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y4) tptp.pi)) (= (tptp.aa_real_real tptp.sin_real Y4) (tptp.aa_real_real tptp.sin_real X)) (= (tptp.aa_real_real tptp.cos_real Y4) (tptp.aa_real_real tptp.cos_real X))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real X)) X)))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real X)) tptp.one_one_real))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cos_real X)) tptp.one_one_real))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.sin_real X))) (tptp.aa_real_real tptp.abs_abs_real X)))) (forall ((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.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_1))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_1))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.sin_real X))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real X))))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) (tptp.aa_real_real tptp.sin_real X)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.pi)) (=> (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real tptp.cos_real Y)) (= X Y)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.pi)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 X)))))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))))))) (forall ((X tptp.real)) (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)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_complex_complex tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex W) Z)) _let_1)))) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex Z) W)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_real_real tptp.cos_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)) _let_1)))) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z) W)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_complex_complex tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex W) Z)) _let_1)))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex W) Z)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_real_real tptp.sin_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)) _let_1)))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_complex_complex tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex W) Z)) _let_1)))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex W) Z)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_real_real tptp.sin_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)) _let_1)))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_complex_complex tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex W) Z))) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex W) Z)))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_real_real tptp.sin_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z))) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_complex_complex tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex W) Z))) (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex W) Z)))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_real_real tptp.cos_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z))) (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_complex_complex tptp.sin_complex Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex W) Z))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex W) Z)))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_real_real tptp.sin_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) X)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex X)) _let_2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex X)) _let_2)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real X)) _let_2)))))) (forall ((W tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)))) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex _let_2 W)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.sin_complex W)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))) (forall ((W tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_2 W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_real_real _let_2 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sin_real W)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))) (not (= _let_66 tptp.zero_zero_real)) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.pi)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.cos_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X))))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cos_real Y)) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((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 ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) tptp.pi)) (= X (tptp.aa_real_real tptp.cos_real T5)) (= Y (tptp.aa_real_real tptp.sin_real T5)))))))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X))) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc M))) tptp.pi)) _let_1))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))) (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc M))) tptp.pi)) _let_1))) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real _let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real X))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_66) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_66) tptp.zero_zero_real)) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real X3) tptp.zero_zero_real) (forall ((Y2 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y2) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real Y2) tptp.zero_zero_real)) (= Y2 X3))))) (forall ((B tptp.nat) (A tptp.nat) (F tptp.fun_nat_fun_nat_nat) (Acc2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat F A) B) Acc2))) (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 Acc2)) (=> (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) Acc2)))))))) (forall ((X tptp.fun_nat_fun_nat_nat) (Xa2 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) Xa2)))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat X Xa2) 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 Xa2) tptp.one_one_nat)) Xb) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat X Xa2) Xc)))))))) (forall ((Y tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cos_real Y)) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (exists ((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 ((Y2 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y2) tptp.pi)) (= (tptp.aa_real_real tptp.cos_real Y2) Y)) (= Y2 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 ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= X (tptp.aa_real_real tptp.cos_real T5)) (= Y (tptp.aa_real_real tptp.sin_real T5)))))))))) (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 ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (= X (tptp.aa_real_real tptp.cos_real T5)) (= Y (tptp.aa_real_real tptp.sin_real T5))))))) (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 ((T5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T5)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (=> (= X (tptp.aa_real_real tptp.cos_real T5)) (not (= Y (tptp.aa_real_real tptp.sin_real T5))))))))))) (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2))))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_complex_complex tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex W) Z)) _let_1)))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex W) Z)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_real_real tptp.cos_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)) _let_1)))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_complex_complex tptp.cos_complex Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex W) Z))) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex W) Z)))) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_real_real tptp.cos_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real W) Z))) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real W) Z)))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real X))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.pi) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) X))) tptp.one_one_real)))))) (= (tptp.aa_real_real tptp.sin_real _let_58) _let_64) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.cos_real X))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) _let_1)) (=> (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real tptp.sin_real Y)) (= X Y))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) _let_2)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real Y)) (tptp.aa_real_real tptp.sin_real X)))))))) (= (tptp.aa_real_real tptp.cos_real _let_60) _let_64) (forall ((F tptp.fun_nat_complex) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) (tptp.set_or1269000886237332187st_nat A B)) (tptp.aa_complex_complex (tptp.aa_nat3829984526574172007omplex (tptp.set_fo1517530859248394432omplex (tptp.aTP_Lamm_sl F) A) B) tptp.zero_zero_complex))) (forall ((F tptp.fun_nat_rat) (A tptp.nat) (B tptp.nat)) (= (tptp.groups2906978787729119204at_rat F (tptp.set_or1269000886237332187st_nat A B)) (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_sm F) A B) tptp.zero_zero_rat))) (forall ((F tptp.fun_nat_int) (A tptp.nat) (B tptp.nat)) (= (tptp.groups3539618377306564664at_int F (tptp.set_or1269000886237332187st_nat A B)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.set_fo2581907887559384638at_int (tptp.aTP_Lamm_sn F) A) B) tptp.zero_zero_int))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) (tptp.set_or1269000886237332187st_nat A B)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat (tptp.aTP_Lamm_so F) A) B) tptp.zero_zero_nat))) (forall ((F tptp.fun_nat_real) (A tptp.nat) (B tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.set_or1269000886237332187st_nat A B)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.set_fo3111899725591712190t_real (tptp.aTP_Lamm_sp F) A) B) tptp.zero_zero_real))) (forall ((W tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)))) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex _let_2 W)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.cos_complex W)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))) tptp.one_one_complex))))) (forall ((W tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_2 W)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_2 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real W)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))) tptp.one_one_real))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.cos_complex X))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_3 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_2)))) (= (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex _let_3 X)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.aa_com8181001469867462503omplex tptp.power_power_complex _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (tptp.aa_complex_complex _let_3 _let_1))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real X))) (let ((_let_2 (tptp.aa_num_num tptp.bit1 tptp.one))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_2)))) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real _let_3 X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_2)))) (tptp.aa_real_real _let_3 _let_1))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.pi) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) _let_1)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sin_real Y)) (tptp.aa_real_real tptp.sin_real X)))))))) (forall ((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.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) _let_1)) (= (tptp.aa_real_real tptp.sin_real X3) Y) (forall ((Y2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y2) _let_1)) (= (tptp.aa_real_real tptp.sin_real Y2) Y)) (= Y2 X3)))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.cos_real X))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.one_one_real) (or (exists ((X4 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 X4)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X4 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 X4)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))))))) (forall ((N2 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))) N2)) (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 N2))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (exists ((N 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)) N)) (= 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.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5)) (= X (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real) (exists ((N 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)) N))) (= 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.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5))) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))) (exists ((N5 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (and (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N5))) (= X (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))))))) (forall ((N2 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) N2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (exists ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sq X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2))))))))) (forall ((X tptp.real) (N2 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) N2)) (exists ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5) X)) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sq X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2))))))))) (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T5 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 T5)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sq X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2))))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_complex_complex tptp.tan_complex X))) (let ((_let_3 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (tptp.aa_complex_complex _let_3 X))) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (tptp.aa_complex_complex tptp.tan_complex _let_4) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_3 _let_2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex _let_2) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_real_real tptp.tan_real X))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (tptp.aa_real_real _let_3 X))) (=> (not (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real _let_4) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.tan_real _let_4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_3 _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X tptp.num) (Y tptp.num) (F tptp.fun_num_nat)) (= (tptp.member7279096912039735102um_num (tptp.product_Pair_num_num X Y) (tptp.measure_num F)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_num_nat F X)) (tptp.aa_num_nat F Y))))) (forall ((X tptp.nat) (Y tptp.nat) (F tptp.fun_nat_nat)) (= (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Y) (tptp.measure_nat F)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat F X)) (tptp.aa_nat_nat F Y))))) (forall ((X tptp.int) (Y tptp.int) (F tptp.fun_int_nat)) (= (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X) Y) (tptp.measure_int F)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat F X)) (tptp.aa_int_nat F Y))))) (forall ((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))) (= (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_real tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat) (= (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_real tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_38) tptp.one_one_complex) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_38) tptp.one_one_rat) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_38) tptp.one_one_int) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_38) tptp.one_one_real) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_38) tptp.one_one_nat) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_1) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (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 N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger _let_1) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger _let_1)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (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 N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (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 N2))))) (forall ((N2 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 N2)) tptp.pi)) tptp.zero_zero_real)) (forall ((X tptp.real) (N2 tptp.num)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real N2)) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((X tptp.real) (N2 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 N2)) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_2) _let_46) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_2) _let_65) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int _let_2) _let_40) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_2) _let_23) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_2) _let_2) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((N2 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 N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int 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 tptp.semiri2265585572941072030t_real N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((N2 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 N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((N2 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 N2)) tptp.zero_zero_rat)))) (forall ((N2 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 N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.nat)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2)) tptp.zero_zero_real)))) (forall ((N2 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 N2)) tptp.zero_zero_nat)))) (forall ((N2 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 N2)))) (forall ((N2 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 N2)))) (forall ((N2 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 N2)))) (forall ((N2 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 N2)))) (forall ((M tptp.nat) (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_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat M)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))))) (forall ((M tptp.nat) (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_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2))))) (forall ((M tptp.nat) (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_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real M)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))))) (forall ((M tptp.nat) (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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger M))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.dvd_dvd_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real M))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M))))) (forall ((M 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) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2)))))) (forall ((M 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) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2)))))) (forall ((M 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) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2)))))) (forall ((M 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) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger K)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2))) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((K tptp.nat) (N2 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 N2))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((K tptp.nat) (N2 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 N2))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((K tptp.nat) (N2 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 N2))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.modulo364778990260209775nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) N2))))) (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 tptp.semiri773545260158071498ct_rat N2)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) N2))))) (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 tptp.semiri1406184849735516958ct_int N2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) N2))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) N2))))) (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 tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) N2))))) (forall ((X2 tptp.complex)) (= (tptp.aa_complex_complex tptp.tan_complex X2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.sin_complex X2)) (tptp.aa_complex_complex tptp.cos_complex X2)))) (forall ((X2 tptp.real)) (= (tptp.aa_real_real tptp.tan_real X2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real X2)) (tptp.aa_real_real tptp.cos_real X2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger K)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.dvd_dvd_rat (tptp.aa_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 N2) K)))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (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 N2) K)))) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (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 N2) K)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (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 N2) K)))) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))))) (forall ((K tptp.num)) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex K)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real K)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_num_nat tptp.pred_numeral K))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_1) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_num_nat tptp.pred_numeral K)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (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))) N2)))))) (= (tptp.aa_real_real tptp.tan_real _let_63) tptp.one_one_real) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2) (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))) N2) tptp.one_one_nat)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (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))) N2) tptp.one_one_nat)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2) (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))) N2) tptp.one_one_nat)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2) (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))) N2) tptp.one_one_nat)))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.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_Code_integer tptp.semiri3624122377584611663nteger M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri2265585572941072030t_real M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) tptp.one_one_nat))))))))) (forall ((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.aa_nat_rat tptp.semiri773545260158071498ct_rat N2) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) 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.aa_nat_int tptp.semiri1406184849735516958ct_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) 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.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) 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.aa_nat_real tptp.semiri2265585572941072030t_real N2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) 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.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.tan_real X))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) (tptp.aa_real_real tptp.tan_real X3))))))) (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.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) _let_1)) (= (tptp.aa_real_real tptp.tan_real X3) Y) (forall ((Y2 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y2) _let_1)) (= (tptp.aa_real_real tptp.tan_real Y2) Y)) (= Y2 X3)))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real tptp.tan_real X)))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_2)) (= (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real tptp.tan_real X)))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 _let_2)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_2)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))))))))) (forall ((Y tptp.real)) (exists ((X3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) _let_1)) (= (tptp.aa_real_real tptp.tan_real X3) Y))))) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real tptp.uminus_uminus_real _let_63)) _let_53) (forall ((Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.tan_real Y)) (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.cos_complex Y))) (let ((_let_2 (tptp.aa_complex_complex tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.tan_complex X)) (tptp.aa_complex_complex tptp.tan_complex Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.sin_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.tan_real X))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.aa_real_real tptp.tan_real X3) Y))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.tan_real X)) tptp.zero_zero_real))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_1)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_real_real tptp.tan_real Y)))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real tptp.tan_real X))) tptp.one_one_real)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arctan Y))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) _let_2)) (= (tptp.aa_real_real tptp.tan_real _let_1) Y))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (= (tptp.aa_real_real tptp.arctan (tptp.aa_real_real tptp.tan_real X)) X))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_1)) (=> (= (tptp.aa_real_real tptp.tan_real X) Y) (= (tptp.aa_real_real tptp.arctan Y) X)))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff tptp.fun_na5723442673449079972x_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun5746040925223427547t_real (tptp.aTP_Lamm_sr X) Diff)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_complex_real (tptp.aa_nat480766339200631653x_real Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff tptp.fun_na6724076748692969250l_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_ss X) Diff)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) tptp.zero_zero_real))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff tptp.fun_nat_fun_rat_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun507281639146497029t_real (tptp.aTP_Lamm_st X) Diff)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_rat_real (tptp.aa_nat_fun_rat_real Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff tptp.fun_nat_fun_nat_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun7039663905532832253t_real (tptp.aTP_Lamm_su X) Diff)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))) (forall ((X tptp.real) (N2 tptp.nat) (Diff tptp.fun_nat_fun_int_real)) (=> (= X tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun241848180832411225t_real (tptp.aTP_Lamm_sv X) Diff)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.aa_int_real (tptp.aa_nat_fun_int_real Diff tptp.zero_zero_nat) tptp.zero_zero_int))))) (forall ((H tptp.real) (F tptp.fun_real_real) (J tptp.fun_nat_real) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H)) (exists ((B7 tptp.real)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_sw H) J)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B7) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real H) N2)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2)))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.tan_complex Y))) (let ((_let_2 (tptp.aa_complex_complex tptp.tan_complex X))) (let ((_let_3 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y))) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (tptp.aa_complex_complex tptp.tan_complex _let_3) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_2) _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.aa_complex_complex tptp.tan_complex Y))) (let ((_let_2 (tptp.aa_complex_complex tptp.tan_complex X))) (let ((_let_3 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y))) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex X) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex Y) tptp.zero_zero_complex)) (=> (not (= (tptp.aa_complex_complex tptp.cos_complex _let_3) tptp.zero_zero_complex)) (= (tptp.aa_complex_complex tptp.tan_complex _let_3) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex _let_2) _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_2) _let_1))))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.tan_real Y))) (let ((_let_2 (tptp.aa_real_real tptp.tan_real X))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y))) (=> (not (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real Y) tptp.zero_zero_real)) (=> (not (= (tptp.aa_real_real tptp.cos_real _let_3) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.tan_real _let_3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_2) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1))))))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.cos_complex Y))) (let ((_let_2 (tptp.aa_complex_complex tptp.cos_complex X))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.tan_complex X)) (tptp.aa_complex_complex tptp.tan_complex Y))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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 ((Z3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 tptp.one)))))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Z3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) _let_1)) (= (tptp.aa_real_real tptp.tan_real Z3) X)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) X))) (= (tptp.aa_complex_complex tptp.tan_complex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.sin_complex _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.cos_complex _let_1)) tptp.one_one_complex))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) X))) (= (tptp.aa_real_real tptp.tan_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sin_real _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.cos_real _let_1)) tptp.one_one_real))))) (forall ((X2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.cos_coeff X2))) (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) X2)))) (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 X2) _let_2))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real X2)))) (=> (not _let_3) (= _let_1 tptp.zero_zero_real))))))) (forall ((N2 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) N2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (exists ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5) X)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sx X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2))))))))) (forall ((X tptp.real) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (exists ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) X)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sx X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)))))))) (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T5 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 T5)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sx X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2))))))) (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T5 tptp.real)) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sx X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.pi)))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)))))) (forall ((X2 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 X2))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) X2)))) (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 X2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) _let_1))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real X2))))))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((M tptp.nat) (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 (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat M)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))))) (forall ((M 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) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)) (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 N2)))))) (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 tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((M tptp.nat) (N2 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) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat M) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))))) (forall ((N2 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) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) _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) N2)))))))) (forall ((R2 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R2) 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.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) R2)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) R2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (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 N2)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (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 N2))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_real_real tptp.tan_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (= (tptp.aa_real_real tptp.sin_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (= (tptp.aa_real_real tptp.cos_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.tan_real X)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))))))) (forall ((Z tptp.complex)) (=> (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T5 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T5)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (not (= Z (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real tptp.cos_real T5)) (tptp.aa_real_real tptp.sin_real T5)))))))))) (forall ((X tptp.real) (N2 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) N2)) (exists ((T5 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real T5))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.exp_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sy X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)))))))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sz X)) (tptp.aa_real_real tptp.sin_real X)))) (forall ((X tptp.real) (Y tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) (tptp.aa_real_real tptp.sqrt Y)) (= X Y))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))) (= (tptp.aa_real_real tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real) (forall ((X tptp.real) (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 ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex tptp.aTP_Lamm_nx) tptp.zero_zero_complex)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real tptp.aTP_Lamm_fb) tptp.zero_zero_real)) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat tptp.aTP_Lamm_bl) tptp.zero_zero_nat)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int tptp.aTP_Lamm_ny) tptp.zero_zero_int)) (= (tptp.aa_complex_complex 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 ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((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.aa_real_real tptp.sqrt _let_62) _let_23) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((A tptp.fun_nat_complex) (X tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_kp A)) X)) (= (tptp.aa_nat_complex A tptp.zero_zero_nat) X))) (forall ((A tptp.fun_nat_real) (X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_kr A)) X)) (= (tptp.aa_nat_real A tptp.zero_zero_nat) X))) (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) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Xa2) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Ya) _let_1))))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sqrt _let_2)) _let_1) _let_2)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y))))) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real) (S2 tptp.real) (T tptp.real)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N)) (tptp.aa_nat_real G N)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) S2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) T)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real S2) T)))))) (forall ((F tptp.fun_nat_nat) (G tptp.fun_nat_nat) (S2 tptp.nat) (T tptp.nat)) (=> (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 F N)) (tptp.aa_nat_nat G N)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat F) S2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat G) T)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat S2) T)))))) (forall ((F tptp.fun_nat_int) (G tptp.fun_nat_int) (S2 tptp.int) (T tptp.int)) (=> (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 F N)) (tptp.aa_nat_int G N)))) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int F) S2)) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int G) T)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int S2) T)))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.exp_real X))) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X))))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex tptp.exp_complex X))) (tptp.aa_real_real tptp.exp_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real tptp.sqrt X)))) (forall ((X tptp.real) (K tptp.nat)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.sqrt X)) K))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real tptp.sqrt Y)))) (forall ((A2 tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.exp_complex A2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) A2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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 ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_real_complex (tptp.complex2 A) B)) (tptp.aa_real_complex (tptp.complex2 C) D)) (tptp.aa_real_complex (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 ((I2 tptp.nat) (F tptp.fun_nat_complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_fn I2) F)) (tptp.aa_nat_complex F I2)))) (forall ((I2 tptp.nat) (F tptp.fun_nat_real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_oo I2) F)) (tptp.aa_nat_real F I2)))) (forall ((I2 tptp.nat) (F tptp.fun_nat_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_op I2) F)) (tptp.aa_nat_nat F I2)))) (forall ((I2 tptp.nat) (F tptp.fun_nat_int)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_oq I2) F)) (tptp.aa_nat_int F I2)))) (forall ((F tptp.fun_nat_complex) (A tptp.complex) (C tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) A)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_pf F) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C) A))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_pg F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) A))))) (forall ((F tptp.fun_nat_complex) (A tptp.complex) (C tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) A)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_pe F) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) C))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_hg F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) C))))) (forall ((F tptp.fun_nat_complex) (A tptp.complex) (G tptp.fun_nat_complex) (B tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) A)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex G) B)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ph F) G)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (G tptp.fun_nat_real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) B)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ho F) G)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)))))) (forall ((F tptp.fun_nat_nat) (A tptp.nat) (G tptp.fun_nat_nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat F) A)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat G) B)) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hn F) G)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B)))))) (forall ((F tptp.fun_nat_int) (A tptp.int) (G tptp.fun_nat_int) (B tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int F) A)) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int G) B)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_pi F) G)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)))))) (forall ((F tptp.fun_nat_complex) (A tptp.complex) (G tptp.fun_nat_complex) (B tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) A)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex G) B)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_pj F) G)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) B)))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (G tptp.fun_nat_real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) B)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hr F) G)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))))) (forall ((F tptp.fun_nat_complex) (A tptp.complex) (C tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) A)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ot F) C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) C))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ht F) C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C))))) (forall ((F tptp.fun_nat_real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) A)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_fy F)) (tptp.aa_real_real tptp.uminus_uminus_real A))))) (forall ((F tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) A)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_pl F)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A))))) (forall ((I6 tptp.set_complex) (F tptp.fun_co8378349014452122532t_real) (X tptp.fun_complex_real)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_com20334259897932645t_real F I3)) (tptp.aa_complex_real X I3))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun471735231769099483t_real (tptp.aTP_Lamm_pn I6) F)) (tptp.groups5808333547571424918x_real X I6))))) (forall ((I6 tptp.set_real) (F tptp.fun_re4238438383274954274t_real) (X tptp.fun_real_real)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real F I3)) (tptp.aa_real_real X I3))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun628238740774635481t_real (tptp.aTP_Lamm_po I6) F)) (tptp.groups8097168146408367636l_real X I6))))) (forall ((I6 tptp.set_int) (F tptp.fun_int_fun_nat_real) (X tptp.fun_int_real)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_int_fun_nat_real F I3)) (tptp.aa_int_real X I3))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun2842512154077127769t_real (tptp.aTP_Lamm_pq I6) F)) (tptp.groups8778361861064173332t_real X I6))))) (forall ((I6 tptp.set_real) (F tptp.fun_re2084383175013312036omplex) (X tptp.fun_real_complex)) (=> (forall ((I3 tptp.real)) (=> (tptp.member_real I3 I6) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_rea1531280491672885477omplex F I3)) (tptp.aa_real_complex X I3))))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun7632768522510439005omplex (tptp.aTP_Lamm_ps I6) F)) (tptp.groups5754745047067104278omplex X I6))))) (forall ((I6 tptp.set_nat) (F tptp.fun_na1142814060743658952omplex) (X tptp.fun_nat_complex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_nat6454746962644518025omplex F I3)) (tptp.aa_nat_complex X I3))))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun4886358607025424513omplex (tptp.aTP_Lamm_pu I6) F)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex X) I6))))) (forall ((I6 tptp.set_int) (F tptp.fun_in8056368165505483812omplex) (X tptp.fun_int_complex)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_int4144929030551567077omplex F I3)) (tptp.aa_int_complex X I3))))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun3543561798013398749omplex (tptp.aTP_Lamm_pw I6) F)) (tptp.groups3049146728041665814omplex X I6))))) (forall ((I6 tptp.set_int) (F tptp.fun_int_fun_nat_int) (X tptp.fun_int_int)) (=> (forall ((I3 tptp.int)) (=> (tptp.member_int I3 I6) (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aa_int_fun_nat_int F I3)) (tptp.aa_int_int X I3))))) (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aa_fun8710705519803144921at_int (tptp.aTP_Lamm_py I6) F)) (tptp.groups4538972089207619220nt_int X I6))))) (forall ((I6 tptp.set_complex) (F tptp.fun_co3258106519541737638omplex) (X tptp.fun_complex_complex)) (=> (forall ((I3 tptp.complex)) (=> (tptp.member_complex I3 I6) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex F I3)) (tptp.aa_complex_complex X I3))))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun5003373910569599327omplex (tptp.aTP_Lamm_qa I6) F)) (tptp.groups7754918857620584856omplex X I6))))) (forall ((I6 tptp.set_nat) (F tptp.fun_nat_fun_nat_nat) (X tptp.fun_nat_nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat (tptp.aa_nat_fun_nat_nat F I3)) (tptp.aa_nat_nat X I3))))) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat (tptp.aa_fun8466562714962205125at_nat (tptp.aTP_Lamm_qb I6) F)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat X) I6))))) (forall ((I6 tptp.set_nat) (F tptp.fun_nat_fun_nat_real) (X tptp.fun_nat_real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I3) I6)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_nat_fun_nat_real F I3)) (tptp.aa_nat_real X I3))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun7039663905532832253t_real (tptp.aTP_Lamm_qc I6) F)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real X) I6))))) (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)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.exp_real X)))) (forall ((X tptp.real)) (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) tptp.zero_zero_real)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sqrt X)))))) (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Y) X)) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.exp_complex X)) (tptp.aa_complex_complex tptp.exp_complex Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) X)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.exp_complex X)) (tptp.aa_complex_complex tptp.exp_complex Y)) (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.exp_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.exp_complex X)) (tptp.aa_complex_complex tptp.exp_complex Y)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real tptp.exp_real Y)))) (forall ((C tptp.complex) (F tptp.fun_nat_complex) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_os C) F)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex C) D))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) D))))) (forall ((C tptp.real) (F tptp.fun_nat_real) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hk C) F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real C) D))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) D))))) (forall ((C tptp.complex) (F tptp.fun_nat_complex) (D tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ta C) F)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex D) C))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) D))))) (forall ((C tptp.real) (F tptp.fun_nat_real) (D tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_tb C) F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real D) C))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) D))))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (tptp.aa_real_complex (tptp.complex2 A) B) (tptp.numera6690914467698888265omplex W)) (and (= A (tptp.aa_num_real tptp.numeral_numeral_real W)) (= B tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_real_complex (tptp.complex2 A) B)) (tptp.aa_real_complex (tptp.complex2 C) D)) (tptp.aa_real_complex (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)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_real_complex (tptp.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)) (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 ((C tptp.complex) (F tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_os C) F)) A)) (=> (not (= C tptp.zero_zero_complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) C)))))) (forall ((C tptp.real) (F tptp.fun_nat_real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hk C) F)) A)) (=> (not (= C tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) C)))))) (forall ((F tptp.fun_nat_complex) (S2 tptp.complex)) (=> (= (tptp.aa_nat_complex F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_pk F)) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) S2))))) (forall ((F tptp.fun_nat_real) (S2 tptp.real)) (=> (= (tptp.aa_nat_real F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_lp F)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) S2))))) (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) (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 ((F tptp.fun_nat_complex) (L tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_pk F)) L)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex L) (tptp.aa_nat_complex F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_real) (L tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_lp F)) L)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real L) (tptp.aa_nat_real F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_nat) (L tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat (tptp.aTP_Lamm_lo F)) L)) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat F) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat L) (tptp.aa_nat_nat F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_int) (L tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aTP_Lamm_lz F)) L)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int F) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int L) (tptp.aa_nat_int F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_complex) (S2 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_pk F)) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex S2) (tptp.aa_nat_complex F tptp.zero_zero_nat)))))) (forall ((F tptp.fun_nat_real) (S2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_lp F)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real S2) (tptp.aa_nat_real F tptp.zero_zero_nat)))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_complex) (S2 tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2)) (= (tptp.aa_nat_complex F I3) tptp.zero_zero_complex))) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_tc N2) F)) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) S2))))) (forall ((N2 tptp.nat) (F tptp.fun_nat_real) (S2 tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat I3) N2)) (= (tptp.aa_nat_real F I3) tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_td N2) F)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) S2))))) (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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.exp_complex X)) (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)) (forall ((N2 tptp.nat) (X tptp.complex)) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2)) X)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.exp_complex X)) N2))) (forall ((N2 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 N2)) X)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.exp_real X)) N2))) (forall ((X tptp.complex) (N2 tptp.nat)) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.exp_complex X)) N2))) (forall ((X tptp.real) (N2 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 N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.exp_real X)) N2))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (tptp.aa_real_complex (tptp.complex2 A) B) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))) (and (= A (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_oy A2) F)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) A2))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_pb A2) F)) (tptp.groups3539618377306564664at_int F A2))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_pa A2) F)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) A2))))) (forall ((A2 tptp.set_nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_oz A2) F)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) A2))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_complex)) (let ((_let_1 (tptp.collect_nat P))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat _let_1)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ou P) F)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) _let_1)))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_int)) (let ((_let_1 (tptp.collect_nat P))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat _let_1)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_ox P) F)) (tptp.groups3539618377306564664at_int F _let_1)))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_nat)) (let ((_let_1 (tptp.collect_nat P))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat _let_1)) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_ow P) F)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) _let_1)))))) (forall ((P tptp.fun_nat_bool) (F tptp.fun_nat_real)) (let ((_let_1 (tptp.collect_nat P))) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ov P) F)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) _let_1)))))) (forall ((N3 tptp.set_nat) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (=> (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) N3))) (= (tptp.aa_nat_complex F N) tptp.zero_zero_complex))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) N3)))))) (forall ((N3 tptp.set_nat) (F tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (=> (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) N3))) (= (tptp.aa_nat_int F N) tptp.zero_zero_int))) (tptp.pp (tptp.aa_int_bool (tptp.sums_int F) (tptp.groups3539618377306564664at_int F N3)))))) (forall ((N3 tptp.set_nat) (F tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (=> (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) N3))) (= (tptp.aa_nat_nat F N) tptp.zero_zero_nat))) (tptp.pp (tptp.aa_nat_bool (tptp.sums_nat F) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat F) N3)))))) (forall ((N3 tptp.set_nat) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)) (=> (forall ((N tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N) N3))) (= (tptp.aa_nat_real F N) tptp.zero_zero_real))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) N3)))))) (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.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex (tptp.complex2 A) B)) (tptp.aa_real_complex (tptp.complex2 C) D)) (tptp.aa_real_complex (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 ((M tptp.nat) (Z tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_te M) Z)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Z) M)))) (forall ((M tptp.nat) (Z tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_tf M) Z)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Z) M)))) (forall ((M tptp.nat) (Z tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.sums_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_tg M) Z)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Z) M)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_44) _let_23)) (forall ((A tptp.fun_nat_complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_kp A)) (tptp.aa_nat_complex A tptp.zero_zero_nat)))) (forall ((A tptp.fun_nat_real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_kr A)) (tptp.aa_nat_real A tptp.zero_zero_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 (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_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real tptp.ln_ln_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real Y)) X))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real Y)) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real X)) X)))))) (forall ((F tptp.fun_nat_complex) (N2 tptp.nat) (S2 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_or F) N2)) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex S2) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((F tptp.fun_nat_real) (N2 tptp.nat) (S2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr F) N2)) S2)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real S2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((F tptp.fun_nat_complex) (S2 tptp.complex) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) S2)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_or F) N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex S2) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((F tptp.fun_nat_real) (S2 tptp.real) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) S2)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr F) N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real S2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))))) (forall ((F tptp.fun_nat_complex) (N2 tptp.nat) (S2 tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_or F) N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex S2) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) S2)))) (forall ((F tptp.fun_nat_real) (N2 tptp.nat) (S2 tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr F) N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real S2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real F) S2)))) (forall ((G tptp.fun_nat_complex) (S3 tptp.complex) (A2 tptp.set_nat) (S4 tptp.complex) (F tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex G) S3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (= S4 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex S3) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_th G) F)) A2))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aa_set5115289136882354743omplex (tptp.aTP_Lamm_ti G) A2) F)) S4)))))) (forall ((G tptp.fun_nat_real) (S3 tptp.real) (A2 tptp.set_nat) (S4 tptp.real) (F tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.sums_real G) S3)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat A2)) (=> (= S4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real S3) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_tj G) F)) A2))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_set1316517696749040435t_real (tptp.aTP_Lamm_tk G) A2) F)) S4)))))) (forall ((F tptp.fun_nat_real) (S2 tptp.set_nat)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aTP_Lamm_tl F)) S2) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real F) S2)) tptp.zero_zero_real))) (forall ((F tptp.fun_complex_real) (S2 tptp.set_complex)) (= (tptp.groups7754918857620584856omplex (tptp.aTP_Lamm_tm F) S2) (tptp.aa_real_complex (tptp.complex2 (tptp.groups5808333547571424918x_real F S2)) 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_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.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_55)) (forall ((N2 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) N2)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2)))) N2) (tptp.aa_complex_complex tptp.exp_complex X)))) (forall ((N2 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) N2)) (= (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 N2)))) N2) (tptp.aa_real_real tptp.exp_real X)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X)))) (let ((_let_2 (tptp.aa_real_real tptp.exp_real X))) (= (tptp.aa_real_real tptp.tanh_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_2) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_2) _let_1)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (tptp.aa_complex_complex tptp.exp_complex X))) (= (tptp.aa_complex_complex tptp.tanh_complex X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex _let_2) _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_2) _let_1)))))) (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.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) U)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) 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))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real _let_64)) _let_23)) (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_63) _let_61) (= (tptp.aa_real_real tptp.sin_real _let_63) _let_61) (= (tptp.aa_real_real tptp.tan_real _let_60) _let_56) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex _let_1)) Z)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.exp_complex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))) (forall ((Z tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) Z)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.exp_real Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))))) (forall ((C tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real C)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.power_power_real C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) C)))))) (forall ((C tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)) tptp.one_one_real)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex C)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.one_one_complex) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) C)))))) (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))))))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real tptp.aTP_Lamm_tn) 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)))) (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)))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_2) N2)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_nat_real _let_3 N2)) (tptp.aa_nat_real _let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_2)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real Y)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (= (tptp.aa_real_real tptp.cos_real _let_58) _let_59) (= (tptp.aa_real_real tptp.sin_real _let_60) _let_59) (forall ((Z tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.exp_real Z))) _let_1))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex tptp.exp_complex Z))) _let_1))))) (forall ((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_to 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_tp G) F)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_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 ((N2 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) N2)) (=> (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)) N2) (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 N2) _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_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) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Xa2) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Ya) _let_1)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (= (tptp.aa_real_real tptp.tan_real _let_58) (tptp.aa_real_real _let_57 _let_56)) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_1))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.exp_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) X)))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_1)))))) tptp.one_one_real)))) (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) (tptp.aa_real_real tptp.sqrt (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) _let_3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real Y)) _let_3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2)))) U)))))))) (forall ((X tptp.real)) (=> (tptp.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 ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (=> (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) N2)) (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))) N2)) (tptp.aa_real_real tptp.exp_real X))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (=> (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) N2)) (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))) N2)) (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real tptp.uminus_uminus_real X)))))))) (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 ((Z tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real tptp.exp_real Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) _let_2))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex tptp.exp_complex Z))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) _let_1)))))))) (forall ((X tptp.real) (N2 tptp.nat)) (exists ((T5 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 T5)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real tptp.exp_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sy X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2))))))) (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real U) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) _let_4)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) _let_4)) (=> (tptp.pp (tptp.aa_real_bool _let_3 X)) (=> (tptp.pp (tptp.aa_real_bool _let_3 Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) _let_2)))) U))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (tptp.aa_real_real tptp.exp_real X)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sin_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (= _let_1 (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real))) (= (tptp.aa_real_real tptp.arctan X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_real_real tptp.arctan (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) (tptp.aa_real_real _let_2 (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real _let_2 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)))) (= (tptp.aa_real_real tptp.tanh_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) _let_1))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_tq X)) (tptp.aa_real_real tptp.cos_real X)))) (forall ((Z tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_tr Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((Z tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_ts Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.one_one_complex) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex) Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((C tptp.fun_nat_complex) (X tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_tt C) X))) (=> (tptp.summable_complex _let_1) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_tu C) X)) (tptp.suminf_complex _let_1)))))) (forall ((C tptp.fun_nat_real) (X tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_tv C) X))) (=> (tptp.summable_real _let_1) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_tw C) X)) (tptp.suminf_real _let_1)))))) (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 ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (let ((_let_3 (tptp.aa_nat_nat _let_2 K))) (let ((_let_4 (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2))) (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)) N2) tptp.one_one_nat)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat K)))))))))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial _let_1) N2) _let_1))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) N2) tptp.one_one_nat)) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2)) (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 ((N2 tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K) tptp.zero_zero_nat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((N2 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 N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc N2)) _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 ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((N2 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 N2) K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arccos Y)) Y)))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real tptp.arcsin Y)) Y)))) (= (tptp.aa_real_real tptp.arccos tptp.zero_zero_real) _let_25) (= (tptp.aa_real_real tptp.arcsin tptp.one_one_real) _let_25) (= (tptp.aa_real_real tptp.arcsin _let_53) _let_28) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) tptp.one_one_nat) N2)) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K) tptp.zero_zero_nat))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (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 N2) K)))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (= (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 N2) 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 ((M tptp.nat) (R2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M))) (let ((_let_2 (tptp.aa_nat_nat _let_1 R2))) (let ((_let_3 (tptp.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 ((R2 tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat R2) 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.binomial N2) R2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat N2) R2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (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 N2) K)))))) (forall ((C tptp.fun_nat_real) (X2 tptp.nat)) (= (tptp.aa_nat_real (tptp.diffs_real (tptp.aTP_Lamm_fy C)) X2) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real (tptp.diffs_real C) X2)))) (forall ((C tptp.fun_nat_int) (X2 tptp.nat)) (= (tptp.aa_nat_int (tptp.diffs_int (tptp.aTP_Lamm_tx C)) X2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int (tptp.diffs_int C) X2)))) (forall ((C tptp.fun_nat_complex) (X2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.diffs_complex (tptp.aTP_Lamm_pl C)) X2) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex (tptp.diffs_complex C) X2)))) (forall ((C tptp.fun_nat_rat) (X2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.diffs_rat (tptp.aTP_Lamm_ty C)) X2) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat (tptp.diffs_rat C) X2)))) (forall ((C tptp.fun_nat_Code_integer) (X2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.diffs_Code_integer (tptp.aTP_Lamm_tz C)) X2) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer (tptp.diffs_Code_integer C) X2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (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 N2) 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 ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (= (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 N2) K))) _let_1))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (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) N2)) (= (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 N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K)))))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2))) (= (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 N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat _let_1 tptp.one_one_nat)) K))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real tptp.arccos X))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real))) (= (= (tptp.aa_real_real tptp.arccos X) (tptp.aa_real_real tptp.arccos Y)) (= X Y)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos X)) (tptp.aa_real_real tptp.arccos Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) X)))))) (forall ((X tptp.real) (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.aa_real_real tptp.arcsin X) (tptp.aa_real_real tptp.arcsin Y)) (= X Y))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))))) (forall ((K tptp.nat) (N2 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 N2) _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (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 N2) tptp.one_one_nat)) K))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (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 N2) K)))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)))) (forall ((C tptp.fun_nat_rat) (X2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X2))) (= (tptp.aa_nat_rat (tptp.diffs_rat C) X2) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat C _let_1))))) (forall ((C tptp.fun_nat_int) (X2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X2))) (= (tptp.aa_nat_int (tptp.diffs_int C) X2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _let_1)) (tptp.aa_nat_int C _let_1))))) (forall ((C tptp.fun_nat_real) (X2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X2))) (= (tptp.aa_nat_real (tptp.diffs_real C) X2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_nat_real C _let_1))))) (forall ((C tptp.fun_nat_Code_integer) (X2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X2))) (= (tptp.aa_nat_Code_integer (tptp.diffs_Code_integer C) X2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger _let_1)) (tptp.aa_nat_Code_integer C _let_1))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (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 N2)) (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 N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) (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 N2) K)))))) (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (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)) N2)) (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 ((N2 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))) N2)))) (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 N2))))) (forall ((N2 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 N2) 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))) N2)))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (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 N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (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 N2) (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) N2)) (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 ((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 ((N2 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 N2) 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 N2)) (=> (tptp.pp (tptp.aa_nat_bool _let_2 K)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) 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) (N2 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 N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (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 N2) 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) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arccos X)) (tptp.aa_real_real tptp.arccos Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos Y)) tptp.pi))))) (forall ((C tptp.fun_nat_complex) (X tptp.complex)) (=> (forall ((X3 tptp.complex)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql C) X3))) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_tt C) X)))) (forall ((C tptp.fun_nat_real) (X tptp.real)) (=> (forall ((X3 tptp.real)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj C) X3))) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_tv C) 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.pi)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.cos_real X)) X)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.arcsin X)) (tptp.aa_real_real tptp.arcsin Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real Y)) tptp.one_one_real)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real tptp.arccos Y)) Y))) (forall ((Theta tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real Theta))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.cos_real Theta)) _let_1)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2)) (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 N2) K))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (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 N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat _let_1 K)) (tptp.aa_nat_nat _let_1 (tptp.aa_nat_nat tptp.suc K))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (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)) N2)) (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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (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 N2) (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) N2)) (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 ((N2 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 N2) _let_1))) (let ((_let_3 (tptp.aa_nat_fun_nat_nat tptp.binomial N2))) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) N2))) (= (tptp.aa_nat_nat _let_3 (tptp.aa_nat_nat tptp.suc _let_2)) (tptp.aa_nat_nat _let_3 _let_2))))))) (forall ((N2 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 N2) 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) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_1 _let_2)) (tptp.aa_nat_nat _let_1 K))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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 N2) K))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N2)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_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 N2) K))) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (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 N2) K))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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 N2) K))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)) (tptp.aa_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 N2) K))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2)) (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 N2) K))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arccos Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) X)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.cos_real X)) (tptp.aa_real_real tptp.uminus_uminus_real X))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.uminus_uminus_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.pi) (tptp.aa_real_real tptp.arccos X)))))) (forall ((N2 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 N2) _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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat))) _let_1)))) (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 ((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) (K5 tptp.real) (C tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X)) K5)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real X3)) K5)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj C) X3)))) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ua X) C))))) (forall ((X tptp.complex) (K5 tptp.real) (C tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) K5)) (=> (forall ((X3 tptp.complex)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X3)) K5)) (tptp.summable_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql C) X3)))) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ub X) C))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arccos Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_real_real tptp.arcsin Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_2) _let_1)))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (let ((_let_2 (tptp.aa_real_real tptp.arcsin Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) _let_2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_2) _let_1)))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.aa_real_real tptp.arcsin Y)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) _let_1)) (= (tptp.aa_real_real tptp.arcsin (tptp.aa_real_real tptp.sin_real X)) X))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_2)) Y)) (=> (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) _let_2))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.arcsin X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sin_real Y)) X)))))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_2)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) _let_2))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.arcsin X)) Y)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sin_real Y))))))))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arcsin Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi)) (= (tptp.aa_real_real tptp.sin_real _let_1) Y)))))) (forall ((Y tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.arcsin Y))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Y)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.one_one_real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) _let_2)) (= (tptp.aa_real_real tptp.sin_real _let_1) Y))))))) (forall ((N2 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) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 _let_1))) N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)))) (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)) N2)) N2))))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.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 ((N2 tptp.nat)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_uc N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_1) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ud N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_ue N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (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) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_uf N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_ug N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_uh N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_1) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ui N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_rat (tptp.power_power_rat _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_uj N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (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) N2)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger _let_1) (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_uk N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_ul N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) N2))))) (forall ((X6 tptp.fun_nat_real)) (= (tptp.topolo6980174941875973593q_real X6) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 M6)) (tptp.aa_nat_real X6 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 N5)) (tptp.aa_nat_real X6 M6)))))))) (forall ((X6 tptp.fun_nat_set_int)) (= (tptp.topolo3100542954746470799et_int X6) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X6 M6) (tptp.aa_nat_set_int X6 N5)))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X6 N5) (tptp.aa_nat_set_int X6 M6))))))) (forall ((X6 tptp.fun_nat_rat)) (= (tptp.topolo4267028734544971653eq_rat X6) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X6 M6)) (tptp.aa_nat_rat X6 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X6 N5)) (tptp.aa_nat_rat X6 M6)))))))) (forall ((X6 tptp.fun_nat_num)) (= (tptp.topolo1459490580787246023eq_num X6) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X6 M6)) (tptp.aa_nat_num X6 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X6 N5)) (tptp.aa_nat_num X6 M6)))))))) (forall ((X6 tptp.fun_nat_nat)) (= (tptp.topolo4902158794631467389eq_nat X6) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X6 M6)) (tptp.aa_nat_nat X6 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X6 N5)) (tptp.aa_nat_nat X6 M6)))))))) (forall ((X6 tptp.fun_nat_int)) (= (tptp.topolo4899668324122417113eq_int X6) (or (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X6 M6)) (tptp.aa_nat_int X6 N5))))) (forall ((M6 tptp.nat) (N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M6) N5)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X6 N5)) (tptp.aa_nat_int X6 M6)))))))) (forall ((X6 tptp.fun_nat_real)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 N)) (tptp.aa_nat_real X6 M2))))) (tptp.topolo6980174941875973593q_real X6))) (forall ((X6 tptp.fun_nat_set_int)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X6 N) (tptp.aa_nat_set_int X6 M2)))) (tptp.topolo3100542954746470799et_int X6))) (forall ((X6 tptp.fun_nat_rat)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X6 N)) (tptp.aa_nat_rat X6 M2))))) (tptp.topolo4267028734544971653eq_rat X6))) (forall ((X6 tptp.fun_nat_num)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X6 N)) (tptp.aa_nat_num X6 M2))))) (tptp.topolo1459490580787246023eq_num X6))) (forall ((X6 tptp.fun_nat_nat)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X6 N)) (tptp.aa_nat_nat X6 M2))))) (tptp.topolo4902158794631467389eq_nat X6))) (forall ((X6 tptp.fun_nat_int)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X6 N)) (tptp.aa_nat_int X6 M2))))) (tptp.topolo4899668324122417113eq_int X6))) (forall ((X6 tptp.fun_nat_real)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 M2)) (tptp.aa_nat_real X6 N))))) (tptp.topolo6980174941875973593q_real X6))) (forall ((X6 tptp.fun_nat_set_int)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X6 M2) (tptp.aa_nat_set_int X6 N)))) (tptp.topolo3100542954746470799et_int X6))) (forall ((X6 tptp.fun_nat_rat)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X6 M2)) (tptp.aa_nat_rat X6 N))))) (tptp.topolo4267028734544971653eq_rat X6))) (forall ((X6 tptp.fun_nat_num)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X6 M2)) (tptp.aa_nat_num X6 N))))) (tptp.topolo1459490580787246023eq_num X6))) (forall ((X6 tptp.fun_nat_nat)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X6 M2)) (tptp.aa_nat_nat X6 N))))) (tptp.topolo4902158794631467389eq_nat X6))) (forall ((X6 tptp.fun_nat_int)) (=> (forall ((M2 tptp.nat) (N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M2) N)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X6 M2)) (tptp.aa_nat_int X6 N))))) (tptp.topolo4899668324122417113eq_int X6))) (forall ((I2 tptp.real) (K tptp.real)) (= (tptp.member_real I2 (tptp.set_ord_atMost_real K)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real I2) K)))) (forall ((I2 tptp.set_nat) (K tptp.set_nat)) (= (tptp.member_set_nat I2 (tptp.set_or4236626031148496127et_nat K)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat I2) K)))) (forall ((I2 tptp.set_int) (K tptp.set_int)) (= (tptp.member_set_int I2 (tptp.set_or58775011639299419et_int K)) (tptp.ord_less_eq_set_int I2 K))) (forall ((I2 tptp.rat) (K tptp.rat)) (= (tptp.member_rat I2 (tptp.set_ord_atMost_rat K)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat I2) K)))) (forall ((I2 tptp.num) (K tptp.num)) (= (tptp.member_num I2 (tptp.set_ord_atMost_num K)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num I2) K)))) (forall ((I2 tptp.nat) (K tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat I2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat K))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I2) K)))) (forall ((I2 tptp.int) (K tptp.int)) (= (tptp.member_int I2 (tptp.set_ord_atMost_int K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) K)))) (forall ((X tptp.set_int) (Y tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or58775011639299419et_int X) (tptp.set_or58775011639299419et_int Y)) (tptp.ord_less_eq_set_int X Y))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_ord_atMost_rat X) (tptp.set_ord_atMost_rat Y)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)))) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_ord_atMost_num X) (tptp.set_ord_atMost_num Y)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat X)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Y))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.ord_less_eq_set_int (tptp.set_ord_atMost_int X) (tptp.set_ord_atMost_int Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Y)))) (forall ((L tptp.set_int) (H tptp.set_int) (H2 tptp.set_int)) (= (tptp.ord_le4403425263959731960et_int (tptp.set_or370866239135849197et_int L H) (tptp.set_or58775011639299419et_int H2)) (or (not (tptp.ord_less_eq_set_int L H)) (tptp.ord_less_eq_set_int H H2)))) (forall ((L tptp.rat) (H tptp.rat) (H2 tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_or633870826150836451st_rat L H) (tptp.set_ord_atMost_rat H2)) (or (not (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat L) H))) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat H) H2))))) (forall ((L tptp.num) (H tptp.num) (H2 tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_or7049704709247886629st_num L H) (tptp.set_ord_atMost_num H2)) (or (not (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num L) H))) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num H) H2))))) (forall ((L tptp.nat) (H tptp.nat) (H2 tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_or1269000886237332187st_nat L H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat H2))) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat L) H))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat H) H2))))) (forall ((L tptp.int) (H tptp.int) (H2 tptp.int)) (= (tptp.ord_less_eq_set_int (tptp.set_or1266510415728281911st_int L H) (tptp.set_ord_atMost_int H2)) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int L) H))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int H) H2))))) (forall ((L tptp.real) (H tptp.real) (H2 tptp.real)) (= (tptp.ord_less_eq_set_real (tptp.set_or1222579329274155063t_real L H) (tptp.set_ord_atMost_real H2)) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L) H))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real H) H2))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.groups2906978787729119204at_rat G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_rat G _let_1))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.groups3539618377306564664at_int G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_int G _let_1))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups3542108847815614940at_nat G))) (= (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_nat G _let_1)))))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (let ((_let_2 (tptp.groups6591440286371151544t_real G))) (= (tptp.aa_set_nat_real _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_nat_real G _let_1)))))) (forall ((U tptp.set_nat)) (= (tptp.set_or4236626031148496127et_nat U) (tptp.collect_set_nat (tptp.aTP_Lamm_cb U)))) (forall ((U tptp.set_int)) (= (tptp.set_or58775011639299419et_int U) (tptp.collect_set_int (tptp.aTP_Lamm_cd U)))) (forall ((U tptp.rat)) (= (tptp.set_ord_atMost_rat U) (tptp.collect_rat (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_um U)))) (forall ((U tptp.num)) (= (tptp.set_ord_atMost_num U) (tptp.collect_num (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_un U)))) (forall ((U tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat U) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_bz U)))) (forall ((U tptp.int)) (= (tptp.set_ord_atMost_int U) (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_uo U)))) (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 ((H tptp.int) (L2 tptp.int) (H2 tptp.int)) (not (tptp.ord_less_eq_set_int (tptp.set_ord_atMost_int H) (tptp.set_or1266510415728281911st_int L2 H2)))) (forall ((H tptp.real) (L2 tptp.real) (H2 tptp.real)) (not (tptp.ord_less_eq_set_real (tptp.set_ord_atMost_real H) (tptp.set_or1222579329274155063t_real L2 H2)))) (forall ((S3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (exists ((K3 tptp.nat)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat S3) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat K3)))))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.ord_less_eq_set_rat (tptp.set_ord_atMost_rat A) (tptp.set_ord_lessThan_rat B)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat A) B)))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.ord_less_eq_set_num (tptp.set_ord_atMost_num A) (tptp.set_ord_lessThan_num B)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num A) B)))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat A)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat B))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.ord_less_eq_set_int (tptp.set_ord_atMost_int A) (tptp.aa_int_set_int tptp.set_ord_lessThan_int B)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.ord_less_eq_set_real (tptp.set_ord_atMost_real A) (tptp.set_or5984915006950818249n_real B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)))) (forall ((A tptp.bool) (B tptp.bool)) (= (tptp.ord_less_eq_set_bool (tptp.set_ord_atMost_bool A) (tptp.aa_bool_set_bool tptp.set_or4454636193642143162n_bool B)) (tptp.pp (tptp.aa_bool_bool (tptp.ord_less_bool A) B)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_up M)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_nat_nat tptp.suc M)))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ly G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_lz G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_lo G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G tptp.zero_zero_nat)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_lp G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((F tptp.fun_nat_rat) (I2 tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_rf F) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat I2)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat F tptp.zero_zero_nat)) (tptp.aa_nat_rat F (tptp.aa_nat_nat tptp.suc I2))))) (forall ((F tptp.fun_nat_int) (I2 tptp.nat)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_rg F) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat I2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int F tptp.zero_zero_nat)) (tptp.aa_nat_int F (tptp.aa_nat_nat tptp.suc I2))))) (forall ((F tptp.fun_nat_real) (I2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_rh F)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat I2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real F tptp.zero_zero_nat)) (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc I2))))) (forall ((C tptp.fun_nat_complex) (N2 tptp.nat) (D tptp.fun_nat_complex)) (= (forall ((X4 tptp.complex)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql C) X4)) _let_1) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql D) X4)) _let_1)))) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I5) N2)) (= (tptp.aa_nat_complex C I5) (tptp.aa_nat_complex D I5)))))) (forall ((C tptp.fun_nat_real) (N2 tptp.nat) (D tptp.fun_nat_real)) (= (forall ((X4 tptp.real)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj C) X4)) _let_1) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj D) X4)) _let_1)))) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I5) N2)) (= (tptp.aa_nat_real C I5) (tptp.aa_nat_real D I5)))))) (forall ((A tptp.fun_nat_int) (B3 tptp.int)) (=> (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 A N)))) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.groups3539618377306564664at_int A (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N))) B3))) (tptp.summable_int A)))) (forall ((A tptp.fun_nat_nat) (B3 tptp.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) (tptp.aa_nat_nat A N)))) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N))) B3))) (tptp.summable_nat A)))) (forall ((A tptp.fun_nat_real) (B3 tptp.real)) (=> (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 A N)))) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N))) B3))) (tptp.summable_real A)))) (forall ((A tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_uq A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_ur A) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((A tptp.fun_nat_fun_nat_real) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_us A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_ut A) N2)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((R2 tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_uu R2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (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 R2) N2))) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_uv N2)) (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 ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_uv N2)) (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 N2) M)) tptp.one_one_nat)) M))) (forall ((C tptp.fun_nat_complex) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.complex)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql C) W2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_complex C K) tptp.zero_zero_complex)))) (forall ((C tptp.fun_nat_real) (N2 tptp.nat) (K tptp.nat)) (=> (forall ((W2 tptp.real)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj C) W2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (tptp.aa_nat_real C K) tptp.zero_zero_real)))) (forall ((C tptp.fun_nat_complex) (N2 tptp.nat)) (= (forall ((X4 tptp.complex)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql C) X4)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I5) N2)) (= (tptp.aa_nat_complex C I5) tptp.zero_zero_complex))))) (forall ((C tptp.fun_nat_real) (N2 tptp.nat)) (= (forall ((X4 tptp.real)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj C) X4)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (forall ((I5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I5) N2)) (= (tptp.aa_nat_real C I5) tptp.zero_zero_real))))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat G tptp.zero_zero_nat)) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ly G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int G tptp.zero_zero_nat)) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_lz G) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat G tptp.zero_zero_nat)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_lo G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real G tptp.zero_zero_nat)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_lp G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((F tptp.fun_nat_rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))) (= (tptp.groups2906978787729119204at_rat F (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.groups2906978787729119204at_rat F (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (tptp.groups2906978787729119204at_rat F (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) _let_1)))))) (forall ((F tptp.fun_nat_int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))) (= (tptp.groups3539618377306564664at_int F (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.groups3539618377306564664at_int F (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (tptp.groups3539618377306564664at_int F (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) _let_1)))))) (forall ((F tptp.fun_nat_nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))) (let ((_let_2 (tptp.groups3542108847815614940at_nat F))) (= (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_set_nat_nat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (tptp.aa_set_nat_nat _let_2 (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) _let_1))))))) (forall ((F tptp.fun_nat_real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2))) (let ((_let_2 (tptp.groups6591440286371151544t_real F))) (= (tptp.aa_set_nat_real _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (tptp.aa_set_nat_real _let_2 (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) _let_1))))))) (forall ((G tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.groups977919841031483927at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_uw N2)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_uy G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_fun_nat_real) (N2 tptp.nat)) (= (tptp.groups4567486121110086003t_real (tptp.produc1703576794950452218t_real G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_uw N2)))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_va G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_vb M) N2)) (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 N2)) M)))) (forall ((M tptp.nat) (N2 tptp.nat) (R2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_vc M) N2) R2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat R2)) (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) N2)) R2))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (let ((_let_2 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex _let_2 X)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_1) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_complex_complex _let_2 (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat X))) (let ((_let_2 (tptp.minus_minus_rat tptp.one_one_rat))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat _let_2 X)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_rat_rat _let_2 (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((X tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (let ((_let_2 (tptp.aa_int_fun_int_int tptp.minus_minus_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int _let_2 X)) (tptp.groups3539618377306564664at_int _let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_int_int _let_2 (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_2 X)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_1) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_real_real _let_2 (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat tptp.suc N2))))))) (forall ((C tptp.fun_nat_complex) (N2 tptp.nat)) (= (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_vd C) N2))) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I5) N2)) (not (= (tptp.aa_nat_complex C I5) tptp.zero_zero_complex)))))) (forall ((C tptp.fun_nat_real) (N2 tptp.nat)) (= (tptp.finite_finite_real (tptp.collect_real (tptp.aa_nat_fun_real_bool (tptp.aTP_Lamm_ve C) N2))) (exists ((I5 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I5) N2)) (not (= (tptp.aa_nat_real C I5) tptp.zero_zero_real)))))) (forall ((C tptp.fun_nat_complex) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (tptp.aa_nat_complex C K) tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.finite3207457112153483333omplex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_vd C) N2)))))) (forall ((C tptp.fun_nat_real) (K tptp.nat) (N2 tptp.nat)) (=> (not (= (tptp.aa_nat_real C K) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (tptp.finite_finite_real (tptp.collect_real (tptp.aa_nat_fun_real_bool (tptp.aTP_Lamm_ve C) N2)))))) (forall ((C tptp.fun_nat_complex) (A tptp.complex) (N2 tptp.nat)) (=> (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql C) A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex) (not (forall ((B2 tptp.fun_nat_complex)) (not (forall ((Z4 tptp.complex)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql C) Z4)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex Z4) A)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql B2) Z4)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))))) (forall ((C tptp.fun_nat_rat) (A tptp.rat) (N2 tptp.nat)) (=> (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_vf C) A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat) (not (forall ((B2 tptp.fun_nat_rat)) (not (forall ((Z4 tptp.rat)) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_vf C) Z4) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat Z4) A)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_vf B2) Z4) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))))) (forall ((C tptp.fun_nat_int) (A tptp.int) (N2 tptp.nat)) (=> (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_vg C) A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int) (not (forall ((B2 tptp.fun_nat_int)) (not (forall ((Z4 tptp.int)) (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_vg C) Z4) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (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 Z4) A)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_vg B2) Z4) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))))) (forall ((C tptp.fun_nat_real) (A tptp.real) (N2 tptp.nat)) (=> (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj C) A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real) (not (forall ((B2 tptp.fun_nat_real)) (not (forall ((Z4 tptp.real)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj C) Z4)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z4) A)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj B2) Z4)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))))) (forall ((C tptp.fun_nat_complex) (N2 tptp.nat) (A tptp.complex)) (exists ((B2 tptp.fun_nat_complex)) (forall ((Z4 tptp.complex)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_ql C))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 Z4)) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex Z4) A)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql B2) Z4)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 A)) _let_1)))))))) (forall ((C tptp.fun_nat_rat) (N2 tptp.nat) (A tptp.rat)) (exists ((B2 tptp.fun_nat_rat)) (forall ((Z4 tptp.rat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_vf C))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 Z4) _let_1) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat Z4) A)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_vf B2) Z4) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 A) _let_1)))))))) (forall ((C tptp.fun_nat_int) (N2 tptp.nat) (A tptp.int)) (exists ((B2 tptp.fun_nat_int)) (forall ((Z4 tptp.int)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_vg C))) (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 Z4) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Z4) A)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_vg B2) Z4) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 A) _let_1)))))))) (forall ((C tptp.fun_nat_real) (N2 tptp.nat) (A tptp.real)) (exists ((B2 tptp.fun_nat_real)) (forall ((Z4 tptp.real)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_qj C))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 Z4)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Z4) A)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj B2) Z4)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 A)) _let_1)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (let ((_let_2 (tptp.groups2073611262835488442omplex _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_complex _let_2 (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 M)) (tptp.aa_set_nat_complex _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.rat)) (let ((_let_1 (tptp.power_power_rat X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups2906978787729119204at_rat _let_1 (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_1 M)) (tptp.groups2906978787729119204at_rat _let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.groups3539618377306564664at_int _let_1 (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 M)) (tptp.groups3539618377306564664at_int _let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.groups6591440286371151544t_real _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_set_nat_real _let_2 (tptp.set_or1269000886237332187st_nat M N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_set_nat_real _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))))) (forall ((G tptp.fun_nat_fun_nat_nat) (N2 tptp.nat)) (= (tptp.groups977919841031483927at_nat (tptp.produc6842872674320459806at_nat G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_vh N2)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_uy G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((G tptp.fun_nat_fun_nat_real) (N2 tptp.nat)) (= (tptp.groups4567486121110086003t_real (tptp.produc1703576794950452218t_real G) (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool (tptp.aTP_Lamm_vh N2)))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_va G)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (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))) N2))) (forall ((A tptp.fun_nat_complex) (B tptp.fun_nat_complex)) (=> (tptp.summable_real (tptp.aTP_Lamm_nz A)) (=> (tptp.summable_real (tptp.aTP_Lamm_nz B)) (tptp.summable_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_vj A) B))))) (forall ((A tptp.fun_nat_real) (B tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aTP_Lamm_ob A)) (=> (tptp.summable_real (tptp.aTP_Lamm_ob B)) (tptp.summable_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_vl A) B))))) (forall ((A tptp.fun_nat_complex) (B tptp.fun_nat_complex)) (=> (tptp.summable_real (tptp.aTP_Lamm_nz A)) (=> (tptp.summable_real (tptp.aTP_Lamm_nz B)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.suminf_complex A)) (tptp.suminf_complex B)) (tptp.suminf_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_vj A) B)))))) (forall ((A tptp.fun_nat_real) (B tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aTP_Lamm_ob A)) (=> (tptp.summable_real (tptp.aTP_Lamm_ob B)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real A)) (tptp.suminf_real B)) (tptp.suminf_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_vl A) B)))))) (forall ((A tptp.nat) (B tptp.nat) (N2 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)) N2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_vm A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_rat) (N2 tptp.nat)) (= (tptp.groups2906978787729119204at_rat G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_mv G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_int) (N2 tptp.nat)) (= (tptp.groups3539618377306564664at_int G (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_mw G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aTP_Lamm_mx G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((G tptp.fun_nat_real) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real G) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_my G)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((M tptp.nat) (A tptp.fun_nat_complex) (N2 tptp.nat) (B tptp.fun_nat_complex) (X tptp.complex)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_complex A I3) tptp.zero_zero_complex))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) J2)) (= (tptp.aa_nat_complex B J2) tptp.zero_zero_complex))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql A) X)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql B) X)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_fun3721018923249493343omplex (tptp.aTP_Lamm_vn 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) N2))))))) (forall ((M tptp.nat) (A tptp.fun_nat_rat) (N2 tptp.nat) (B tptp.fun_nat_rat) (X tptp.rat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_rat A I3) tptp.zero_zero_rat))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) J2)) (= (tptp.aa_nat_rat B J2) tptp.zero_zero_rat))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_vf A) X) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_vf B) X) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_fun5559679822142647773at_rat (tptp.aTP_Lamm_vp 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) N2))))))) (forall ((M tptp.nat) (A tptp.fun_nat_int) (N2 tptp.nat) (B tptp.fun_nat_int) (X tptp.int)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_int A I3) tptp.zero_zero_int))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) J2)) (= (tptp.aa_nat_int B J2) tptp.zero_zero_int))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_vg A) X) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_vg B) X) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_fun2315716387381795033at_int (tptp.aTP_Lamm_vr 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) N2))))))) (forall ((M tptp.nat) (A tptp.fun_nat_real) (N2 tptp.nat) (B tptp.fun_nat_real) (X tptp.real)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_real A I3) tptp.zero_zero_real))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) J2)) (= (tptp.aa_nat_real B J2) tptp.zero_zero_real))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj A) X)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj B) X)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_fun4732485501138722137t_real (tptp.aTP_Lamm_vs 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) N2))))))) (forall ((C tptp.fun_nat_complex) (N2 tptp.nat) (K tptp.complex)) (= (forall ((X4 tptp.complex)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql C) X4)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) K)) (and (= (tptp.aa_nat_complex C tptp.zero_zero_nat) K) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N2))) (= (tptp.aa_nat_complex C X4) tptp.zero_zero_complex)))))) (forall ((C tptp.fun_nat_real) (N2 tptp.nat) (K tptp.real)) (= (forall ((X4 tptp.real)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj C) X4)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) K)) (and (= (tptp.aa_nat_real C tptp.zero_zero_nat) K) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N2))) (= (tptp.aa_nat_real C X4) tptp.zero_zero_real)))))) (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) B)) N2) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_vt A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) N2) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_vu A) B) N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) N2) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_vv A) B) N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.plus_p5714425477246183910nteger A B)) N2) (tptp.groups7501900531339628137nteger (tptp.aa_nat2010205248571845816nteger (tptp.aa_Cod3140087502949435154nteger (tptp.aTP_Lamm_vw A) B) N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 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)) N2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_vm A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) N2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_vx A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((M tptp.nat) (A tptp.fun_nat_nat) (N2 tptp.nat) (B tptp.fun_nat_nat) (X tptp.nat)) (=> (forall ((I3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) I3)) (= (tptp.aa_nat_nat A I3) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) 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_vy 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_vy B) X)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_wa 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) N2))))))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_wb N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (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))) N2)) N2))) (forall ((A tptp.fun_nat_complex) (B tptp.fun_nat_complex)) (=> (tptp.summable_real (tptp.aTP_Lamm_nz A)) (=> (tptp.summable_real (tptp.aTP_Lamm_nz B)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_vj A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.suminf_complex A)) (tptp.suminf_complex B))))))) (forall ((A tptp.fun_nat_real) (B tptp.fun_nat_real)) (=> (tptp.summable_real (tptp.aTP_Lamm_ob A)) (=> (tptp.summable_real (tptp.aTP_Lamm_ob B)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_vl A) B)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.suminf_real A)) (tptp.suminf_real B))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_complex) (H tptp.fun_nat_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_wc K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P2)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_wd K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_rat) (H tptp.fun_nat_rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_we K) G) H) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P2)) (tptp.groups2906978787729119204at_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_wf K) G) H) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_int) (H tptp.fun_nat_int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.groups3539618377306564664at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_wg K) G) H) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P2)) (tptp.groups3539618377306564664at_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_wh K) G) H) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_nat) (H tptp.fun_nat_nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_wi K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P2)) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_wj K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((P2 tptp.nat) (K tptp.nat) (G tptp.fun_nat_real) (H tptp.fun_nat_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) P2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) P2)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_wk K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat P2)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_wl K) G) H)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat P2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))))) (forall ((N2 tptp.nat) (Z tptp.int) (A tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Z) N2) A) (= (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aTP_Lamm_wm N2) Z) A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (Z tptp.complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Z) N2) A) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aTP_Lamm_wn N2) Z) A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))) (forall ((N2 tptp.nat) (Z tptp.rat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (= (tptp.aa_nat_rat (tptp.power_power_rat Z) N2) A) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aTP_Lamm_wo N2) Z) A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat)))) (forall ((N2 tptp.nat) (Z tptp.code_integer) (A tptp.code_integer)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (= (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Z) N2) A) (= (tptp.groups7501900531339628137nteger (tptp.aa_Cod1578151519121547077nteger (tptp.aa_Cod6397266357770349983nteger (tptp.aTP_Lamm_wp N2) Z) A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger)))) (forall ((N2 tptp.nat) (Z tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Z) N2) A) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_wq N2) Z) A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))) (forall ((X tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X))) (let ((_let_3 (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex _let_2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex _let_2 (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_complex_complex _let_1 X)))))))))) (forall ((X tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (tptp.power_power_rat X))) (let ((_let_3 (tptp.groups2906978787729119204at_rat _let_2 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat _let_2 (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_rat_rat _let_1 X)))))))))) (forall ((X tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_3 (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real _let_2 (tptp.aa_nat_nat tptp.suc N2)))) (tptp.aa_real_real _let_1 X)))))))))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_wr N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ws N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (tptp.groups3539618377306564664at_int (tptp.aTP_Lamm_wt N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (tptp.groups7501900531339628137nteger (tptp.aTP_Lamm_wu N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.one_one_nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_wv N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))) (forall ((N2 tptp.nat) (A tptp.fun_nat_complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_ql A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 X)) _let_1)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 Y)) _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_fun5031706661949900810omplex (tptp.aTP_Lamm_wx N2) A) X) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))) (forall ((N2 tptp.nat) (A tptp.fun_nat_rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_vf A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 X) _let_1)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 Y) _let_1)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_fun8528462509625601970at_rat (tptp.aTP_Lamm_wz N2) A) X) Y) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))) (forall ((N2 tptp.nat) (A tptp.fun_nat_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_vg A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 X) _let_1)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 Y) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aa_fun7421131748584218370at_int (tptp.aTP_Lamm_xb N2) A) X) Y) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))) (forall ((N2 tptp.nat) (A tptp.fun_nat_real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_qj A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 X)) _let_1)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 Y)) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_fun2548873334967081986t_real (tptp.aTP_Lamm_xd N2) A) X) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))) (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 ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_xe N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (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 N2) tptp.one_one_nat))))) (forall ((A tptp.fun_nat_int)) (=> (tptp.topolo4899668324122417113eq_int A) (tptp.topolo4899668324122417113eq_int (tptp.aTP_Lamm_tx A)))) (forall ((A tptp.fun_nat_rat)) (=> (tptp.topolo4267028734544971653eq_rat A) (tptp.topolo4267028734544971653eq_rat (tptp.aTP_Lamm_ty A)))) (forall ((A tptp.fun_nat_Code_integer)) (=> (tptp.topolo2919662092509805066nteger A) (tptp.topolo2919662092509805066nteger (tptp.aTP_Lamm_tz A)))) (forall ((A tptp.fun_nat_real)) (=> (tptp.topolo6980174941875973593q_real A) (tptp.topolo6980174941875973593q_real (tptp.aTP_Lamm_fy A)))) (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.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_xf N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))) (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.groups2906978787729119204at_rat (tptp.aTP_Lamm_xg N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))) (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.groups3539618377306564664at_int (tptp.aTP_Lamm_xh N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))) (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.groups7501900531339628137nteger (tptp.aTP_Lamm_xi N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))) (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.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_xj N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))) (forall ((E tptp.real) (C tptp.fun_nat_complex) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((M8 tptp.real)) (forall ((Z4 tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z4))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real M8) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql C) Z4)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real E) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.aa_nat_nat tptp.suc N2))))))))))) (forall ((E tptp.real) (C tptp.fun_nat_real) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E)) (exists ((M8 tptp.real)) (forall ((Z4 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.real_V7735802525324610683m_real Z4))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real M8) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj C) Z4)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real E) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.aa_nat_nat tptp.suc N2))))))))))) (forall ((N2 tptp.nat) (A tptp.fun_nat_complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_ql A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 X)) _let_1)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex _let_2 Y)) _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_fun5031706661949900810omplex (tptp.aTP_Lamm_xl N2) A) X) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))) (forall ((N2 tptp.nat) (A tptp.fun_nat_rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_vf A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 X) _let_1)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat _let_2 Y) _let_1)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat X) Y)) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_fun8528462509625601970at_rat (tptp.aTP_Lamm_xn N2) A) X) Y) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))) (forall ((N2 tptp.nat) (A tptp.fun_nat_int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_vg A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 X) _let_1)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int _let_2 Y) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int X) Y)) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aa_fun7421131748584218370at_int (tptp.aTP_Lamm_xp N2) A) X) Y) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))) (forall ((N2 tptp.nat) (A tptp.fun_nat_real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))) (let ((_let_2 (tptp.aTP_Lamm_qj A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat tptp.one_one_nat) N2)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 X)) _let_1)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real _let_2 Y)) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_fun2548873334967081986t_real (tptp.aTP_Lamm_xr N2) A) X) Y)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)))))))) (forall ((X6 tptp.fun_nat_real)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 N)) (tptp.aa_nat_real X6 (tptp.aa_nat_nat tptp.suc N))))) (tptp.topolo6980174941875973593q_real X6))) (forall ((X6 tptp.fun_nat_set_int)) (=> (forall ((N tptp.nat)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X6 N) (tptp.aa_nat_set_int X6 (tptp.aa_nat_nat tptp.suc N)))) (tptp.topolo3100542954746470799et_int X6))) (forall ((X6 tptp.fun_nat_rat)) (=> (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 X6 N)) (tptp.aa_nat_rat X6 (tptp.aa_nat_nat tptp.suc N))))) (tptp.topolo4267028734544971653eq_rat X6))) (forall ((X6 tptp.fun_nat_num)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X6 N)) (tptp.aa_nat_num X6 (tptp.aa_nat_nat tptp.suc N))))) (tptp.topolo1459490580787246023eq_num X6))) (forall ((X6 tptp.fun_nat_nat)) (=> (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 X6 N)) (tptp.aa_nat_nat X6 (tptp.aa_nat_nat tptp.suc N))))) (tptp.topolo4902158794631467389eq_nat X6))) (forall ((X6 tptp.fun_nat_int)) (=> (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 X6 N)) (tptp.aa_nat_int X6 (tptp.aa_nat_nat tptp.suc N))))) (tptp.topolo4899668324122417113eq_int X6))) (forall ((X6 tptp.fun_nat_real)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_real X6 N)))) (tptp.topolo6980174941875973593q_real X6))) (forall ((X6 tptp.fun_nat_set_int)) (=> (forall ((N tptp.nat)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X6 (tptp.aa_nat_nat tptp.suc N)) (tptp.aa_nat_set_int X6 N))) (tptp.topolo3100542954746470799et_int X6))) (forall ((X6 tptp.fun_nat_rat)) (=> (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 X6 (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_rat X6 N)))) (tptp.topolo4267028734544971653eq_rat X6))) (forall ((X6 tptp.fun_nat_num)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X6 (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_num X6 N)))) (tptp.topolo1459490580787246023eq_num X6))) (forall ((X6 tptp.fun_nat_nat)) (=> (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 X6 (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_nat X6 N)))) (tptp.topolo4902158794631467389eq_nat X6))) (forall ((X6 tptp.fun_nat_int)) (=> (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 X6 (tptp.aa_nat_nat tptp.suc N))) (tptp.aa_nat_int X6 N)))) (tptp.topolo4899668324122417113eq_int X6))) (forall ((X6 tptp.fun_nat_real)) (= (tptp.topolo6980174941875973593q_real X6) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 N5)) (tptp.aa_nat_real X6 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_real X6 N5))))))) (forall ((X6 tptp.fun_nat_set_int)) (= (tptp.topolo3100542954746470799et_int X6) (or (forall ((N5 tptp.nat)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X6 N5) (tptp.aa_nat_set_int X6 (tptp.aa_nat_nat tptp.suc N5)))) (forall ((N5 tptp.nat)) (tptp.ord_less_eq_set_int (tptp.aa_nat_set_int X6 (tptp.aa_nat_nat tptp.suc N5)) (tptp.aa_nat_set_int X6 N5)))))) (forall ((X6 tptp.fun_nat_rat)) (= (tptp.topolo4267028734544971653eq_rat X6) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X6 N5)) (tptp.aa_nat_rat X6 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat X6 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_rat X6 N5))))))) (forall ((X6 tptp.fun_nat_num)) (= (tptp.topolo1459490580787246023eq_num X6) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X6 N5)) (tptp.aa_nat_num X6 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num (tptp.aa_nat_num X6 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_num X6 N5))))))) (forall ((X6 tptp.fun_nat_nat)) (= (tptp.topolo4902158794631467389eq_nat X6) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X6 N5)) (tptp.aa_nat_nat X6 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat X6 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_nat X6 N5))))))) (forall ((X6 tptp.fun_nat_int)) (= (tptp.topolo4899668324122417113eq_int X6) (or (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X6 N5)) (tptp.aa_nat_int X6 (tptp.aa_nat_nat tptp.suc N5))))) (forall ((N5 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int X6 (tptp.aa_nat_nat tptp.suc N5))) (tptp.aa_nat_int X6 N5))))))) (forall ((A tptp.complex) (M tptp.nat)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_xs A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M)) tptp.one_one_complex)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.one_one_nat))))) (forall ((A tptp.rat) (M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_xt A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M)) tptp.one_one_rat)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_rat (tptp.gbinomial_rat A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.one_one_nat))))) (forall ((A tptp.real) (M tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_xu A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) tptp.one_one_real)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) tptp.one_one_nat))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.numera6690914467698888265omplex _let_1))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_2) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex M))) tptp.one_one_complex))) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) M)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (= (tptp.groups2906978787729119204at_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat _let_2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat M))) tptp.one_one_rat)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_rat (tptp.power_power_rat _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) M)))))) (forall ((M tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) tptp.one_one_real))) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) M)))))) (forall ((Z tptp.complex) (N2 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) N2))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_2) Z)) _let_4) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex Z) N2))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Z) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N2)))))))) (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) N2))) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.times_times_rat _let_2) Z)) _let_4) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_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) N2))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N2)))))))) (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (let ((_let_3 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat _let_3) N2))) (= (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) N2))) (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))) N2)))))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2) (tptp.aa_complex_complex (tptp.aa_nat3829984526574172007omplex (tptp.semiri2816024913162550771omplex tptp.aTP_Lamm_xv) N2) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2) (tptp.aa_rat_rat (tptp.semiri7787848453975740701ux_rat tptp.aTP_Lamm_xw N2) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2) (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.semiri8420488043553186161ux_int tptp.aTP_Lamm_xx) N2) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.semiri7260567687927622513x_real tptp.aTP_Lamm_xy) N2) tptp.zero_zero_real))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.semiri8422978514062236437ux_nat tptp.aTP_Lamm_xz) N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2) (tptp.semiri4055485073559036834nteger tptp.aTP_Lamm_ya N2 tptp.zero_z3403309356797280102nteger))) (forall ((R2 tptp.complex) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_xs R2)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat M)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex R2) _let_1))))) (forall ((R2 tptp.rat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_xt R2) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat M)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_rat (tptp.gbinomial_rat R2) _let_1))))) (forall ((R2 tptp.real) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc M))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_xu R2)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real R2) _let_1))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2) N2)) (forall ((K tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex tptp.zero_zero_complex) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_complex)) (forall ((K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real tptp.zero_zero_real) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_real)) (forall ((K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat tptp.zero_zero_rat) (tptp.aa_nat_nat tptp.suc K)) tptp.zero_zero_rat)) (forall ((K tptp.nat)) (= (tptp.aa_nat_nat (tptp.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.aa_int_fun_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.aa_com8181001469867462503omplex 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.aa_int_fun_nat_int tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A tptp.complex)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((X tptp.real) (N2 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) N2)))))) (forall ((X tptp.rat) (N2 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) N2)))))) (forall ((X tptp.nat) (N2 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) N2)))))) (forall ((X tptp.int) (N2 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.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int X) N2)))))) (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex A))) (=> (not (= (tptp.aa_nat_complex _let_1 M) tptp.zero_zero_complex)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (not (= (tptp.aa_nat_complex _let_1 N2) tptp.zero_zero_complex)))))) (forall ((A tptp.real) (M tptp.nat) (N2 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 N2) M)) (not (= (tptp.aa_nat_real _let_1 N2) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2) M)) (not (= (tptp.aa_nat_rat _let_1 N2) tptp.zero_zero_rat)))))) (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex A))) (=> (= (tptp.aa_nat_complex _let_1 N2) tptp.zero_zero_complex) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_complex _let_1 M) tptp.zero_zero_complex))))) (forall ((A tptp.real) (N2 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 N2) tptp.zero_zero_real) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_real _let_1 M) tptp.zero_zero_real))))) (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat A))) (=> (= (tptp.aa_nat_rat _let_1 N2) tptp.zero_zero_rat) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) M)) (= (tptp.aa_nat_rat _let_1 M) tptp.zero_zero_rat))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N2) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex tptp.one_one_complex) N2))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat tptp.one_one_rat) N2))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int tptp.one_one_int) N2))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real tptp.one_one_real) N2))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat tptp.one_one_nat) N2))) (forall ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) K))) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) K))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)))) (forall ((A tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real tptp.uminus_uminus_real A)) K))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)))) (forall ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)))) (forall ((A tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) tptp.one_one_complex)) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.plus_plus_rat A) tptp.one_one_rat)) _let_1) (tptp.aa_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) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (= (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 N2) K)))))) (forall ((X tptp.real) (N2 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) N2))))) (forall ((X tptp.rat) (N2 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) N2))))) (forall ((X 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) 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) N2))))) (forall ((X tptp.int) (N2 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.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int X) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 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) (K tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) tptp.one_one_complex)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) _let_2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex _let_1 _let_2)) (tptp.aa_nat_complex _let_1 K)))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real _let_1 _let_2)) (tptp.aa_nat_real _let_1 K)))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) _let_2) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat _let_1 _let_2)) (tptp.aa_nat_rat _let_1 K)))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) _let_1)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat _let_1) A)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) _let_1)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)))))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex _let_1 (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex _let_1 tptp.one_one_complex)) K))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.minus_minus_rat A))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat _let_1 (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)) (tptp.aa_rat_rat (tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat _let_1 tptp.one_one_rat)) K))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real _let_1 tptp.one_one_real)) K))))) (forall ((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.times_times_rat A) _let_3) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) _let_3)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat _let_2 _let_1)))))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.gbinomial_real A))) (let ((_let_3 (tptp.aa_nat_real _let_2 K))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) _let_3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_nat_real _let_2 _let_1)))))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.gbinomial_rat A))) (let ((_let_3 (tptp.aa_nat_rat _let_2 K))) (= (tptp.aa_rat_rat (tptp.times_times_rat _let_3) A) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) _let_3)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1)) (tptp.aa_nat_rat _let_2 _let_1)))))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.gbinomial_real A))) (let ((_let_3 (tptp.aa_nat_real _let_2 K))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_3) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_nat_real _let_2 _let_1)))))))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) tptp.one_one_complex)) N2)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) (tptp.aa_nat_nat tptp.suc N2)) (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)) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.times_times_rat A) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) tptp.one_one_rat)) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) (tptp.aa_nat_nat tptp.suc N2)) (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)) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A) (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) (tptp.aa_nat_int (tptp.aa_int_fun_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)) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat A))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_rat_rat (tptp.plus_plus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)))))) (forall ((A tptp.real) (N2 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 N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)))))) (forall ((A tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat N2)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.comm_s8582702949713902594nteger A))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.plus_p5714425477246183910nteger A (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2)))))) (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.comm_s4028243227959126397er_rat Z))) (= (tptp.aa_nat_rat _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Z) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) (tptp.aa_nat_rat _let_1 N2))))) (forall ((Z tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int Z))) (= (tptp.aa_nat_int _let_1 (tptp.aa_nat_nat tptp.suc N2)) (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 N2))) (tptp.aa_nat_int _let_1 N2))))) (forall ((Z tptp.real) (N2 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 N2)) (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 N2))) (tptp.aa_nat_real _let_1 N2))))) (forall ((Z tptp.nat) (N2 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 N2)) (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 N2))) (tptp.aa_nat_nat _let_1 N2))))) (forall ((Z tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (tptp.comm_s8582702949713902594nteger Z))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger Z (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) (tptp.aa_nat_Code_integer _let_1 N2))))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) 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 N2))) K) tptp.zero_zero_real))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((N2 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 N2))) K) tptp.zero_zero_real) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex A) N2) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) N2)) (= A (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K3))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N2) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) N2)) (= A (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K3))))))) (forall ((A tptp.real) (N2 tptp.nat)) (= (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K3) N2)) (= A (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K3))))))) (forall ((Z tptp.rat) (N2 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 N2) M)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Z) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) M))))) (forall ((Z tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int 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 N2) M)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_1 N2)) (tptp.aa_nat_int (tptp.aa_int_fun_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 N2))) M))))) (forall ((Z tptp.real) (N2 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 N2) M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 N2)) (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 N2))) M))))) (forall ((Z tptp.nat) (N2 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 N2) M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat _let_1 N2)) (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 N2))) M))))) (forall ((Z tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.comm_s8582702949713902594nteger Z))) (= (tptp.aa_nat_Code_integer _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) M)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 N2)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger Z (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) M))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (not (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (not (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (not (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (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 N2))) K) tptp.zero_zero_real)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) N2)) (not (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger)))) (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) tptp.one_one_complex))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex _let_1) _let_2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_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.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.times_times_rat _let_1) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real _let_1) _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real _let_1) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)))))) (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) _let_1)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) tptp.one_one_complex)) K))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_rat_rat (tptp.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.times_times_rat A) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)) K))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)) K))))) (forall ((K tptp.nat) (M tptp.nat) (A tptp.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.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.times_times_rat (tptp.aa_nat_rat _let_1 K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K))))))) (forall ((K tptp.nat) (M tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.gbinomial_real A))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) M)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) K))))))) (forall ((M tptp.nat) (N2 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) N2)) (= (tptp.aa_nat_rat _let_1 N2) (tptp.aa_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.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 N2) M))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_int _let_1 N2) (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.aa_int_fun_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 N2) M))))))) (forall ((M tptp.nat) (N2 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) N2)) (= (tptp.aa_nat_real _let_1 N2) (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 N2) M))))))) (forall ((M tptp.nat) (N2 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) N2)) (= (tptp.aa_nat_nat _let_1 N2) (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 N2) M))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.code_integer)) (let ((_let_1 (tptp.comm_s8582702949713902594nteger Z))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.aa_nat_Code_integer _let_1 N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer _let_1 M)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger Z (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger M))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_yb A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) N2))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_yc A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) N2))) (forall ((A tptp.real) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_yd A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) tptp.one_one_real)) N2))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) tptp.one_one_complex))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex _let_2) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex _let_2) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1))))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_rat_rat (tptp.plus_plus_rat A) tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat _let_2) _let_1) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)) (tptp.aa_rat_rat (tptp.divide_divide_rat _let_2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1))))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real _let_2) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))))))) (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) tptp.one_one_complex))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex _let_2) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex _let_2) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex _let_1))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K)))))) (forall ((A tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_rat_rat (tptp.plus_plus_rat A) tptp.one_one_rat))) (= (tptp.aa_nat_rat (tptp.gbinomial_rat _let_2) _let_1) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat _let_2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat _let_1))) (tptp.aa_nat_rat (tptp.gbinomial_rat A) K)))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) tptp.one_one_real))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real _let_2) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K)))))) (forall ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K)) A)) tptp.one_one_complex)) K)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K)) A)) tptp.one_one_rat)) K)))) (forall ((A tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K)) A)) tptp.one_one_real)) K)))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 K)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) K)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_1 N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_1 K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) K)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_1 N2)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N2))))) (forall ((K tptp.nat) (N2 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 N2))) tptp.one_one_real)) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_1 N2)) (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)) N2))))) (forall ((R2 tptp.complex) (K tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex R2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex R2) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex _let_1) K)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex R2) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))) (forall ((R2 tptp.rat) (K tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat tptp.uminus_uminus_rat R2))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat R2) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat _let_1) K)) (tptp.aa_rat_rat (tptp.times_times_rat R2) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))) (forall ((R2 tptp.int) (K tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int R2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int R2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int _let_1) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R2) (tptp.aa_nat_int (tptp.aa_int_fun_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 ((R2 tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real R2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real _let_1) K)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))) (forall ((R2 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger R2))) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.minus_8373710615458151222nteger R2 (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger K))) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger _let_1) K)) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger R2) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer)) K))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2))) N2) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2))) N2) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))) N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) N2)) (tptp.aa_nat_int tptp.semiri1406184849735516958ct_int N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger N2))) N2) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (tptp.aa_nat_Code_integer tptp.semiri3624122377584611663nteger N2)))) (forall ((N2 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 N2))) N2) (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)) N2)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2)))) (forall ((A tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex A)) K) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex A) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))) (forall ((A tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat A)) K) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))) (forall ((A tptp.real) (K tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real tptp.uminus_uminus_real A)) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) K)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) K)))) (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex 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.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat))) (tptp.aa_nat_complex _let_1 K)))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat))) (tptp.aa_nat_real _let_1 K)))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.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 ((B tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex B) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) K)))) (forall ((B tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) K)))) (forall ((B tptp.int) (K tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) K)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int tptp.uminus_uminus_int 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.code_integer) (K tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger B (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger K)) tptp.one_one_Code_integer)) K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) K)))) (forall ((B tptp.complex) (K tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex B)) K) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) K)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex B) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) K)))) (forall ((B tptp.rat) (K tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat B)) K) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) K)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_rat_rat (tptp.minus_minus_rat B) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) K)))) (forall ((B tptp.int) (K tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) K)) (tptp.aa_nat_int (tptp.aa_int_fun_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.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.code_integer) (K tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger B)) K) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) K)) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger (tptp.minus_8373710615458151222nteger B (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger K)) tptp.one_one_Code_integer)) K)))) (forall ((A tptp.complex) (M tptp.nat)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_ye A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) M)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) tptp.one_one_complex)) M)))) (forall ((A tptp.rat) (M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_yf A) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) M)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)) M)))) (forall ((A tptp.real) (M tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_yg A)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)) M)))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.plus_plus_rat A) B)) N2) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_yh A) B) N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int A) B)) N2) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_yi A) B) N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger (tptp.plus_p5714425477246183910nteger A B)) N2) (tptp.groups7501900531339628137nteger (tptp.aa_nat2010205248571845816nteger (tptp.aa_Cod3140087502949435154nteger (tptp.aTP_Lamm_yj A) B) N2) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) N2) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_yk A) B) N2)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)))) (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_yl M) A) X) Y)) _let_1) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_ym M) A) X) Y)) _let_1)))) (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_yn M) A) X) Y) _let_1) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_yo M) A) X) Y) _let_1)))) (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_yp M) A) X) Y)) _let_1) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_yq M) A) X) Y)) _let_1)))) (forall ((K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_yr K)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((K tptp.nat) (N2 tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_ys K) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((K tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_yt K)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat)))) (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.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex K))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex A) tptp.one_one_complex)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((K tptp.nat) (A tptp.rat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_rat (tptp.gbinomial_rat A) K) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat K))) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat A) tptp.one_one_rat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((K tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) K)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) tptp.one_one_real)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.aa_nat3829984526574172007omplex (tptp.set_fo1517530859248394432omplex (tptp.aTP_Lamm_yu A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_complex))))))) (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_yv A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_rat))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.set_fo2581907887559384638at_int (tptp.aTP_Lamm_yw A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_int))))))) (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.set_fo3111899725591712190t_real (tptp.aTP_Lamm_yx A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_real))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_Code_integer)) (=> (not _let_2) (= _let_1 (tptp.set_fo1084959871951514735nteger (tptp.aTP_Lamm_yy A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat) tptp.one_one_Code_integer))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.comm_s4663373288045622133er_nat A) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.set_fo2584398358068434914at_nat (tptp.aTP_Lamm_yz A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) tptp.one_one_nat))))))) (forall ((M tptp.nat)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_za M)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (forall ((M tptp.nat)) (= (tptp.groups2906978787729119204at_rat (tptp.aTP_Lamm_zb M) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (forall ((M tptp.nat)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_zc M)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) M))) (forall ((M tptp.nat) (A tptp.complex) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_yl M) A) X) Y)) _let_1) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_zd M) A) X) Y)) _let_1)))) (forall ((M tptp.nat) (A tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (= (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_yn M) A) X) Y) _let_1) (tptp.groups2906978787729119204at_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_ze M) A) X) Y) _let_1)))) (forall ((M tptp.nat) (A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat M))) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_yp M) A) X) Y)) _let_1) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_zf M) A) X) Y)) _let_1)))) (forall ((N2 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)) N2))) (= (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex _let_3) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex _let_2) _let_3)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N2))) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex N2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2))) (= (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat _let_3) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat _let_2) _let_3)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) _let_2)) N2))) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat N2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2))) (= (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)) N2))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))))))) (forall ((K tptp.nat) (A tptp.complex)) (let ((_let_1 (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex A) K))) (let ((_let_2 (= K tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_nat3829984526574172007omplex (tptp.set_fo1517530859248394432omplex (tptp.aTP_Lamm_zg A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)) tptp.one_one_complex)) (tptp.aa_nat_complex tptp.semiri5044797733671781792omplex K)))))))) (forall ((K tptp.nat) (A tptp.rat)) (let ((_let_1 (tptp.aa_nat_rat (tptp.gbinomial_rat A) K))) (let ((_let_2 (= K tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.set_fo1949268297981939178at_rat (tptp.aTP_Lamm_zh A) tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)) tptp.one_one_rat)) (tptp.aa_nat_rat tptp.semiri773545260158071498ct_rat K)))))))) (forall ((K tptp.nat) (A tptp.real)) (let ((_let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real A) K))) (let ((_let_2 (= K tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.set_fo3111899725591712190t_real (tptp.aTP_Lamm_zi A) tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) tptp.one_one_nat)) tptp.one_one_real)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real K)))))))) (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex Z) _let_2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.comm_s2602460028002588243omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Z) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex tptp.one_one_complex) (tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (tptp.aa_set_nat_complex (tptp.groups6464643781859351333omplex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_zj Z)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))) (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Z) _let_2)) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Z) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat _let_1)))) _let_2)) (tptp.groups73079841787564623at_rat (tptp.aTP_Lamm_zk Z) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))) (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Z) _let_2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) _let_2)) (tptp.aa_set_nat_real (tptp.groups129246275422532515t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_zl Z)) (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_zn X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_real_real tptp.sin_real Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_zp X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.sin_complex X)) (tptp.aa_complex_complex tptp.sin_complex Y))))) (forall ((X tptp.real) (N2 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real tptp.sin_real X)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sx X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (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 N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real X)) N2))))) (forall ((X tptp.real) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_zr X) Y)) (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_zt X) Y)) (tptp.aa_complex_complex tptp.cos_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y))))) (forall ((X tptp.vEBT_VEBT) (Y tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (let ((_let_2 (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (let ((_let_3 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X)) _let_3) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool _let_2 X)) (=> (=> (= X _let_1) (=> _let_3 (not (tptp.pp (tptp.aa_VEBT_VEBT_bool _let_2 _let_1))))) (=> (forall ((Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf tptp.fTrue Uv2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))) (=> (forall ((Uu2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 tptp.fTrue))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2))) (=> (= X _let_1) (=> (tptp.pp Y) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2))) (=> (= X _let_1) (=> (not (tptp.pp Y)) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))) (forall ((X tptp.real) (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.aa_com3342990543769683525omplex tptp.times_times_complex X))) (let ((_let_2 (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex A))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex _let_2 Y)) (tptp.aa_complex_complex _let_2 (tptp.aa_complex_complex _let_1 Y)))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 X)) Y) (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y))))) (forall ((A tptp.real) (X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex A))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex _let_1 X)) Y) (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y))))) (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.aa_complex_complex tptp.invers8013647133539491842omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.invers8013647133539491842omplex A)) (tptp.aa_complex_complex tptp.invers8013647133539491842omplex B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat (tptp.times_times_rat A) B)) (tptp.aa_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.aa_complex_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.aa_complex_complex 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 ((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.aa_complex_complex tptp.invers8013647133539491842omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (tptp.aa_rat_rat tptp.inverse_inverse_rat (tptp.aa_rat_rat (tptp.divide_divide_rat A) B)) (tptp.aa_rat_rat (tptp.divide_divide_rat B) A))) (forall ((A tptp.real) (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.aa_complex_complex (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex A) (tptp.aa_complex_complex (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex B) X)) (tptp.aa_complex_complex (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) B)) X))) (forall ((A2 tptp.set_nat)) (= (tptp.groups705719431365010083at_int tptp.aTP_Lamm_zu A2) tptp.one_one_int)) (forall ((A2 tptp.set_int)) (= (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_zv A2) tptp.one_one_int)) (forall ((N2 tptp.int)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.pi) (tptp.aa_int_real tptp.ring_1_of_int_real N2))) tptp.zero_zero_real)) (forall ((X tptp.real) (I2 tptp.int)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I2)) tptp.pi))) (tptp.aa_real_real tptp.tan_real X))) (forall ((N2 tptp.int)) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) (tptp.aa_int_real tptp.ring_1_of_int_real N2))) tptp.zero_zero_real)) (forall ((N2 tptp.int)) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) (tptp.aa_int_real tptp.ring_1_of_int_real N2))) tptp.one_one_real)) (forall ((N2 tptp.int)) (let ((_let_1 (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real tptp.pi) (tptp.aa_int_real tptp.ring_1_of_int_real N2))))) (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))) N2)))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real))))))) (forall ((A tptp.real) (X tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real A) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) X))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real tptp.inverse_inverse_real X)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) (tptp.aa_real_real tptp.inverse_inverse_real Y)))) (forall ((R2 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (= (tptp.aa_complex_complex (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex R2) (tptp.aa_real_complex (tptp.complex2 A) B)) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B))))) (forall ((N2 tptp.int) (X tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int N2) X))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real N2)) (tptp.aa_int_real tptp.ring_1_of_int_real X))))) (forall ((P tptp.fun_real_bool) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real D3) E2)) (=> (tptp.pp (tptp.aa_real_bool P D3)) (tptp.pp (tptp.aa_real_bool P E2))))) (=> (forall ((N 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 N)))))) (=> (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 ((N2 tptp.int) (M tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int N2) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_int_real tptp.ring_1_of_int_real N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real M)) tptp.one_one_real))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.sqrt X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_1) X) (tptp.aa_real_real tptp.inverse_inverse_real _let_1))))) (forall ((N2 tptp.int) (M tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int N2) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (tptp.aa_int_real tptp.ring_1_of_int_real M))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I5)) tptp.pi))))) (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real D))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real X)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int X) D))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int X) D))) _let_1))))) (forall ((N2 tptp.int) (X tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real N2)) (tptp.aa_int_real tptp.ring_1_of_int_real X))) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int N2) X)))))) (forall ((N2 tptp.int) (X tptp.int)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real N2)) (tptp.aa_int_real tptp.ring_1_of_int_real X))) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int N2) X)))) tptp.one_one_real))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) 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 N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_ai) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc N2) M)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) (tptp.aa_real_real tptp.inverse_inverse_real _let_1)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) 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 N2)) (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.aTP_Lamm_ai) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) tptp.one_one_nat) M))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.inverse_inverse_real X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X))) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_real_real tptp.inverse_inverse_real X)))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.one_one_real) (exists ((X4 tptp.int)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real X4)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.pi))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.tan_real X)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_1) (tptp.aa_real_real tptp.inverse_inverse_real _let_1))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.exp_real X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real X)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_1) (tptp.aa_real_real tptp.inverse_inverse_real _let_1))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.vEBT_VEBT)) (=> (not (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X))) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X)) (=> (forall ((Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf tptp.fTrue Uv2))) (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 tptp.fTrue))) (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node (tptp.some_P7363390416028606310at_nat Uz2) Va3 Vb2 Vc2))) (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))) (forall ((Theta tptp.real)) (not (forall ((K2 tptp.int)) (not (= (tptp.aa_real_real tptp.arccos (tptp.aa_real_real tptp.cos_real Theta)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Theta) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real K2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))))))))) (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Leaf tptp.fFalse tptp.fFalse))) (let ((_let_2 (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool tptp.vEBT_VEBT_minNull X)) (=> (tptp.pp (tptp.aa_VEBT_VEBT_bool _let_2 X)) (=> (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool _let_2 _let_1)))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node tptp.none_P5556105721700978146at_nat Uw2 Ux2 Uy2))) (=> (= X _let_1) (not (tptp.pp (tptp.aa_VEBT_VEBT_bool (tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.cos_real X) tptp.zero_zero_real) (exists ((I5 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)) I5))) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 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)) I5)) (= X (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real I5)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))))))))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.sinh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sinh_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sinh_real X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) (tptp.aa_complex_complex tptp.invers8013647133539491842omplex Y)))) (forall ((I2 tptp.nat) (J tptp.nat)) (= (tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat I2 J)) (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_aj (tptp.set_or1266510415728281911st_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) J))) (= (tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int (tptp.set_or1269000886237332187st_nat I2 _let_1)) (tptp.groups1705073143266064639nt_int tptp.aTP_Lamm_aj (tptp.set_or1266510415728281911st_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int I2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int _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.aa_complex_complex tptp.invers8013647133539491842omplex (tptp.aa_real_complex (tptp.complex2 A) B)) (tptp.aa_real_complex (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 ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.sinh_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) (tptp.aa_real_real tptp.inverse_inverse_real X))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int L) _let_1))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.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 ((M tptp.num)) (= (tptp.unique5052692396658037445od_int (tptp.aa_num_num tptp.bitM M) (tptp.aa_num_num tptp.bit0 tptp.one)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cot_real X)) tptp.zero_zero_real))))) (forall ((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 ((K tptp.num)) (= (tptp.aa_num_nat tptp.pred_numeral (tptp.aa_num_num tptp.bit0 K)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bitM K)))) (forall ((N2 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 N2))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((N2 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 N2))))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))) (forall ((N2 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 N2)) tptp.pi)) tptp.zero_zero_real)) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.cot_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))) (tptp.aa_real_real tptp.cot_real X))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sinh_real X)) (tptp.aa_real_real tptp.cosh_real X)))) (= (tptp.aa_num_num tptp.bitM tptp.one) tptp.one) (forall ((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 ((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.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real tptp.cosh_real X)))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool _let_1 tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (tptp.pp (tptp.aa_real_bool _let_1 X))))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real tptp.cosh_real X)))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num tptp.bitM (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bitM N2)))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num tptp.bitM (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 N2)))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y)))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y))))))) (forall ((X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y) tptp.zero_zero_real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.cosh_real X)) (tptp.aa_real_real tptp.cosh_real Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y) X)))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.arcosh_real (tptp.aa_real_real tptp.cosh_real X)) X))) (forall ((N2 tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_nat_nat tptp.suc (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bitM N2))))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num tptp.one) (tptp.aa_num_num tptp.bitM N2)) (tptp.aa_num_num tptp.bit0 N2))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.bitM N2)) tptp.one) (tptp.aa_num_num tptp.bit0 N2))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (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 ((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 ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real tptp.cosh_real (tptp.aa_real_real tptp.ln_ln_real X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) (tptp.aa_real_real tptp.inverse_inverse_real X))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.cot_real X))))))) (forall ((X tptp.real)) (= (tptp.aa_real_real tptp.tan_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) X)) (tptp.aa_real_real tptp.cot_real X))) (forall ((N2 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 N2)))) tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) (tptp.aa_num_num tptp.bitM N2)))))) (forall ((N2 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 N2)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) (tptp.aa_num_num tptp.bitM N2)))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.imaginary_unit) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 tptp.one)))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log _let_1) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real (tptp.aa_real_real tptp.exp_real tptp.one_one_real))) (tptp.aa_real_real tptp.ln_ln_real _let_1))) (tptp.aa_real_real tptp.ln_ln_real X)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit))) (= (tptp.aa_complex_complex _let_1 (tptp.aa_complex_complex _let_1 X)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)))) (forall ((X tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))) (= (tptp.aa_complex_complex _let_49 tptp.imaginary_unit) _let_50) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y))))))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X)) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) A)))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X)))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)))))) (forall ((A tptp.real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)))))) (forall ((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 ((Z tptp.complex) (N2 tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex N2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex Z) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_1) tptp.imaginary_unit)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) Z))) _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 ((A tptp.real) (B tptp.nat)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (not (= A tptp.one_one_real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) B)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B))))) (forall ((N2 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 N2)))) (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bit0 N2)))))) (forall ((M tptp.num) (N2 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 N2)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bit0 N2)))))) (forall ((N2 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 N2)))) (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bitM N2)))))) (forall ((M tptp.num) (N2 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 N2)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) (tptp.aa_num_num tptp.bitM N2)))))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.imaginary_unit) _let_2) _let_50) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one) (forall ((W tptp.num)) (not (= tptp.imaginary_unit (tptp.numera6690914467698888265omplex W)))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit0 N2)) tptp.one) (tptp.aa_num_num tptp.bit0 tptp.one))) (forall ((N2 tptp.num) (M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M)))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit1 N2)) tptp.one) tptp.one)) (forall ((M tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M))) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit))) (= (= (tptp.aa_complex_complex _let_1 W) Z) (= W (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex _let_1 Z)))))) (forall ((N2 tptp.num) (M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M)))) (forall ((N2 tptp.num) (M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_num tptp.bit1 M)) (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M)))) (forall ((W tptp.num)) (not (= tptp.imaginary_unit (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W))))) (forall ((M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg tptp.one) (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bit1 M))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex (tptp.complex2 A) B)) tptp.imaginary_unit) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real tptp.uminus_uminus_real B)) A))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex (tptp.complex2 A) B)) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real tptp.uminus_uminus_real B)) A))) (forall ((M tptp.nat) (B tptp.real) (N2 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) N2)) (=> (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 N2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) _let_1)))))) (forall ((B tptp.real) (N2 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) N2)) 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 N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) M)))))) (forall ((N2 tptp.num) (M tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_num tptp.bit0 M)) (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y)))))))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log A))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (=> (tptp.pp (tptp.aa_real_bool _let_2 Y)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y)))))))))) (forall ((B tptp.real) (N2 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) N2)) 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 N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) M)))))) (forall ((A tptp.real) (N2 tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real A) N2)) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))))) (forall ((X tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real _let_1 (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_real_real _let_1 X)))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg X) Xa2) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M2 tptp.num)) (=> (= Xa2 (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))) (=> (= Xa2 _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N tptp.num)) (= X (tptp.aa_num_num tptp.bit0 N))) (=> _let_1 (not (= Y (tptp.aa_num_num tptp.bit0 tptp.one))))) (=> (forall ((N tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N)) (forall ((M2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 M2)) (not (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M2)))))))) (=> (forall ((N tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N)) (forall ((M2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 M2)) (not (= Y (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M2)))))))) (=> (=> (exists ((N tptp.num)) (= X (tptp.aa_num_num tptp.bit1 N))) _let_2) (=> (forall ((N tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N)) (forall ((M2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit0 M2)) (not (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M2)))))))) (not (forall ((N tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N)) (forall ((M2 tptp.num)) (=> (= Xa2 (tptp.aa_num_num tptp.bit1 M2)) (not (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M2)))))))))))))))))))))) (forall ((M tptp.nat) (N2 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)) N2)) (= (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M)))))) (forall ((M tptp.nat) (B tptp.real) (N2 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) N2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)))))))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (not (= A tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_1 B)) (=> (not (= B tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log A) X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.ln_ln_real B)) (tptp.aa_real_real tptp.ln_ln_real A))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) X)))))))))) (forall ((M tptp.nat) (B tptp.real) (N2 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) N2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)))))))) (forall ((N2 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)) N2)) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))))))) (forall ((N2 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)) N2)) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))))))) (forall ((N2 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)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (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))) N2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) (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))) N2))))) (forall ((M tptp.nat) (N2 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) N2) (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 N2))))) (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 N2) _let_1)))))))) (forall ((M tptp.nat) (N2 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)) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))))))) (forall ((M tptp.nat) (N2 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) N2))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (let ((_let_4 (= M tptp.zero_zero_nat))) (and (=> _let_4 (= _let_2 N2)) (=> (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 N2) _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 N2) _let_1)))))))))))))) (forall ((M tptp.nat) (N2 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)) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) M)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real M))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 tptp.one))))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.exp_real tptp.one_one_real))) (tptp.aa_real_real tptp.ln_ln_real X)))))) (= (tptp.aa_complex_real tptp.arg _let_52) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_23)) (forall ((B tptp.nat) (K tptp.nat) (N2 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.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) 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 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)))))))))) (= (tptp.aa_complex_real tptp.arg tptp.imaginary_unit) _let_25) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) N2)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_num_real tptp.numeral_numeral_real A)) (tptp.aa_num_real tptp.numeral_numeral_real B))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int A))) (tptp.aa_num_int tptp.numeral_numeral_int B))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_num_real tptp.numeral_numeral_real A)) (tptp.aa_num_real tptp.numeral_numeral_real B)))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int A)) (tptp.aa_num_int tptp.numeral_numeral_int B))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.arg Z))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi))))) (forall ((B tptp.nat) (N2 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 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)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B)) (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))))) (= (tptp.aa_real_complex tptp.cis _let_28) _let_52) (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (= (= (tptp.aa_real_int tptp.archim7802044766580827645g_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_real_real _let_1 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) tptp.one_one_nat))))))))))) (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg X) Xa2) Y) (=> (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num X Xa2))) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool _let_2 (tptp.product_Pair_num_num tptp.one tptp.one))))))) (=> (=> _let_1 (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bit1 M2)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (=> _let_1 (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= Xa2 _let_1) (=> (= Y _let_1) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num tptp.one _let_1))))))))) (=> (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 N))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (tptp.aa_num_num tptp.bit0 tptp.one)) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((N tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N)) (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 N) _let_1)))))))))) (=> (forall ((N tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit0 N)) (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit0 N) _let_1)))))))))) (=> (forall ((N tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 N))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num _let_1 tptp.one))))))))) (=> (forall ((N tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N)) (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 M2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 N) _let_1)))))))))) (not (forall ((N tptp.num)) (=> (= X (tptp.aa_num_num tptp.bit1 N)) (forall ((M2 tptp.num)) (let ((_let_1 (tptp.aa_num_num tptp.bit1 M2))) (=> (= Xa2 _let_1) (=> (= Y (tptp.aa_num_num tptp.bitM (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N) M2))) (not (tptp.pp (tptp.aa_Pro762926636801165566m_bool (tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (tptp.product_Pair_num_num (tptp.aa_num_num tptp.bit1 N) _let_1)))))))))))))))))))))))) (forall ((B tptp.nat) (K tptp.nat) (N2 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.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2)) (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) (X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real A) X)) tptp.zero_zero_real)) (= A tptp.zero_zero_real))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) tptp.one_one_real) X))) (forall ((X tptp.real)) (= (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) tptp.one_one_real) X) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)))) (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real M))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real _let_1) (tptp.aa_num_real tptp.numeral_numeral_real N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_1) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))))) (forall ((A tptp.num) (B tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_num_real tptp.numeral_numeral_real A)) (tptp.aa_num_real tptp.numeral_numeral_real B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_num_int tptp.numeral_numeral_int A)) (tptp.aa_num_int tptp.numeral_numeral_int B)))) (forall ((X tptp.real) (N2 tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_num_real tptp.numeral_numeral_real N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))))) (= (tptp.aa_real_complex tptp.cis _let_25) tptp.imaginary_unit) (forall ((B tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int B)))) (= (tptp.aa_real_complex tptp.cis _let_51) tptp.one_one_complex) (forall ((A tptp.num) (B tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_num_real tptp.numeral_numeral_real A)) (tptp.aa_num_real tptp.numeral_numeral_real B)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int A))) (tptp.aa_num_int tptp.numeral_numeral_int B)))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real _let_1))) (tptp.aa_real_real tptp.abs_abs_real X)))) (forall ((B tptp.num)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real B)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_num_int tptp.numeral_numeral_int B)))) (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) (Y tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A)))))))) (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real X))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 A)) (tptp.aa_real_real _let_1 B))))))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex tptp.cis A)) (tptp.aa_real_complex tptp.cis B)) (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_real_complex tptp.cis A)) (tptp.aa_real_complex tptp.cis B)) (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real A) B)))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) A)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))))) (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) tptp.zero_zero_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A))))))) (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 A)) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) tptp.one_one_real))))))) (forall ((A tptp.real) (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 ((X tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) A)) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A))))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real X) Y)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))))) (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_1 X)) (=> (tptp.pp (tptp.aa_real_bool _let_1 Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) Y)) A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))))) (forall ((Y tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real tptp.inverse_inverse_real Y)) A) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Y) A))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real B))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_real_real _let_1 C)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real A) (tptp.aa_real_real _let_1 (tptp.aa_real_real tptp.uminus_uminus_real C)))))) (forall ((X tptp.real) (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.log B))) (=> (not (= X tptp.zero_zero_real)) (= (tptp.aa_real_real _let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) (tptp.aa_real_real _let_1 X)))))) (forall ((X tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.powr_real B))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) B)) (= (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) X)) K) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real _let_1 (tptp.aa_int_real tptp.ring_1_of_int_real K))) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real _let_1 (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int))))))))))) (forall ((X tptp.real) (N2 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 N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)))) (forall ((R2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R2))) tptp.one_one_real)))) (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real N2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real X) N2))))) (forall ((R2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R2))) tptp.one_one_real)))) (forall ((R2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R2) tptp.one_one_real)) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R2))))) (forall ((R2 tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R2) tptp.one_one_real)) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_real_int tptp.archim6058952711729229775r_real R2))))) (forall ((A tptp.real) (N2 tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_real_complex tptp.cis A)) N2) (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) A)))) (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 Y) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log B) X))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real B) 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_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log 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 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.log 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.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.log B) X))))))) (forall ((N2 tptp.int) (X tptp.real)) (let ((_let_1 (tptp.aa_int_real tptp.ring_1_of_int_real N2))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real X) N2))))) (forall ((B tptp.int) (A tptp.real)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) B)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real A) (tptp.aa_int_real tptp.ring_1_of_int_real B))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_real_int tptp.archim6058952711729229775r_real A)) B)))) (forall ((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.log B))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B)) (=> (not (= B tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real 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.log B))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B)) (=> (not (= B tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_1 X)) 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.log B))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B)) (=> (not (= B tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real 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 ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (=> (tptp.pp (tptp.aa_real_bool _let_2 B)) (=> (not (= B tptp.one_one_real)) (=> (tptp.pp (tptp.aa_real_bool _let_2 X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_1 X)) 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 ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real tptp.sqrt X)))) (forall ((X tptp.real) (N2 tptp.num)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_num_real tptp.numeral_numeral_real N2))) (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 N2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_num_real tptp.numeral_numeral_real _let_1)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) N2)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real _let_3 (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat N2) _let_2))))) tptp.one_one_int))))))) (forall ((B tptp.nat) (N2 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 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)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) B)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_nat_real tptp.semiri5074537144036343181t_real B)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real K))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))))) (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.bij_betw_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_zw N2) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2) (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool tptp.aTP_Lamm_cf N2))))) (forall ((F tptp.fun_nat_real)) (= (tptp.summable_complex (tptp.aTP_Lamm_zx F)) (tptp.summable_real F))) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex _let_48 tptp.imaginary_unit)) _let_50) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex _let_49 _let_47)) _let_50) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex _let_46) _let_47)) tptp.imaginary_unit)) tptp.one_one_complex) (= (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex _let_49 (tptp.aa_complex_complex _let_48 _let_46))) tptp.one_one_complex) (forall ((Z tptp.complex)) (exists ((A3 tptp.complex) (R3 tptp.real)) (= Z (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R3)) (tptp.aa_complex_complex tptp.exp_complex A3))))) (forall ((R2 tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R2)) (tptp.aa_real_complex (tptp.complex2 X) Y)) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real _let_1 X)) (tptp.aa_real_real _let_1 Y))))) (forall ((X tptp.real) (Y tptp.real) (R2 tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex (tptp.complex2 X) Y)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R2)) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X) R2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Y) R2)))) (forall ((R2 tptp.real) (X tptp.real) (Y tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R2)) (tptp.aa_real_complex (tptp.complex2 X) Y)) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real R2) X)) Y))) (forall ((X tptp.real) (Y tptp.real) (R2 tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_real_complex (tptp.complex2 X) Y)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R2)) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) R2)) Y))) (forall ((B tptp.real)) (= (tptp.aa_real_complex tptp.cis B) (tptp.aa_complex_complex tptp.exp_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex B))))) (forall ((R2 tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R2)) (tptp.aa_real_complex (tptp.complex2 tptp.zero_zero_real) R2))) (forall ((R2 tptp.real)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R2)) tptp.imaginary_unit) (tptp.aa_real_complex (tptp.complex2 tptp.zero_zero_real) R2))) (forall ((A tptp.real) (B tptp.real)) (= (tptp.aa_real_complex (tptp.complex2 A) B) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex A)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex B))))) (forall ((Z tptp.complex)) (exists ((R3 tptp.real) (A3 tptp.real)) (= Z (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R3)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real A3))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real A3)))))))) (forall ((A tptp.real)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real A))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real A))))) tptp.one_one_real)) (forall ((R2 tptp.real) (A tptp.real)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex R2)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.cos_real A))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sin_real A)))))) (tptp.aa_real_real tptp.abs_abs_real R2))) (= (tptp.aa_complex_complex tptp.csqrt tptp.imaginary_unit) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex _let_45 tptp.imaginary_unit)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex _let_44))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than D) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_zy D))))) (forall ((D tptp.int)) (= (tptp.int_ge_less_than2 D) (tptp.collec213857154873943460nt_int (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_zz D))))) (forall ((A0 tptp.int) (A1 tptp.int) (P tptp.fun_int_fun_int_bool)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((I3 tptp.int) (J2 tptp.int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int I3) J2))) (=> (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I3) J2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I3) tptp.one_one_int)) J2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P I3) J2))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A0) A1))))) (forall ((Z tptp.complex)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.csqrt Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Z)) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (= (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sqrt X)) (tptp.aa_complex_complex tptp.csqrt (tptp.aa_real_complex tptp.real_V4546457046886955230omplex X))))) (forall ((C tptp.complex) (N2 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) N2)) (tptp.bij_be1856998921033663316omplex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex C)))) (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.arg C)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2))))) (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool tptp.aTP_Lamm_cf N2)) (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_aaa C) N2)))))) (forall ((Y tptp.real)) (= (tptp.aa_real_real tptp.arctan Y) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_aab Y)))) (forall ((Y tptp.real)) (= (tptp.aa_real_real tptp.arcsin Y) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_aac Y)))) (forall ((L tptp.int) (K tptp.int) (N2 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) N2)))) (let ((_let_2 (tptp.aa_int_int tptp.sgn_sgn_int L))) (let ((_let_3 (tptp.aa_int_fun_int_int tptp.times_times_int _let_2))) (let ((_let_4 (tptp.aa_int_int tptp.sgn_sgn_int K))) (let ((_let_5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_4) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int _let_5) (tptp.aa_int_int _let_3 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N2 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 N2) (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 N2) M)))))) _let_1)))))))))))))))) (forall ((N2 tptp.nat)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) 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 ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (= (tptp.aa_real_real _let_1 X) (tptp.aa_real_real _let_1 Y)) (= X Y))))) (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 ((N2 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) N2)) (= (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))) (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root 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_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 ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root 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_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 ((N2 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) N2)) (= (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X) tptp.one_one_real) (= X tptp.one_one_real)))) (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.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) tptp.one_one_real) tptp.one_one_real))) (forall ((R2 tptp.int) (L tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int R2)) L)) K)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int L) (tptp.aa_int_int tptp.sgn_sgn_int R2))) K)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K)) (=> (= R2 tptp.zero_zero_int) (= K tptp.zero_zero_int))))) (forall ((L tptp.int) (R2 tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int R2)) K))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (= R2 tptp.zero_zero_int))))) (forall ((L tptp.int) (K tptp.int) (R2 tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) (tptp.aa_int_int tptp.sgn_sgn_int R2)))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (= R2 tptp.zero_zero_int))))) (forall ((N2 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) N2)) (= (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 N2) 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 ((N2 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) N2)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N2 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) N2)) (= (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 N2) 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 ((N2 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) N2)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N2 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) N2)) (= (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 N2) 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 ((N2 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) N2)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N2 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) N2)) (= (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 N2) 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 ((N2 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) N2)) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) Y))) (tptp.pp (tptp.aa_real_bool _let_1 Y)))))) (forall ((N2 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) N2)) (=> (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 N2) X)) N2) X)))) (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N2))) (= (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 ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N2))) (= (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) (N2 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) N2)) 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 N2) X)))) (forall ((M tptp.nat) (N2 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 N2))) (= (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 ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N2))) (= (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 ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N2))) (= (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 ((X tptp.real) (N2 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 N2) X)))))) (forall ((K tptp.int)) (not (forall ((N tptp.nat) (L3 tptp.int)) (not (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int L3)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N))))))) (forall ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root 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_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 ((N2 tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root 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_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 ((X tptp.real)) (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_aad X)))) (forall ((N2 tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (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 ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (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 ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K))) (= (tptp.aa_int_int tptp.sgn_sgn_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L)) (tptp.aa_int_int tptp.sgn_sgn_int L))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.ln_ln_real X) (tptp.the_real tptp.aTP_Lamm_bb)))) (forall ((N2 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) N2)) (=> (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 N2) X))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N3) X)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X))))))) (= tptp.sqrt (tptp.aa_nat_fun_real_real tptp.root _let_2)) (forall ((N2 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) N2)) (= (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N2))) (tptp.aa_real_real tptp.abs_abs_real Y)))) (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 ((N2 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) N2)) (=> (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 N2) X)))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N3) X)))))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.one_one_real) X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N3) X)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X))))))) (forall ((N2 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))) N2))) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)) X))) (forall ((N2 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))) N2))) (=> (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Y) N2) X) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X) Y)))) (forall ((N2 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))) N2))) (= (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 N2) X)) N2) X))) (forall ((N2 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) N2)) (=> (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 N2) X)) N2) X)))) (forall ((N2 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) N2)) (=> (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 N2) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)) X)))) (forall ((N2 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) N2)) (=> (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) N2) X) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X) Y))))) (forall ((N2 tptp.nat) (N3 tptp.nat) (X tptp.real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) N3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X)) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N3) X)))))))) (forall ((Y tptp.real)) (= (tptp.aa_real_real tptp.arccos Y) (tptp.the_real (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_aae Y)))) (forall ((R2 tptp.int) (L tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int R2) (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 R2)) (tptp.aa_int_int tptp.abs_abs_int L))) (=> (= K (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q2) L)) R2)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int K L) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q2) R2))))))) (forall ((N2 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) N2)) (=> (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 N2) 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 N2)))))) (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.log B))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (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 N2) 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 N2))))))) (forall ((N2 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) N2)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) B)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.log (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) B)) 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.log B) X)))))) (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A1 A22) A32)) (or (exists ((K3 tptp.int)) (and (= A1 K3) (= A22 tptp.zero_zero_int) (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) K3)))) (exists ((L4 tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A1 K3) (= A22 L4) (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q4) tptp.zero_zero_int)) (not (= L4 tptp.zero_zero_int)) (= K3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q4) L4)))) (exists ((R5 tptp.int) (L4 tptp.int) (K3 tptp.int) (Q4 tptp.int)) (and (= A1 K3) (= A22 L4) (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q4) R5)) (= (tptp.aa_int_int tptp.sgn_sgn_int R5) (tptp.aa_int_int tptp.sgn_sgn_int L4)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R5)) (tptp.aa_int_int tptp.abs_abs_int L4))) (= K3 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q4) L4)) R5))))))) (forall ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.eucl_rel_int A1 A22) A32)) (=> (=> (= A22 tptp.zero_zero_int) (not (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) A1)))) (=> (forall ((Q3 tptp.int)) (=> (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A22 tptp.zero_zero_int)) (not (= A1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q3) A22)))))) (not (forall ((R3 tptp.int) (Q3 tptp.int)) (=> (= A32 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Q3) R3)) (=> (= (tptp.aa_int_int tptp.sgn_sgn_int R3) (tptp.aa_int_int tptp.sgn_sgn_int A22)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.abs_abs_int R3)) (tptp.aa_int_int tptp.abs_abs_int A22))) (not (= A1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Q3) A22)) R3)))))))))))) (forall ((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 ((N2 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) N2)) (=> (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 N2) 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 N2))))))) (= _let_25 _let_42) (= tptp.pi (tptp.aa_real_real _let_43 _let_42)) (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (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 N2))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N2 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 N2) M)))))))))))))))))) (forall ((X tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_real_real tptp.sgn_sgn_real X))) (tptp.pp (tptp.aa_real_bool _let_1 X))))) (forall ((X tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.sgn_sgn_real X)) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)))) (forall ((N2 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) N2)) (= (tptp.aa_real_real tptp.sgn_sgn_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X)) (tptp.aa_real_real tptp.sgn_sgn_real X)))) (forall ((A tptp.real) (N2 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)) N2)) 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)) N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= A B))))) (forall ((N2 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) N2)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) (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)) N2))) Y))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= (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)) N2)) X)))) (forall ((Z tptp.complex) (X tptp.real)) (=> (= (tptp.aa_complex_complex tptp.sgn_sgn_complex Z) (tptp.aa_real_complex tptp.cis X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.pi)) (= (tptp.aa_complex_real tptp.arg Z) X))))) (forall ((P tptp.fun_real_bool) (N2 tptp.nat) (X tptp.real)) (= (tptp.pp (tptp.aa_real_bool P (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X))) (and (=> (= N2 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) N2)) (forall ((Y3 tptp.real)) (=> (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real Y3)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.abs_abs_real Y3)) N2)) X) (tptp.pp (tptp.aa_real_bool P Y3)))))))) (forall ((X tptp.real)) (= (tptp.aa_real_int tptp.archim6058952711729229775r_real X) (tptp.the_int (tptp.aa_real_fun_int_bool tptp.aTP_Lamm_aag X)))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (tptp.aa_complex_complex tptp.sgn_sgn_complex Z) (tptp.aa_real_complex tptp.cis _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.pi)))))) (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (tptp.aa_real_real tptp.arctan (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sgn_sgn_real X)) tptp.pi)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_real_real tptp.arctan X))))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (tptp.aa_int_int tptp.abs_abs_int L))) (let ((_let_2 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int K))) (tptp.aa_int_nat tptp.nat2 _let_1))))) (let ((_let_3 (tptp.aa_int_int tptp.sgn_sgn_int L))) (let ((_let_4 (tptp.aa_int_fun_int_int tptp.times_times_int _let_3))) (let ((_let_5 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) L))) (let ((_let_6 (= (tptp.aa_int_int tptp.sgn_sgn_int K) _let_3))) (let ((_let_7 (= L tptp.zero_zero_int))) (and (=> _let_7 (= _let_5 K)) (=> (not _let_7) (and (=> _let_6 (= _let_5 (tptp.aa_int_int _let_4 _let_2))) (=> (not _let_6) (= _let_5 (tptp.aa_int_int _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int L) K))))) _let_2))))))))))))))) (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 ((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 ((N2 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 N2))) (tptp.pp (tptp.aa_nat_bool _let_1 N2))))) (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))) (= _let_41 _let_38) (forall ((I2 tptp.int)) (= (= (tptp.aa_int_nat tptp.nat2 I2) tptp.zero_zero_nat) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) tptp.zero_zero_int)))) (forall ((Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Z) tptp.zero_zero_int)) (= (tptp.aa_int_nat tptp.nat2 Z) tptp.zero_zero_nat))) (forall ((W tptp.int) (Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W)) (tptp.aa_int_nat tptp.nat2 Z))) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z))))) (forall ((K tptp.num)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.zero_zero_nat)) (forall ((Z tptp.int)) (let ((_let_1 (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 Z)))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)))) (forall ((V tptp.num) (V3 tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) (tptp.aa_num_nat tptp.numeral_numeral_nat V3)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int V)) (tptp.aa_num_int tptp.numeral_numeral_int V3))))) (forall ((X tptp.num) (N2 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)) N2) (tptp.aa_int_nat tptp.nat2 Y)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2) Y))) (forall ((Y tptp.int) (X tptp.num) (N2 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)) N2)) (= Y (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)))) (forall ((X tptp.real) (A tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim7802044766580827645g_real X))) A)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real A))))) (forall ((Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.one_one_int) Z)))) (forall ((V tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_num_nat tptp.numeral_numeral_nat V)) tptp.one_one_nat) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_num_int tptp.numeral_numeral_int V)) tptp.one_one_int)))) (forall ((A tptp.int) (X tptp.num) (N2 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)) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))))) (forall ((X tptp.num) (N2 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)) N2)) (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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)) A)))) (forall ((A tptp.int) (X tptp.num) (N2 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)) N2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int A) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2))))) (forall ((X tptp.num) (N2 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)) N2)) (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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int X)) N2)) A)))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N2)) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N2))) (forall ((X2 tptp.num)) (= (tptp.aa_num_nat tptp.numeral_numeral_nat X2) (tptp.aa_int_nat tptp.nat2 (tptp.aa_num_int tptp.numeral_numeral_int X2)))) (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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_12))) (exists ((X4 tptp.int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X4)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 X4))))))) (forall ((P tptp.fun_nat_bool)) (= (forall ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_12))) (forall ((X4 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) X4)) (tptp.pp (tptp.aa_nat_bool P (tptp.aa_int_nat tptp.nat2 X4))))))) (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_41) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se4205575877204974255it_nat M) N2) (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 N2))))) (forall ((N2 tptp.nat)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N2)))) (forall ((N2 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 N2)) tptp.zero_zero_int)))) (forall ((Z tptp.int) (W tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) Z)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z))))) (forall ((M tptp.nat) (Z tptp.int)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)) Z)))) (forall ((X tptp.int) (N2 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)) N2)) (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 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_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat tptp.nat2 Z)) Z))) (forall ((M tptp.nat) (Z tptp.int)) (= (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M) Z) (and (= M (tptp.aa_int_nat tptp.nat2 Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z))))) (forall ((A tptp.nat) (B tptp.nat)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int A)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int B))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat A) B))) (forall ((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 ((N2 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 N2) 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 N2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M)))))) (forall ((X2 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat X2) Xa) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((X2 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat X2) Xa) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat M) N2) (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 N2))))) (forall ((X tptp.real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim7802044766580827645g_real X)))))) (forall ((N2 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)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N2))))) (forall ((X2 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X2) Xa) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((X2 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X2) Xa) (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 X2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((X2 tptp.nat) (Xa tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X2) Xa) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int X2)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Xa))))) (forall ((W tptp.int) (Z tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_int_nat tptp.nat2 W)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int W) Z))))) (forall ((W tptp.int) (Z tptp.int)) (=> (or (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) W)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_int_nat tptp.nat2 W)) (tptp.aa_int_nat tptp.nat2 Z))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int W) Z))))) (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W)))) (= (= (tptp.aa_int_nat tptp.nat2 W) M) (and (=> _let_1 (= W (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) W)))) (= (= M (tptp.aa_int_nat tptp.nat2 W)) (and (=> _let_1 (= W (tptp.aa_nat_int tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((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 ((K tptp.int) (N2 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 N2) (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 N2)) 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 ((X2 tptp.nat)) (= (tptp.aa_nat_nat tptp.suc X2) (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 X2)) tptp.one_one_int)))) (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 ((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 ((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 ((Z tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int Z) N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_int_nat tptp.nat2 Z)) N2)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.zero_zero_real)) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))) (forall ((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 ((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.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 ((N2 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 N2)) 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 N2)))) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) N2)))) (forall ((X tptp.nat) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real X)) A)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X) (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real A)))))) (= (tptp.aa_int_nat tptp.nat2 _let_40) _let_39) (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 ((N2 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 N2)) 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 N2)))) (= (tptp.aa_int_nat tptp.nat2 (tptp.aa_real_int tptp.archim6058952711729229775r_real X)) N2)))) (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 ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N2)) (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))) N2))) (forall ((N2 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 N2)) (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))) N2)))) (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 ((N2 tptp.nat)) (= (tptp.aa_nat_nat tptp.bit_se2002935070580805687sk_nat N2) (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))) N2)) tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N2)) (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 N2) tptp.one_one_nat)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) 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)))))) (= tptp.nat_set_encode (tptp.groups3542108847815614940at_nat _let_3)) (forall ((X tptp.real) (N2 tptp.int)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_int_real tptp.ring_1_of_int_real N2)))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) N2)))) (=> (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 N2)))) (=> (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 N2)))))))))))) (forall ((X tptp.real) (I2 tptp.int)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real X))) (let ((_let_2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real X) (tptp.aa_int_real tptp.ring_1_of_int_real I2)))) (let ((_let_3 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) I2)))) (=> (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 I2)))) (=> (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 I2)))))))))))) (forall ((X tptp.rat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat X) (tptp.the_int (tptp.aTP_Lamm_aah X)))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.arg Z))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (tptp.fChoice_real (tptp.aTP_Lamm_aai Z)))))))) (forall ((X32 tptp.num)) (= (tptp.aa_num_nat tptp.size_num (tptp.aa_num_num tptp.bit1 X32)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_num X32)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit N2) K) tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (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) N2)))) (forall ((K tptp.int) (N2 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 N2) (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_se2923211474154528505it_int N2) K))))) (forall ((K tptp.int) (N2 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.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (tptp.aa_int_nat tptp.nat2 K))))) (forall ((R2 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) R2)) (not (forall ((S tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) S)) (forall ((T5 tptp.rat)) (=> (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat tptp.zero_zero_rat) T5)) (not (= R2 (tptp.aa_rat_rat (tptp.plus_plus_rat S) T5)))))))))) (forall ((N2 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 N2) M)) M))) (forall ((M tptp.nat) (N2 tptp.nat) (Q2 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 (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 N2) Q2))))) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat X) Y)) (or (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat X) Y)) (= X Y)))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (= (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 ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (= (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 ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (= (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 ((N2 tptp.nat) (B tptp.int)) (let ((_let_1 (tptp.bit_concat_bit N2))) (= (tptp.aa_int_fun_int_int _let_1 (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) B)) (tptp.aa_int_fun_int_int _let_1 B)))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int) (R2 tptp.int) (S2 tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (tptp.bit_concat_bit N2))) (= (= (tptp.aa_int_int (tptp.aa_int_fun_int_int _let_2 K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int _let_2 R2) S2)) (and (= (tptp.aa_int_int _let_1 K) (tptp.aa_int_int _let_1 R2)) (= L S2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (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_se2923211474154528505it_int M) K)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K))))) (forall ((N2 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_se2923211474154528505it_int N2) 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 ((N2 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.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)))) (forall ((N2 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.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int)))) (forall ((K tptp.int) (N2 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.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 tptp.zero_zero_int))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (= (= (tptp.aa_int_int _let_1 K) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N2)) (= (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 ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (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) (N2 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))) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) M) M))) (forall ((N2 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 N2) 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))) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) 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))) N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) 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))) N2)))) (forall ((N2 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_se2923211474154528505it_int N2) K)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (= (tptp.aa_num_nat tptp.size_num tptp.one) tptp.zero_zero_nat) (forall ((N2 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 N2) 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))) N2)) M)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N2)) (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.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((K tptp.int) (N2 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_se2923211474154528505it_int N2) K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((N2 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_se2923211474154528505it_int N2) K)) K)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) K)))) (forall ((K tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K) K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_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.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K)))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2))) (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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) 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 ((N2 tptp.nat) (K tptp.int)) (= (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K) (tptp.aa_nat_int tptp.bit_se2000444600071755411sk_int N2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) tptp.one_one_int))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (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) N2)) (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_se2923211474154528505it_int N2) K)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) _let_1))))))) (forall ((K tptp.int) (N2 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) _let_1))) _let_1)))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (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.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) (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 ((X22 tptp.num)) (= (tptp.aa_num_nat tptp.size_num (tptp.aa_num_num tptp.bit0 X22)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_num_nat tptp.size_num X22)) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_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.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc K))))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((K tptp.num)) (= (tptp.aa_num_nat tptp.pred_numeral (tptp.aa_num_num tptp.inc K)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (forall ((Q2 tptp.rat) (R2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat Q2) R2) (tptp.aa_rat_rat (tptp.plus_plus_rat Q2) (tptp.aa_rat_rat tptp.uminus_uminus_rat R2)))) (forall ((P tptp.fun_num_bool) (X tptp.num)) (=> (tptp.pp (tptp.aa_num_bool P tptp.one)) (=> (forall ((X3 tptp.num)) (=> (tptp.pp (tptp.aa_num_bool P X3)) (tptp.pp (tptp.aa_num_bool P (tptp.aa_num_num tptp.inc X3))))) (tptp.pp (tptp.aa_num_bool P X))))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.plus_plus_num X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.inc Y)) (tptp.aa_num_num tptp.inc (tptp.aa_num_num _let_1 Y))))) (= (tptp.aa_num_num tptp.inc tptp.one) _let_1) (forall ((X tptp.num)) (= (tptp.aa_num_num tptp.inc (tptp.aa_num_num tptp.bit0 X)) (tptp.aa_num_num tptp.bit1 X))) (forall ((X tptp.num)) (= (tptp.aa_num_num tptp.inc (tptp.aa_num_num tptp.bit1 X)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.inc X)))) (forall ((X tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num X) tptp.one) (tptp.aa_num_num tptp.inc X))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num tptp.inc (tptp.aa_num_num tptp.bitM N2)) (tptp.aa_num_num tptp.bit0 N2))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num tptp.bitM (tptp.aa_num_num tptp.inc N2)) (tptp.aa_num_num tptp.bit1 N2))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.times_times_num X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.inc Y)) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num _let_1 Y)) X)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N2)) (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.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc K))))) (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_nat_fun_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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) _let_1)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))))))) (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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int L) _let_1))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.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 ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L))) (or (tptp.pp (tptp.aa_int_bool _let_1 K)) (tptp.pp (tptp.aa_int_bool _let_1 L)))))) (forall ((K tptp.int) (L tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int))))) (forall ((N2 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.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))))) (forall ((N2 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_ri631733984087533419it_int N2) K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)))) (forall ((W tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W)))) (tptp.aa_nat_nat tptp.suc N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) N2)))) (forall ((W tptp.num) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 W)))) (tptp.aa_nat_nat tptp.suc N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int W)) N2))))) (forall ((N2 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 N2)))) tptp.one_one_int) tptp.one_one_int)) (forall ((N2 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 N2)))) tptp.one_one_int)) (forall ((N2 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 N2)))) tptp.zero_zero_int)) (forall ((N2 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 N2)))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((W tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 W)))) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) (tptp.aa_num_nat tptp.pred_numeral N2))))) (forall ((W tptp.num) (N2 tptp.num)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 W)))) (tptp.aa_num_nat tptp.numeral_numeral_nat N2))) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_num_int tptp.numeral_numeral_int W)) (tptp.aa_num_nat tptp.pred_numeral N2)))))) (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L)) N2)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int L) N2))))) (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int K) L)) N2)) (or (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int L) N2))))) (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 ((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) (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 ((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 ((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.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 ((X tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.pow X) tptp.one) X)) (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Y)) Z))))) (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) Y)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Y) Z)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int Y) Ya)) Z))))) (forall ((L tptp.int) (K tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int L) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L)) K)))) (forall ((K tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int tptp.uminus_uminus_int K)) tptp.one_one_int)) N2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))))) (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 ((N2 tptp.nat) (M tptp.nat) (K tptp.int)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)) (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_nat_fun_int_int tptp.bit_se2923211474154528505it_int M) K)))))) (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit M) K) L)) N2)) (or (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) M)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))) (and (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 (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int L) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M))))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_ri631733984087533419it_int N2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit N2) K) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)))))) (forall ((K tptp.int)) (not (forall ((N tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M3 tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N) M3)) (= (tptp.pp (tptp.aa_nat_bool _let_1 M3)) (tptp.pp (tptp.aa_nat_bool _let_1 N)))))) (not (=> (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.minus_minus_nat N) tptp.one_one_nat))) (not (tptp.pp (tptp.aa_nat_bool _let_1 N))))))))))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)) (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.aa_int_fun_nat_int tptp.power_power_int _let_1) N2)))))))) (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 ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int (tptp.aa_nat_nat tptp.suc N2)) 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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)))) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_3 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 K))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 L)))))) (let ((_let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_6 (and (tptp.member_int K _let_5) (tptp.member_int L _let_5)))) (and (=> _let_6 (= _let_4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L) _let_1)))))))))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_1))) (let ((_let_3 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 X))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_2 Xa2)))))) (let ((_let_4 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_5 (and (tptp.member_int X _let_4) (tptp.member_int Xa2 _let_4)))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.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 Xa2) _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.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int K) L))) (and (=> _let_6 (= _let_4 (tptp.aa_int_int tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.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 ((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 ((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 ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N2 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)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((N2 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)) N2)) (= N2 tptp.zero_zero_nat))) (forall ((N2 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 N2))))) (forall ((N2 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 N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se727722235901077358nd_nat M) N2) (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 N2))))) (forall ((K tptp.int) (N2 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)) N2)) (and (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))))) (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int tptp.one_one_int) N2))) (=> (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 N2)))))) (forall ((J tptp.int) (I2 tptp.int)) (let ((_let_1 (tptp.set_or1266510415728281911st_int I2 J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (tptp.insert_int I2 (tptp.set_or1266510415728281911st_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) J)))))))) (forall ((M tptp.nat) (N2 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) N2)) (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) N2)))))))) (forall ((A0 tptp.int) (A1 tptp.int) (P tptp.fun_int_fun_int_bool)) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int A0) A1))) (=> (forall ((K2 tptp.int) (L3 tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int K2) L3))) (=> (=> (not (and (tptp.member_int K2 _let_2) (tptp.member_int L3 _let_2))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K2) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int L3) _let_1)))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P K2) L3))))))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool P A0) A1))))) (forall ((M tptp.nat) (N2 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) N2))) (let ((_let_3 (or (= M tptp.zero_zero_nat) (= N2 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 N2) _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 N2) _let_1))))))))))) (forall ((M tptp.nat) (N2 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) N2) (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 N2))))) (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 N2) _let_1)))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X) Xa2))))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_int_fun_int_bool tptp.dvd_dvd_int _let_2))) (let ((_let_4 (tptp.aa_bool_int tptp.zero_n2684676970156552555ol_int (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_3 X))) (tptp.aa_bool_bool tptp.fNot (tptp.aa_int_bool _let_3 Xa2)))))) (let ((_let_5 (tptp.insert_int tptp.zero_zero_int (tptp.insert_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int) tptp.bot_bot_set_int)))) (let ((_let_6 (and (tptp.member_int X _let_5) (tptp.member_int Xa2 _let_5)))) (=> (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (tptp.aa_int_int tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_4) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_int_int (tptp.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 Xa2) _let_2))))))) (not _let_1)))))))))))) (forall ((N2 tptp.real)) (=> (tptp.member_real N2 tptp.ring_1_Ints_real) (= (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.one_one_complex))) (forall ((P2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.inverse_inverse_rat P2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_aaj) (tptp.quotient_of P2)))) (forall ((K tptp.num)) (= (tptp.quotient_of (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K)) tptp.one_one_int))) (forall ((K tptp.num)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.one_one_int))) (forall ((A2 tptp.set_nat) (N2 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 N2) A2))) (= (tptp.aa_set_nat_nat tptp.nat_set_encode (tptp.insert_nat N2 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))) N2)) (tptp.aa_set_nat_nat tptp.nat_set_encode A2)))))) (forall ((Q2 tptp.rat) (R2 tptp.rat)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat Q2) R2) (tptp.aa_rat_rat (tptp.times_times_rat Q2) (tptp.aa_rat_rat tptp.inverse_inverse_rat R2)))) (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 ((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 ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat _let_1) (tptp.insert_nat _let_1 (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.insert_nat M (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N2)) (tptp.set_or1269000886237332187st_nat M N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_1)) (= (tptp.set_or1269000886237332187st_nat M _let_1) (tptp.insert_nat _let_1 (tptp.set_or1269000886237332187st_nat M N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (tptp.set_or1269000886237332187st_nat M N2) (tptp.insert_nat M (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc M) N2))))) (forall ((K tptp.num)) (let ((_let_1 (tptp.aa_num_nat 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 ((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.aa_num_nat tptp.pred_numeral K)))))) (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 ((P2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.abs_abs_rat P2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_aak) (tptp.quotient_of P2)))) (forall ((N2 tptp.nat)) (= (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2) (tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2) (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)))) (forall ((P2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat tptp.uminus_uminus_rat P2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int tptp.aTP_Lamm_aal) (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_rat P2) Q2)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aTP_Lamm_aan Q2)) (tptp.quotient_of P2))))) (forall ((P2 tptp.rat)) (= (tptp.aa_rat_int tptp.archim3151403230148437115or_rat P2) (tptp.aa_Pro6799258434465214121nt_int (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_aap Q2)) (tptp.quotient_of P2))))) (forall ((N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (tptp.nat_set_decode Z))) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat N2) _let_1))) (= (tptp.nat_set_decode (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) Z)) (tptp.insert_nat N2 _let_1))))) (forall ((N2 tptp.real)) (=> (tptp.member_real N2 tptp.ring_1_Ints_real) (= (tptp.aa_real_real tptp.sin_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.zero_zero_real))) (forall ((N2 tptp.real)) (=> (tptp.member_real N2 tptp.ring_1_Ints_real) (= (tptp.aa_real_real tptp.cos_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.one_one_real))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.minus_minus_rat P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_aar Q2)) (tptp.quotient_of P2)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.plus_plus_rat P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_aat Q2)) (tptp.quotient_of P2)))) (forall ((Q2 tptp.int) (S2 tptp.int) (P2 tptp.int) (R2 tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S2 tptp.zero_zero_int)) (=> (= (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int R2) S2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int P2) S2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int R2) Q2)))))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.times_times_rat P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_aav Q2)) (tptp.quotient_of P2)))) (forall ((P2 tptp.rat) (Q2 tptp.rat)) (= (tptp.quotient_of (tptp.aa_rat_rat (tptp.divide_divide_rat P2) Q2)) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aTP_Lamm_aax Q2)) (tptp.quotient_of P2)))) (forall ((K tptp.num)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) (tptp.aa_num_int tptp.numeral_numeral_int K))) (tptp.aa_rat_rat (tptp.divide_divide_rat tptp.one_one_rat) (tptp.aa_num_rat tptp.numeral_numeral_rat K)))) (forall ((N2 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))) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat N2) (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 N2) (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 ((N2 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))) N2))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) N2) (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 N2) (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 ((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 ((K tptp.num)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K)) tptp.one_one_int)) (tptp.aa_num_rat tptp.numeral_numeral_rat K))) (forall ((M tptp.nat) (N2 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) N2))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (let ((_let_4 (= M tptp.zero_zero_nat))) (and (=> _let_4 (= _let_2 N2)) (=> (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 N2) _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 N2) _let_1)))))))))))))) (forall ((M tptp.nat) (N2 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) N2) (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.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 N2)))))) (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 N2) _let_1)))))))) (forall ((K tptp.num) (L tptp.num)) (= (tptp.frct (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_num_int tptp.numeral_numeral_int K)) (tptp.aa_num_int tptp.numeral_numeral_int L))) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_num_rat tptp.numeral_numeral_rat L)))) (forall ((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.aa_int_fun_nat_int tptp.power_power_int _let_1) (tptp.size_size_list_bool Bs)))))) (forall ((N2 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 N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N2 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 N2) 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 ((N2 tptp.nat) (L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit N2) tptp.zero_zero_int) L) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N2) L))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (= (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.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 ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N2) (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))) N2))) (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int K) L)) N2)) (not (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int L) N2)))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2159334234014336723it_int N2) 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 N2) tptp.one_one_int)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N2) (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 N2) K)))) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (tptp.pp (tptp.aa_int_bool _let_1 X)) (=> (tptp.pp (tptp.aa_int_bool _let_1 Y)) (tptp.pp (tptp.aa_int_bool _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int X) Y))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se7882103937844011126it_nat M) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se1412395901928357646or_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) tptp.one_one_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2161824704523386999it_nat M) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat M) tptp.one_one_nat)))) (forall ((M tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int M) K)) N2)) (and (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 (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) M)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se6528837805403552850or_nat M) N2) (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 N2))))) (forall ((M tptp.nat) (Q2 tptp.nat) (N2 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)) N2)) (and (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 (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 N2) M)))))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit N2) K) L) (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_se2923211474154528505it_int N2) K)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N2) L)))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.bit_concat_bit N2) K) L) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int N2) K)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N2) L)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se7879613467334960850it_int N2) 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 N2) tptp.one_one_int)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se547839408752420682it_nat N2) 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))) N2)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N2) (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.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((X tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (=> (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 ((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.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 ((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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int L) _let_1)))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_1) (tptp.aa_int_int (tptp.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 ((X6 tptp.fun_nat_real)) (= (tptp.topolo4055970368930404560y_real X6) (forall ((J3 tptp.nat)) (exists ((M9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) M6)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M9) N5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real X6 M6)) (tptp.aa_nat_real X6 N5)))) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc J3))))))))))))) (forall ((K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int K) tptp.zero_zero_int)))) (forall ((K tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) K)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int M))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se725231765392027082nd_int (tptp.aa_int_int tptp.uminus_uminus_int _let_2)) (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_2) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int _let_1) tptp.one_one_int))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (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 ((K tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int K)) N2)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int K) N2))))) (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 ((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_37) tptp.zero_zero_int) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_37) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se4203085406695923979it_int N2) 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 N2) tptp.one_one_int))))) (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 ((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 ((N2 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 N2)))) tptp.one_one_int)) (forall ((M tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 M)))) (= (tptp.aa_int_int (tptp.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 ((N2 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 N2))))) (= (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))) (forall ((K tptp.int) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.uminus_uminus_int K)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool tptp.bit_se1146084159140164899it_int (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int K) tptp.one_one_int))) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) N2)) (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 N2)))))) (forall ((M tptp.num) (N2 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 N2)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg N2) M))))) (forall ((M tptp.num) (N2 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 N2))) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.bit_or_not_num_neg M) N2))))) (forall ((M tptp.num) (N2 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 N2)))) (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 N2)))))) (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 ((N2 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 N2)))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 N2))))) (forall ((N2 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 N2)))) tptp.zero_zero_int)) (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 ((M tptp.num) (N2 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 N2)))) (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 N2)))))) (forall ((M tptp.num) (N2 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 N2)))) (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 N2)))))) (forall ((M tptp.num) (N2 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 N2)))) (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 N2)))))) (forall ((M tptp.num) (N2 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 N2)))) (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 N2))))))) (forall ((M tptp.num) (N2 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 N2)))) (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 N2))))))) (forall ((M tptp.num) (N2 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 N2)))) (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 N2))))))) (forall ((M tptp.num) (N2 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 N2)))) (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 N2))))))) (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 ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_ai) (tptp.set_or4665077453230672383an_nat M N2)) (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 N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat N2) 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 ((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)) (= (tptp.set_or4665077453230672383an_nat M (tptp.aa_nat_nat tptp.suc M)) (tptp.insert_nat M tptp.bot_bot_set_nat))) (forall ((N2 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) N2)) (tptp.pp (tptp.aa_nat_bool P M6)))) (forall ((X4 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N2))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((N2 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) N2)) (tptp.pp (tptp.aa_nat_bool P M6)))) (exists ((X4 tptp.nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat X4) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N2))) (tptp.pp (tptp.aa_nat_bool P X4)))))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.set_or4665077453230672383an_nat L (tptp.aa_nat_nat tptp.suc U)) (tptp.set_or1269000886237332187st_nat L U))) (forall ((N2 tptp.nat)) (= (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.insert_nat N2 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N2)))) (forall ((N3 tptp.set_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N3) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N2))) (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat N3)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat M (tptp.aa_nat_nat tptp.suc N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)))) (and (=> _let_2 (= _let_1 (tptp.insert_nat N2 (tptp.set_or4665077453230672383an_nat M N2)))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_nat)))))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.suc) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat (tptp.groups708209901874060359at_nat tptp.suc) (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2)) (tptp.aa_nat_nat tptp.semiri1408675320244567234ct_nat N2))) (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat M (tptp.aa_num_nat tptp.numeral_numeral_nat K)))) (let ((_let_2 (tptp.aa_num_nat tptp.pred_numeral K))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) _let_2)))) (and (=> _let_3 (= _let_1 (tptp.insert_nat _let_2 (tptp.set_or4665077453230672383an_nat M _let_2)))) (=> (not _let_3) (= _let_1 tptp.bot_bot_set_nat))))))) (forall ((N2 tptp.nat)) (= (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat) N2) (tptp.minus_minus_set_nat (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2) (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.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 ((N2 tptp.nat) (A tptp.fun_nat_nat) (B tptp.fun_nat_nat)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N2))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J2) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat A I3)) (tptp.aa_nat_nat A J2)))))) (=> (forall ((I3 tptp.nat) (J2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat I3) J2)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat J2) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat B J2)) (tptp.aa_nat_nat B I3)))))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_aay 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 ((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 ((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 ((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 ((X21 tptp.bool) (X222 tptp.bool)) (= (tptp.aa_VEBT_VEBT_nat tptp.vEBT_size_VEBT (tptp.vEBT_Leaf X21 X222)) tptp.zero_zero_nat)) (= tptp.code_Target_positive tptp.numeral_numeral_int) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex tptp.csqrt Z)) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_complex_real tptp.re Z))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((V tptp.num)) (= (tptp.aa_complex_real tptp.re (tptp.numera6690914467698888265omplex V)) (tptp.aa_num_real tptp.numeral_numeral_real V))) (forall ((Z tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex Z) (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.re Z)) (tptp.aa_num_real tptp.numeral_numeral_real W)))) (forall ((X6 tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex X6) A)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_aaz X6)) (tptp.aa_complex_real tptp.re A))))) (forall ((X6 tptp.fun_nat_complex)) (=> (tptp.topolo6517432010174082258omplex X6) (tptp.topolo4055970368930404560y_real (tptp.aTP_Lamm_aaz X6)))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.re Y)))) (forall ((R2 tptp.real) (X tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex R2) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_complex_real tptp.re X)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.re Y)))) (forall ((F tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (tptp.summable_real (tptp.aTP_Lamm_aaz F)))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re X))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (forall ((Z tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex tptp.csqrt Z))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (tptp.aa_complex_real tptp.re Z))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real)) (= _let_2 (tptp.aa_real_real tptp.uminus_uminus_real _let_1)))))) (forall ((N2 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 N2)) A)) (tptp.aa_complex_real tptp.re (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_real_complex tptp.cis A)) N2)))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.re Z))) (let ((_let_3 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))) (let ((_let_4 (tptp.aa_complex_real tptp.im Z))) (= (tptp.aa_complex_complex tptp.csqrt Z) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_3) _let_2)) _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real _let_4) tptp.zero_zero_real)) tptp.one_one_real) (tptp.aa_real_real tptp.sgn_sgn_real _let_4))) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.im Z))) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex tptp.csqrt Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real _let_1) tptp.zero_zero_real)) tptp.one_one_real) (tptp.aa_real_real tptp.sgn_sgn_real _let_1))) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_complex_real tptp.re Z))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re X))) (=> (= (tptp.aa_complex_real tptp.im X) tptp.zero_zero_real) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) tptp.zero_zero_real)) (= (tptp.aa_complex_complex tptp.csqrt X) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real tptp.abs_abs_real _let_1))))))))) (forall ((X tptp.complex) (N2 tptp.nat)) (=> (= (tptp.aa_complex_real tptp.im X) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.im (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2)) tptp.zero_zero_real))) (forall ((V tptp.num)) (= (tptp.aa_complex_real tptp.im (tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) Z)) (tptp.aa_complex_real tptp.re Z))) (forall ((X tptp.complex) (N2 tptp.nat)) (=> (= (tptp.aa_complex_real tptp.im X) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.re (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re X)) N2)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) Z)) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_complex_real tptp.im Z)))) (forall ((Z tptp.complex) (W tptp.num)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex Z) (tptp.numera6690914467698888265omplex W))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.im Z)) (tptp.aa_num_real tptp.numeral_numeral_real W)))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re X))) (=> (= (tptp.aa_complex_real tptp.im X) tptp.zero_zero_real) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) _let_1)) (= (tptp.aa_complex_complex tptp.csqrt X) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.sqrt _let_1))))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.im X))) (=> (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) tptp.zero_zero_real)) (and (= _let_1 tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.re X))))) (= (tptp.aa_complex_complex tptp.csqrt (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex X)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_complex_complex tptp.csqrt X)))))) (forall ((X6 tptp.fun_nat_complex) (A tptp.complex)) (=> (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex X6) A)) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_aba X6)) (tptp.aa_complex_real tptp.im A))))) (forall ((X6 tptp.fun_nat_complex)) (=> (tptp.topolo6517432010174082258omplex X6) (tptp.topolo4055970368930404560y_real (tptp.aTP_Lamm_aba X6)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.im Y)))) (forall ((R2 tptp.real) (X tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex R2) X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_complex_real tptp.im X)))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.im Y)))) (forall ((F tptp.fun_nat_complex) (X tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) X)) (and (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_aaz F)) (tptp.aa_complex_real tptp.re X))) (tptp.pp (tptp.aa_real_bool (tptp.sums_real (tptp.aTP_Lamm_aba F)) (tptp.aa_complex_real tptp.im X)))))) (forall ((F tptp.fun_nat_complex)) (=> (tptp.summable_complex F) (tptp.summable_real (tptp.aTP_Lamm_aba F)))) (forall ((X tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im X))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)))) (forall ((F tptp.fun_nat_complex)) (= (tptp.summable_complex F) (and (tptp.summable_real (tptp.aTP_Lamm_aaz F)) (tptp.summable_real (tptp.aTP_Lamm_aba F))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.im Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.re Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (tptp.aa_complex_real tptp.im X) (tptp.aa_complex_real tptp.im Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re X))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re Y))))))) (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (tptp.aa_complex_real tptp.re X) (tptp.aa_complex_real tptp.re Y)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex X)) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Y))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im X))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im Y))))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.re Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.im Y))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.re Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.im Y))))) (forall ((R2 tptp.real) (X tptp.complex)) (let ((_let_1 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2))) (= (tptp.aa_complex_complex (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex R2) X) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real _let_1 (tptp.aa_complex_real tptp.re X))) (tptp.aa_real_real _let_1 (tptp.aa_complex_real tptp.im X)))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.re X)) (tptp.aa_complex_real tptp.re Y))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_complex_real tptp.im X)) (tptp.aa_complex_real tptp.im Y))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex tptp.csqrt Z))) (let ((_let_2 (tptp.aa_complex_real tptp.re _let_1))) (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (and (= _let_2 tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.im _let_1)))))))) (forall ((Z tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re Z))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im Z)))))) (forall ((N2 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 N2)) A)) (tptp.aa_complex_real tptp.im (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_real_complex tptp.cis A)) N2)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex tptp.exp_complex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real (tptp.aa_complex_real tptp.re Z))) (tptp.aa_real_real tptp.cos_real (tptp.aa_complex_real tptp.im Z))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex tptp.exp_complex Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.exp_real (tptp.aa_complex_real tptp.re Z))) (tptp.aa_real_real tptp.sin_real (tptp.aa_complex_real tptp.im Z))))) (forall ((A tptp.complex)) (= A (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_complex_real tptp.re A))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_complex_real tptp.im A)))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re Y))) (let ((_let_2 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)))) (let ((_let_3 (tptp.aa_complex_real tptp.im Y))) (let ((_let_4 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real _let_4 _let_1)) (tptp.aa_real_real _let_2 _let_3))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real _let_4 _let_3)) (tptp.aa_real_real _let_2 _let_1))))))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex tptp.exp_complex Z) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real tptp.exp_real (tptp.aa_complex_real tptp.re Z)))) (tptp.aa_real_complex tptp.cis (tptp.aa_complex_real tptp.im Z))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (= (tptp.aa_complex_real tptp.im (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) (tptp.aa_num_nat tptp.numeral_numeral_nat _let_1))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real _let_1)) (tptp.aa_complex_real tptp.re X))) (tptp.aa_complex_real tptp.im X))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_real tptp.re (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im X)) _let_1))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (= Z tptp.zero_zero_complex) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1)) tptp.zero_zero_real)))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1)))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.re X))) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex tptp.invers8013647133539491842omplex X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im X)) _let_1))))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im Y))) (let ((_let_3 (tptp.aa_complex_real tptp.re Y))) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_3) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)))))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re W))) (=> (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex W) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Z) (=> (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (and (= _let_1 tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.im W))))) (= (tptp.aa_complex_complex tptp.csqrt Z) W))))) (forall ((B tptp.complex)) (let ((_let_1 (tptp.aa_complex_real tptp.re B))) (=> (or (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (and (= _let_1 tptp.zero_zero_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_complex_real tptp.im B))))) (= (tptp.aa_complex_complex tptp.csqrt (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex B) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) B)))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im X))) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex tptp.invers8013647133539491842omplex X)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re X)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im Y))) (let ((_let_3 (tptp.aa_complex_real tptp.re Y))) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)) _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_3) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)))))))) (forall ((Z tptp.complex)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.re Z))) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_complex_real tptp.im Z)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.sqrt (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))))) (forall ((Z tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z))) (=> (not (= Z tptp.zero_zero_complex)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.re Z)) _let_2)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real tptp.im Z)) _let_2)) _let_1)) tptp.one_one_real))))) (forall ((X tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im X))) (let ((_let_3 (tptp.aa_complex_real tptp.re X))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_3) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)))) (= (tptp.aa_complex_complex tptp.invers8013647133539491842omplex X) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real _let_3) _let_4)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.uminus_uminus_real _let_2)) _let_4)))))))) (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_complex_real tptp.im Y))) (let ((_let_3 (tptp.aa_complex_real tptp.re Y))) (let ((_let_4 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_3) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re X)))) (let ((_let_6 (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.im X)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex X) Y) (tptp.aa_real_complex (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 ((R2 tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R2 tptp.real_V2521375963428798218omplex) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex R2) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_complex_real tptp.re R2))) (tptp.aa_complex_real tptp.im Z))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((R2 tptp.complex) (Z tptp.complex)) (=> (tptp.member_complex R2 tptp.real_V2521375963428798218omplex) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex R2) Z)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.re R2)) (tptp.aa_complex_real tptp.re Z))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((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.aa_com3342990543769683525omplex 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.aa_com3342990543769683525omplex tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex Z) (tptp.aa_complex_complex tptp.cnj Z)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_real tptp.im Z)))) tptp.imaginary_unit))) (forall ((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.aa_com3342990543769683525omplex tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj Z)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.re Z)) _let_1)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.im Z)) _let_1)))))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex tptp.cnj (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.cnj X)) (tptp.aa_complex_complex tptp.cnj Y)))) (forall ((X tptp.complex) (N2 tptp.nat)) (= (tptp.aa_complex_complex tptp.cnj (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex X) N2)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.cnj X)) N2))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex tptp.cnj (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex tptp.cnj X)) (tptp.aa_complex_complex tptp.cnj Y)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.numera6690914467698888265omplex W))) (= (tptp.aa_complex_complex tptp.cnj _let_1) _let_1))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex tptp.cnj (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex tptp.cnj X)) (tptp.aa_complex_complex tptp.cnj Y)))) (forall ((W tptp.num)) (let ((_let_1 (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.numera6690914467698888265omplex W)))) (= (tptp.aa_complex_complex tptp.cnj _let_1) _let_1))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj Z))) tptp.zero_zero_real)) (forall ((F tptp.fun_nat_complex) (L tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex (tptp.aTP_Lamm_abb F)) (tptp.aa_complex_complex tptp.cnj L))) (tptp.pp (tptp.aa_complex_bool (tptp.sums_complex F) L)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B))) tptp.zero_zero_real))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B))) tptp.zero_zero_real))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z) (tptp.aa_real_real tptp.sqrt (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Z) (tptp.aa_complex_complex 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.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B)))))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.re (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B)))))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B)))))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B)))) tptp.zero_zero_real)))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real))) (= (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B)))) (tptp.pp (tptp.aa_real_bool _let_1 (tptp.aa_complex_real tptp.im (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B)))))))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj Z))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B)))) (let ((_let_2 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B))) (and (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_complex_real tptp.re _let_3))) (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_complex_real tptp.re _let_1)))) (= (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_complex_real tptp.im _let_3))) (tptp.pp (tptp.aa_real_bool _let_2 (tptp.aa_complex_real tptp.im _let_1))))))))) (forall ((Z tptp.complex)) (= (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex Z)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj Z)))) (forall ((Z tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Z) (tptp.aa_complex_complex tptp.cnj Z)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_real tptp.re Z))))) (forall ((A tptp.complex) (B tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex A) B) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex A) (tptp.aa_complex_complex tptp.cnj B))) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex B)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Z) (tptp.aa_complex_complex tptp.cnj W)))) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex tptp.cnj Z)) W)) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_complex_real tptp.re _let_1)))))) (forall ((L tptp.num) (Qr tptp.produc8923325533196201883nteger)) (= (tptp.unique4921790084139445826nteger L Qr) (tptp.produc6916734918728496179nteger (tptp.aTP_Lamm_fa L) Qr))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_ca N2))) N2)) (forall ((U tptp.nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat U)) (tptp.aa_nat_nat tptp.suc U))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.set_or4665077453230672383an_nat L U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat U) L))) (forall ((N2 tptp.nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_bz N2))) (tptp.aa_nat_nat tptp.suc N2))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.set_or1269000886237332187st_nat L U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat tptp.suc U)) L))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.finite_card_int (tptp.set_or4662586982721622107an_int L U)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int U) L)))) (forall ((L tptp.int) (U tptp.int)) (= (tptp.finite_card_int (tptp.set_or1266510415728281911st_int L U)) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int U) L)) tptp.one_one_int)))) (forall ((L tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger L) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger L))) (forall ((K tptp.code_integer)) (= (tptp.minus_8373710615458151222nteger K tptp.zero_z3403309356797280102nteger) K)) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger M))) (= (tptp.unique3479559517661332726nteger M N2) (tptp.produc1086072967326762835nteger (tptp.divide6298287555418463151nteger _let_2 _let_1) (tptp.modulo364778990260209775nteger _let_2 _let_1)))))) (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.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L) tptp.zero_z3403309356797280102nteger)) (tptp.pp (tptp.aa_Code_integer_bool _let_36 tptp.zero_z3403309356797280102nteger)) (forall ((K tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger K tptp.zero_z3403309356797280102nteger) K)) (forall ((L tptp.code_integer)) (= (tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger L) L)) (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fFalse tptp.aTP_Lamm_abc) 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_az) Nat)))) (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M7))) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_abd M7) I2))) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_abe M7) I2)))))) (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M7)) (= (tptp.aa_nat_nat tptp.suc (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_abd M7) I2)))) (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_abe M7) I2)))))) (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M7)) (not (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_abe M7) I2))) tptp.zero_zero_nat)))) (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (tptp.set_or4665077453230672383an_nat K (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat K) (tptp.aa_set_nat_nat tptp.finite_card_nat A2))))) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat A2) _let_1)) (= A2 _let_1)))) (= tptp.one_one_nat tptp.one_one_nat) (forall ((M tptp.nat) (N2 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)) N2)) (tptp.pp (tptp.aa_nat_bool (tptp.case_nat_bool tptp.fFalse (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M)) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (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_abf N2)) M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc N2))) (= (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_abg N2)) M)))) (forall ((N3 tptp.set_nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat N3) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N2))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat N3)) N2)))) (forall ((S3 tptp.set_nat)) (let ((_let_1 (tptp.groups3542108847815614940at_nat tptp.aTP_Lamm_ai))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat _let_1 (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat (tptp.aa_set_nat_nat tptp.finite_card_nat S3)))) (tptp.aa_set_nat_nat _let_1 S3))))) (forall ((C tptp.complex) (N2 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) N2)) (= (tptp.finite_card_complex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_aaa C) N2))) N2)))) (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.finite_card_complex (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool tptp.aTP_Lamm_cf N2))) N2))) (forall ((M tptp.nat) (N2 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 N2)) (tptp.aa_nat_nat (tptp.case_nat_nat tptp.zero_zero_nat tptp.aTP_Lamm_ai) (tptp.aa_nat_nat _let_1 N2))))) (forall ((K tptp.int)) (let ((_let_1 (tptp.aa_num_num tptp.bit0 tptp.one))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int _let_1))) (let ((_let_3 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger _let_1)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.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.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int K) _let_2)) tptp.zero_zero_int) _let_3 (tptp.plus_p5714425477246183910nteger _let_3 tptp.one_one_Code_integer)))))))))))))) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.plus_p5714425477246183910nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa2) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Xa2) X)))) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa2)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Xa2) X)))) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa2)) (tptp.aa_int_Code_integer tptp.code_integer_of_int X))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Xa2) X)))) (forall ((Xa2 tptp.int) (X tptp.int)) (= (tptp.minus_8373710615458151222nteger (tptp.aa_int_Code_integer tptp.code_integer_of_int Xa2) (tptp.aa_int_Code_integer tptp.code_integer_of_int X)) (tptp.aa_int_Code_integer tptp.code_integer_of_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Xa2) X)))) (= tptp.code_positive tptp.numera6620942414471956472nteger) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.code_integer_of_num N2))) (= (tptp.aa_num_Code_integer tptp.code_integer_of_num (tptp.aa_num_num tptp.bit1 N2)) (tptp.plus_p5714425477246183910nteger (tptp.plus_p5714425477246183910nteger _let_1 _let_1) tptp.one_one_Code_integer)))) (= tptp.code_integer_of_num tptp.numera6620942414471956472nteger) (= (tptp.aa_num_Code_integer tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.code_integer_of_num N2))) (= (tptp.aa_num_Code_integer tptp.code_integer_of_num (tptp.aa_num_num tptp.bit0 N2)) (tptp.plus_p5714425477246183910nteger _let_1 _let_1)))) (= (tptp.aa_num_Code_integer tptp.code_integer_of_num _let_1) _let_35) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.code_int_of_integer K))) (let ((_let_2 (= K tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger K) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_3 (= _let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger K))))) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 (tptp.produc1553301316500091796er_int tptp.aTP_Lamm_abh (tptp.code_divmod_integer K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))))))))))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.code_bit_cut_integer K) (tptp.produc5135875973608410785r_bool (tptp.divide6298287555418463151nteger K _let_1) (tptp.aa_bool_bool tptp.fNot (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer _let_1) K)))))) (forall ((K tptp.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_abi (tptp.code_divmod_integer K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.ord_max_Code_integer K L)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.ord_max_int (tptp.code_int_of_integer K)) (tptp.code_int_of_integer L)))) (forall ((K tptp.num)) (= (tptp.code_int_of_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K)) (tptp.aa_num_int tptp.numeral_numeral_int K))) (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.plus_p5714425477246183910nteger X Xa2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.code_int_of_integer X)) (tptp.code_int_of_integer Xa2)))) (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger X) Xa2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.code_int_of_integer X)) (tptp.code_int_of_integer Xa2)))) (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (tptp.code_int_of_integer (tptp.minus_8373710615458151222nteger X Xa2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.code_int_of_integer X)) (tptp.code_int_of_integer Xa2)))) (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger X) Xa2)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.code_int_of_integer X)) (tptp.code_int_of_integer Xa2))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) L)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.code_int_of_integer K)) (tptp.code_int_of_integer L))))) (forall ((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_abj K) (tptp.code_divmod_abs K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((K tptp.code_integer)) (let ((_let_1 (tptp.code_nat_of_integer K))) (let ((_let_2 (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger)))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.produc1555791787009142072er_nat tptp.aTP_Lamm_abk (tptp.code_divmod_integer K (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))))))))) (forall ((K tptp.code_integer)) (= (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.code_nat_of_integer K)) (tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger K))) (forall ((K tptp.code_integer)) (=> (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger)) (= (tptp.code_nat_of_integer K) tptp.zero_zero_nat))) (forall ((K tptp.num)) (= (tptp.code_nat_of_integer (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger K)) (tptp.aa_num_nat tptp.numeral_numeral_nat K))) (= (tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat) (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_ai) 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_abl 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_abm L) _let_1)))))))))))))))))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial N2) K) (tptp.finite_card_set_nat (tptp.collect_set_nat (tptp.aa_nat8857836526276733660t_bool (tptp.aTP_Lamm_abn N2) K))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit1 K)))) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc K)))))) (forall ((M tptp.nat) (K tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc K))) (let ((_let_2 (tptp.nat_prod_decode_aux K M))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) K)))) (and (=> _let_3 (= _let_2 (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat M) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat K) M)))) (=> (not _let_3) (= _let_2 (tptp.nat_prod_decode_aux _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) _let_1))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc X))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa2) X)))) (=> (= (tptp.nat_prod_decode_aux X Xa2) Y) (and (=> _let_2 (= Y (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (tptp.nat_prod_decode_aux _let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Xa2) _let_1))))))))) (forall ((N2 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_se8568078237143864401it_int N2) K))) (tptp.pp (tptp.aa_int_bool _let_1 K))))) (forall ((N2 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_se8568078237143864401it_int N2) 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 ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int N2) _let_1) _let_1))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat tptp.suc N2)) (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_nat_fun_int_int tptp.bit_se8568078237143864401it_int N2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))))) (forall ((L tptp.num) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.numeral_numeral_nat L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 K)))) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int (tptp.aa_num_nat tptp.pred_numeral L)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat tptp.suc N2)) (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_nat_fun_int_int tptp.bit_se8568078237143864401it_int N2) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.inc K)))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int M) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se545348938243370406it_int N2) K)) (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat M) N2)) (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 N2) M)) K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se8568078237143864401it_int N2) K) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.divide_divide_int K) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) N2)))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Xa2))))) (let ((_let_2 (tptp.aa_nat_nat tptp.suc X))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Xa2) X)))) (=> (= (tptp.nat_prod_decode_aux X Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Xa2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (tptp.nat_prod_decode_aux _let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))) (forall ((K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_Pro4243173770044397973at_nat tptp.product_snd_nat_nat (tptp.unique5055182867167087721od_nat tptp.one K)))) (forall ((K tptp.num)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)) (tptp.aa_num_nat tptp.numeral_numeral_nat K)) (tptp.aa_Pro4243173770044397973at_nat tptp.product_fst_nat_nat (tptp.unique5055182867167087721od_nat tptp.one K)))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N2) (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 N2) tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.aa_Pro4243173770044397973at_nat tptp.product_fst_nat_nat (tptp.divmod_nat M N2)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (forall ((N2 tptp.nat) (K tptp.int)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N2) (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_se8568078237143864401it_int N2) K)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se8570568707652914677it_nat N2) 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))) N2)))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int tptp.one_one_int) (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.adjust_mod _let_1) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int (tptp.unique5052692396658037445od_int tptp.one N2))))))) (forall ((N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.adjust_mod _let_1) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int (tptp.unique5052692396658037445od_int tptp.one N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int M))) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.adjust_mod _let_1) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int (tptp.unique5052692396658037445od_int M N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.aa_int_int tptp.uminus_uminus_int _let_1)) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.adjust_mod _let_1) (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int (tptp.unique5052692396658037445od_int M N2))))))) (forall ((R2 tptp.int) (L tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.adjust_mod L) R2))) (let ((_let_2 (= R2 tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int L) R2))))))) (forall ((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.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_1))) (let ((_let_3 (tptp.bezw X Y))) (let ((_let_4 (= Y tptp.zero_zero_nat))) (and (=> _let_4 (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= _let_3 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Y))))))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (tptp.bezw Xa2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (tptp.bezw X Xa2) Y) (and (=> _let_3 (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_2) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Xa2))))))))))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Xa2))))) (let ((_let_2 (tptp.bezw Xa2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (tptp.bezw X Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_3) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro6799258434465214121nt_int tptp.product_fst_int_int _let_2)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int _let_3) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))) (forall ((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.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_1))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) Y)) (= (tptp.bezw X Y) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_2) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro6799258434465214121nt_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 ((P2 tptp.product_prod_int_int)) (let ((_let_1 (tptp.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int P2))) (let ((_let_2 (tptp.aa_Pro6799258434465214121nt_int 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.aa_Pro6970504127699319548nt_int tptp.normalize P2))) (let ((_let_8 (= _let_1 tptp.zero_zero_int))) (let ((_let_9 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int tptp.zero_zero_int) _let_1)))) (and (=> _let_9 (= _let_7 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int _let_6 _let_3)) (tptp.aa_int_int _let_5 _let_3)))) (=> (not _let_9) (and (=> _let_8 (= _let_7 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))) (=> (not _let_8) (= _let_7 (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int _let_6 _let_4)) (tptp.aa_int_int _let_5 _let_4))))))))))))))))) (forall ((S3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (exists ((R3 tptp.fun_nat_nat)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.strict1292158309912662752at_nat R3) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_set_nat_nat tptp.finite_card_nat S3)))) (forall ((N8 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N8) (tptp.aa_set_nat_nat tptp.finite_card_nat S3))) (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat (tptp.aa_nat_nat R3 N8)) S3)))))))) (forall ((N2 tptp.num) (X tptp.int)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (= (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) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (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 ((X tptp.int) (Y tptp.int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (exists ((U2 tptp.int) (V2 tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int U2) X)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int V2) Y)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int X) Y)))) (forall ((K tptp.int) (M tptp.int) (N2 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) N2)) (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 N2))))) (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 ((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 ((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 ((N2 tptp.nat) (P tptp.fun_nat_bool) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) K2)) (tptp.pp (tptp.aa_nat_bool P K2)))) (=> (forall ((K2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K2) N2)) (=> (forall ((I tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat K2) I)) (tptp.pp (tptp.aa_nat_bool P I)))) (tptp.pp (tptp.aa_nat_bool P K2))))) (tptp.pp (tptp.aa_nat_bool P M))))) (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 ((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) (N2 tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N2))) (or (not (= M tptp.zero_zero_nat)) (not (= N2 tptp.zero_zero_nat))))) (forall ((K tptp.nat) (M tptp.nat) (N2 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) N2)) (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 N2))))) (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 ((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 ((M tptp.nat) (N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat M) N2)) (= (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 N2) M)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) 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) N2)) N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N2)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X3 tptp.nat) (Y4 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) Y4)) (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) (Y4 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 Y4))) (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 Y4))) (let ((_let_7 (tptp.aa_nat_nat _let_2 X3))) (or (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_6) _let_7)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_3) _let_5)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))) (forall ((X tptp.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.aa_Pro6799258434465214121nt_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.aa_Pro6799258434465214121nt_int tptp.product_snd_int_int _let_1)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Y)))))) (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) Xa2))))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat Xa2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat X) Xa2))))) (not _let_1)))))))) (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 ((K tptp.int) (N2 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 N2))) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int _let_1 (tptp.aa_num_int (tptp.neg_numeral_sub_int N2) tptp.one)))))) (forall ((N2 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 N2))) K) (tptp.aa_int_int tptp.bit_ri7919022796975470100ot_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.bit_se6526347334894502574or_int (tptp.aa_num_int (tptp.neg_numeral_sub_int N2) tptp.one)) K)))) (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 ((N2 tptp.num)) (= (tptp.aa_num_int (tptp.neg_numeral_sub_int (tptp.aa_num_num tptp.bitM N2)) tptp.one) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_num_int (tptp.neg_numeral_sub_int N2) tptp.one)))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.set_or5834768355832116004an_nat L U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat U) (tptp.aa_nat_nat tptp.suc L)))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc L) U) (tptp.set_or5834768355832116004an_nat L U))) (forall ((N2 tptp.nat)) (= (tptp.compow_fun_nat_nat N2 tptp.suc) (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2))) (tptp.semila1623282765462674594er_nat tptp.ord_max_nat tptp.zero_zero_nat tptp.aTP_Lamm_bz tptp.aTP_Lamm_ca) (tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat tptp.zero_zero_nat tptp.dvd_dvd_nat tptp.aTP_Lamm_abo) (forall ((M7 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat M7)) (= (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat M7) (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat (tptp.minus_minus_set_nat M7 (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat)))))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_abq) Xa2) X)))) (forall ((Z tptp.int)) (not (forall ((X3 tptp.nat) (Y4 tptp.nat)) (not (= Z (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X3) Y4))))))) (forall ((N3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.one_one_nat) N3)) (= (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat N3) tptp.one_one_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))) (= tptp.zero_zero_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_int tptp.semiri1314217659103216013at_int N2) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))) (forall ((X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_abr) X)))) (= tptp.one_one_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_abt) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X))) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_abv) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_abx) Xa2) X)))) (forall ((Xa2 tptp.product_prod_nat_nat) (X tptp.product_prod_nat_nat)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ Xa2)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ X)) (tptp.aa_Pro4240683299535347697at_int tptp.abs_Integ (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_abz) Xa2) X)))) (forall ((K5 tptp.set_int)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int tptp.zero_zero_int) (tptp.gcd_Gcd_int K5)))) (forall ((X tptp.int) (Xa2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa2)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_abv) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ Xa2))))) (forall ((X tptp.int) (Xa2 tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int X) Xa2)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool (tptp.aa_Pro595088089689268830t_bool (tptp.produc5023667602222594023t_bool tptp.aTP_Lamm_abt) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ Xa2))))) (forall ((X tptp.int)) (= (tptp.aa_int_nat tptp.nat2 X) (tptp.aa_Pro4243173770044397973at_nat (tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (tptp.aa_int1417691210696471063at_nat tptp.rep_Integ X)))) (= tptp.nat_prod_encode (tptp.produc6842872674320459806at_nat tptp.aTP_Lamm_aca)) (= tptp.uminus_uminus_int (tptp.aa_fun8399641135911395862nt_int _let_34 (tptp.produc2626176000494625587at_nat tptp.aTP_Lamm_abr))) (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 ((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 ((K tptp.nat) (M tptp.nat)) (= (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.nat_prod_decode_aux K M)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.nat_triangle K)) M))) (= tptp.times_times_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_34 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_abq))) (= tptp.minus_minus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_34 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_abz))) (= tptp.plus_plus_int (tptp.map_fu8294830438409148311nt_int tptp.rep_Integ _let_34 (tptp.produc4528391901023682385at_nat tptp.aTP_Lamm_abx))) (= tptp.pred_nat (tptp.collec3392354462482085612at_nat (tptp.produc8955392012077580105t_bool tptp.aTP_Lamm_acb))) (forall ((N2 tptp.nat)) (let ((_let_1 (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat tptp.suc N2)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (and (=> _let_2 (= _let_1 (tptp.aa_num_num tptp.inc (tptp.aa_nat_num tptp.num_of_nat N2)))) (=> (not _let_2) (= _let_1 tptp.one)))))) (forall ((Q2 tptp.num)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_num_nat tptp.numeral_numeral_nat Q2)) Q2)) (= (tptp.aa_nat_num tptp.num_of_nat tptp.zero_zero_nat) tptp.one) (forall ((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.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_nat_num tptp.num_of_nat N2)) N2))) (forall ((N2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N2) tptp.one_one_nat)) (= (tptp.aa_nat_num tptp.num_of_nat N2) tptp.one))) (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.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat N2) N2)) (tptp.aa_num_num tptp.bit0 (tptp.aa_nat_num tptp.num_of_nat N2))))) (forall ((M tptp.nat) (N2 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 N2)) (= (tptp.aa_nat_num tptp.num_of_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat M) N2)) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_nat_num tptp.num_of_nat M)) (tptp.aa_nat_num tptp.num_of_nat N2))))))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.pow X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.bit1 Y)) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num (tptp.aa_num_num tptp.sqr (tptp.aa_num_num _let_1 Y))) X)))) (= (tptp.aa_num_num tptp.sqr tptp.one) tptp.one) (forall ((N2 tptp.num)) (= (tptp.aa_num_num tptp.sqr (tptp.aa_num_num tptp.bit0 N2)) (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num tptp.sqr N2))))) (forall ((X tptp.num)) (= (tptp.aa_num_num tptp.sqr X) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.times_times_num X) X))) (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (tptp.aa_num_fun_num_num tptp.pow X))) (= (tptp.aa_num_num _let_1 (tptp.aa_num_num tptp.bit0 Y)) (tptp.aa_num_num tptp.sqr (tptp.aa_num_num _let_1 Y))))) (forall ((N2 tptp.num)) (= (tptp.aa_num_num tptp.sqr (tptp.aa_num_num tptp.bit1 N2)) (tptp.aa_num_num tptp.bit1 (tptp.aa_num_num tptp.bit0 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num (tptp.aa_num_num tptp.sqr N2)) N2))))) (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) (tptp.aa_nat_nat tptp.suc I2)))) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.linord2614967742042102400et_nat (tptp.set_or5834768355832116004an_nat I2 J))) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) N2))))) (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat N2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat J) I2))) (= (tptp.aa_nat_nat (tptp.nth_nat (tptp.linord2614967742042102400et_nat (tptp.set_or6659071591806873216st_nat I2 J))) N2) (tptp.aa_nat_nat tptp.suc (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat I2) N2))))) (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.fract A) B))) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat _let_1)) _let_2)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat _let_2) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((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_acc C) (tptp.set_or4665077453230672383an_nat X Y)))) (let ((_let_2 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat X) Y)))) (let ((_let_3 (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat C) Y)))) (and (=> _let_3 (= _let_1 (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat X) C) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= _let_1 (tptp.insert_nat tptp.zero_zero_nat tptp.bot_bot_set_nat))) (=> (not _let_2) (= _let_1 tptp.bot_bot_set_nat))))))))) (forall ((M7 tptp.set_nat) (N3 tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.bij_betw_nat_nat tptp.suc M7) N3)) (= (tptp.image_nat_nat tptp.suc M7) N3))) (forall ((I2 tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.set_or1269000886237332187st_nat I2 J)) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc I2) (tptp.aa_nat_nat tptp.suc J)))) (forall ((I2 tptp.nat) (J tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.set_or4665077453230672383an_nat I2 J)) (tptp.set_or4665077453230672383an_nat (tptp.aa_nat_nat tptp.suc I2) (tptp.aa_nat_nat tptp.suc J)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_int_rat (tptp.fract A) B)) (tptp.aa_int_rat (tptp.fract C) D)) (tptp.aa_int_rat (tptp.fract (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) C)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int B) D)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_int_rat (tptp.fract A) B)) (tptp.aa_int_rat (tptp.fract C) D)) (tptp.aa_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 ((L tptp.nat) (U tptp.nat)) (= (tptp.aa_set_nat_nat tptp.finite_card_nat (tptp.set_or6659071591806873216st_nat L U)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat U) L))) (forall ((A tptp.int) (B tptp.int)) (= (tptp.aa_rat_rat tptp.sgn_sgn_rat (tptp.aa_int_rat (tptp.fract A) B)) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int A)) (tptp.aa_int_int tptp.sgn_sgn_int 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.fract A) B)) (tptp.aa_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.plus_plus_rat (tptp.aa_int_rat (tptp.fract A) B)) (tptp.aa_int_rat (tptp.fract C) D)) (tptp.aa_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.fract A) B)) (tptp.aa_int_rat (tptp.fract C) D))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int A) D)) _let_1)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int C) B)) _let_1)))))))) (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_int_rat (tptp.fract A) B)) (tptp.aa_int_rat (tptp.fract C) D)) (tptp.aa_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 ((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 ((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.fract A) B) (tptp.aa_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 ((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.fract (tptp.aa_int_int _let_1 A)) (tptp.aa_int_int _let_1 B)) (tptp.aa_int_rat (tptp.fract A) B))))) (forall ((L tptp.nat) (U tptp.nat)) (= (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc L) U) (tptp.set_or6659071591806873216st_nat L U))) (forall ((K tptp.num)) (= (tptp.aa_num_rat tptp.numeral_numeral_rat K) (tptp.aa_int_rat (tptp.fract (tptp.aa_num_int tptp.numeral_numeral_int K)) tptp.one_one_int))) (forall ((W tptp.num)) (= (tptp.aa_int_rat (tptp.fract (tptp.aa_num_int tptp.numeral_numeral_int W)) tptp.one_one_int) (tptp.aa_num_rat tptp.numeral_numeral_rat W))) (forall ((N2 tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2)) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat N2))) (forall ((N2 tptp.nat)) (= (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2)) (tptp.set_or1269000886237332187st_nat tptp.one_one_nat (tptp.aa_nat_nat tptp.suc N2)))) (forall ((N2 tptp.nat)) (= (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat N2))))) (forall ((N2 tptp.nat)) (= (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))))) (forall ((N2 tptp.nat)) (= (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat (tptp.aa_nat_nat tptp.suc N2)) (tptp.insert_nat tptp.zero_zero_nat (tptp.image_nat_nat tptp.suc (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat N2))))) (forall ((N2 tptp.int) (M tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (tptp.aa_int_rat (tptp.fract (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int M) N2)) N2) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_int_rat (tptp.fract M) N2)) 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.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.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.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.fract A) B))) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int B) A))))) (forall ((K tptp.num)) (= (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat K)) (tptp.aa_int_rat (tptp.fract (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int K))) tptp.one_one_int))) (forall ((W tptp.num)) (= (tptp.aa_int_rat (tptp.fract (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int W))) tptp.one_one_int) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_num_rat tptp.numeral_numeral_rat W)))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Gcd_int (tptp.image_int_int tptp.abs_abs_int K5)) (tptp.gcd_Gcd_int K5))) (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 ((N3 tptp.set_nat)) (= (tptp.gcd_Gcd_int (tptp.image_nat_int tptp.semiri1314217659103216013at_int N3)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat N3)))) (forall ((K5 tptp.set_int)) (= (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat (tptp.image_int_nat tptp.aTP_Lamm_acd K5)) (tptp.aa_int_nat tptp.nat2 (tptp.gcd_Gcd_int K5)))) (forall ((S3 tptp.set_int)) (= (tptp.finite_finite_int S3) (exists ((K3 tptp.int)) (tptp.ord_less_eq_set_int (tptp.image_int_int tptp.abs_abs_int S3) (tptp.aa_int_set_int tptp.set_ord_lessThan_int K3))))) (forall ((S3 tptp.set_int)) (= (tptp.finite_finite_int S3) (exists ((K3 tptp.int)) (tptp.ord_less_eq_set_int (tptp.image_int_int tptp.abs_abs_int S3) (tptp.set_ord_atMost_int K3))))) (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 ((L tptp.int) (U tptp.int)) (= (tptp.image_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ace 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 ((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.comple7399068483239264473et_nat (tptp.image_nat_set_nat tptp.set_ord_atMost_nat tptp.top_top_set_nat)) tptp.top_top_set_nat) (= (tptp.comple7399068483239264473et_nat _let_22) tptp.top_top_set_nat) (= tptp.top_top_set_nat (tptp.insert_nat tptp.zero_zero_nat _let_29)) (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.image_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_acf N2) tptp.top_top_set_nat) (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat N2)))) (forall ((X6 tptp.fun_nat_real)) (=> (tptp.summable_real X6) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_nat_real X6 I3)))) (= (tptp.suminf_real X6) (tptp.comple1385675409528146559p_real (tptp.image_nat_real (tptp.aTP_Lamm_acg X6) tptp.top_top_set_nat)))))) (forall ((K5 tptp.set_int)) (= (tptp.gcd_Gcd_int K5) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat (tptp.image_int_nat (tptp.comp_int_nat_int tptp.nat2 tptp.abs_abs_int) K5))))) (= (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.finite_card_bool tptp.top_top_set_bool) _let_2) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root N2) X))) (let ((_let_2 (= N2 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_ach N2)) X))))))) (= (tptp.finite_card_char tptp.top_top_set_char) _let_31) (= _let_33 _let_33) (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_aci L) _let_1))))))))))))) (= tptp.code_negative (tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger tptp.numera6620942414471956472nteger)) (= tptp.code_Target_negative (tptp.comp_int_int_num tptp.uminus_uminus_int tptp.numeral_numeral_int)) (= tptp.top_top_set_char (tptp.image_nat_char tptp.unique3096191561947761185of_nat _let_32)) (forall ((X1 tptp.bool) (X22 tptp.bool) (X32 tptp.bool) (X42 tptp.bool) (X52 tptp.bool) (X62 tptp.bool) (X7 tptp.bool) (X8 tptp.bool)) (= (tptp.size_size_char (tptp.aa_bool_char (tptp.char2 X1 X22 X32 X42 X52 X62 X7) 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_32) (forall ((B0 tptp.bool) (B1 tptp.bool) (B22 tptp.bool) (B32 tptp.bool) (B42 tptp.bool) (B52 tptp.bool) (B62 tptp.bool) (B72 tptp.bool)) (let ((_let_1 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.integer_of_char (tptp.aa_bool_char (tptp.char2 B0 B1 B22 B32 B42 B52 B62) B72)) (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.zero_n356916108424825756nteger B72)) _let_1) (tptp.zero_n356916108424825756nteger B62))) _let_1) (tptp.zero_n356916108424825756nteger B52))) _let_1) (tptp.zero_n356916108424825756nteger B42))) _let_1) (tptp.zero_n356916108424825756nteger B32))) _let_1) (tptp.zero_n356916108424825756nteger B22))) _let_1) (tptp.zero_n356916108424825756nteger B1))) _let_1) (tptp.zero_n356916108424825756nteger B0))))) (forall ((K tptp.code_integer)) (= (tptp.char_of_integer K) (tptp.produc7257819798349884575l_char tptp.aTP_Lamm_acq (tptp.code_bit_cut_integer K)))) (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 ((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 ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_1) J)) (= (tptp.linord2614967742042102400et_nat (tptp.set_or6659071591806873216st_nat I2 J)) (tptp.cons_nat _let_1 (tptp.linord2614967742042102400et_nat (tptp.set_or6659071591806873216st_nat _let_1 J))))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat tptp.suc I2))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat _let_1) J)) (= (tptp.linord2614967742042102400et_nat (tptp.set_or5834768355832116004an_nat I2 J)) (tptp.cons_nat _let_1 (tptp.linord2614967742042102400et_nat (tptp.set_or5834768355832116004an_nat _let_1 J))))))) (forall ((X tptp.list_nat) (Y tptp.nat)) (=> (= (tptp.nat_list_encode X) Y) (=> (=> (= X tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((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.nat_list_encode Xs2)))))))))))) (forall ((J tptp.int) (I2 tptp.int) (Js tptp.list_int)) (let ((_let_1 (tptp.upto_aux I2 J Js))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)))) (and (=> _let_2 (= _let_1 Js)) (=> (not _let_2) (= _let_1 (tptp.upto_aux I2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int) (tptp.cons_int J Js)))))))) (= tptp.sup_sup_nat tptp.ord_max_nat) (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat) (= tptp.sup_sup_int tptp.ord_max_int) (forall ((I2 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 I2) J)) (= (tptp.set_or4665077453230672383an_nat I2 _let_1) (tptp.sup_sup_set_nat (tptp.set_or4665077453230672383an_nat I2 J) (tptp.set_or4665077453230672383an_nat J _let_1)))))) (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (tptp.nat_list_encode (tptp.cons_nat X Xs)) (tptp.aa_nat_nat tptp.suc (tptp.aa_Pro4243173770044397973at_nat tptp.nat_prod_encode (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat X) (tptp.nat_list_encode Xs)))))) (forall ((X tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (tptp.nat_list_encode X) Y) (=> (tptp.pp (tptp.aa_list_nat_bool _let_1 X)) (=> (=> (= X tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (tptp.pp (tptp.aa_list_nat_bool _let_1 tptp.nil_nat))))) (not (forall ((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.nat_list_encode Xs2))))) (not (tptp.pp (tptp.aa_list_nat_bool (tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1))))))))))))) (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.upto I2 J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)))) (=> (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int I2) J))) (and (=> _let_2 (= _let_1 (tptp.cons_int I2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int X) Xa2))))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa2)))) (=> (= (tptp.upto X Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (tptp.cons_int X (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))) (forall ((I2 tptp.int) (J tptp.int)) (= (= (tptp.upto I2 J) tptp.nil_int) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)))) (forall ((I2 tptp.int) (J tptp.int)) (= (= tptp.nil_int (tptp.upto I2 J)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)))) (forall ((J tptp.int) (I2 tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int J) I2)) (= (tptp.upto I2 J) tptp.nil_int))) (forall ((I2 tptp.int)) (= (tptp.upto I2 I2) (tptp.cons_int I2 tptp.nil_int))) (forall ((I2 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 I2) (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 I2 J)) K) _let_1)))) (forall ((I2 tptp.int) (J tptp.int)) (= (tptp.size_size_list_int (tptp.upto I2 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) I2)) tptp.one_one_int)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (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) (N2 tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (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) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_int tptp.numeral_numeral_int N2))) (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) (N2 tptp.num)) (let ((_let_1 (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2)))) (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 ((I2 tptp.int) (J tptp.int)) (= (tptp.set_or1266510415728281911st_int I2 J) (tptp.set_int2 (tptp.upto I2 J)))) (forall ((I2 tptp.int) (J tptp.int)) (tptp.pp (tptp.aa_list_int_bool tptp.distinct_int (tptp.upto I2 J)))) (forall ((I2 tptp.int) (J tptp.int)) (= (tptp.upto I2 J) (tptp.upto_aux I2 J tptp.nil_int))) (forall ((I2 tptp.int) (J tptp.int) (Js tptp.list_int)) (= (tptp.upto_aux I2 J Js) (tptp.append_int (tptp.upto I2 J) Js))) (forall ((I2 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 I2) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I2 K) (tptp.append_int (tptp.upto I2 J) (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int J) tptp.one_one_int) K)))))) (forall ((I2 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 I2) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I2 K) (tptp.append_int (tptp.upto I2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int)) (tptp.upto J K)))))) (forall ((I2 tptp.int) (J tptp.int)) (= (tptp.set_or4662586982721622107an_int I2 J) (tptp.set_int2 (tptp.upto I2 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int))))) (forall ((I2 tptp.int) (J tptp.int)) (= (tptp.set_or6656581121297822940st_int I2 J) (tptp.set_int2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) J)))) (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X) Xa2)))) (=> (= (tptp.upto X Xa2) Y) (and (=> _let_1 (= Y (tptp.cons_int X (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int X) tptp.one_one_int) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))) (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (tptp.upto I2 J))) (let ((_let_2 (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)))) (and (=> _let_2 (= _let_1 (tptp.cons_int I2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int)))))) (forall ((I2 tptp.int) (J tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (= (tptp.upto I2 J) (tptp.cons_int I2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) J))))) (forall ((I2 tptp.int) (J tptp.int)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int I2) J)) (= (tptp.upto I2 J) (tptp.append_int (tptp.upto I2 (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 ((I2 tptp.int) (J tptp.int)) (= (tptp.set_or5832277885323065728an_int I2 J) (tptp.set_int2 (tptp.upto (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int I2) tptp.one_one_int) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int J) tptp.one_one_int))))) (forall ((I2 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 I2) J)) (=> (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int J) K)) (= (tptp.upto I2 K) (tptp.append_int (tptp.upto I2 (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 ((N2 tptp.nat) (X tptp.real) (D2 tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root N2))) (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 N2)) (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 N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D2 _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))) N2)))) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (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)) (= D2 (tptp.aa_real_real tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (tptp.has_fi5821293074295781190e_real _let_1 D2 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4))) D)) (= (tptp.aa_real_real F X) (tptp.aa_real_real F Y4)))) (= L tptp.zero_zero_real))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (S3 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((H3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.member_real _let_1 S3) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D3)) (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) (S3 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((H3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.member_real _let_1 S3) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D3)) (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) (S3 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((H3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.member_real _let_1 S3) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D3)) (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) (S3 tptp.set_real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X S3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((H3 tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H3))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.member_real _let_1 S3) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D3)) (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) (Y tptp.real) (X tptp.real)) (= (tptp.has_fi5821293074295781190e_real F Y (tptp.topolo2177554685111907308n_real (tptp.aa_real_real tptp.uminus_uminus_real X) tptp.top_top_set_real)) (tptp.has_fi5821293074295781190e_real (tptp.aTP_Lamm_acr F) (tptp.aa_real_real tptp.uminus_uminus_real Y) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (tptp.has_fi5821293074295781190e_real F K (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B)) (tptp.aa_real_real F A)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)) K))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((H3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X)) (tptp.aa_real_real F (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H3)))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real L) tptp.zero_zero_real)) (exists ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((H3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real X) H3))) (tptp.aa_real_real F X))))))))))) (forall ((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 ((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 ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((H3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X)) (tptp.aa_real_real F (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H3)))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((D3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D3)) (forall ((H3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) H3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H3) D3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) H3))) (tptp.aa_real_real F X))))))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y2 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y2 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y2) tptp.zero_zero_real))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F B)) (tptp.aa_real_real F A)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y2 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y2 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y2))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F A)) (tptp.aa_real_real F B)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y2 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y2 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Y2))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F A)) (tptp.aa_real_real F B)))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y2 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y2 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y2) tptp.zero_zero_real))))))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F B)) (tptp.aa_real_real F A)))))) (forall ((A tptp.real) (B tptp.real) (G tptp.fun_real_real) (G2 tptp.fun_real_real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1222579329274155063t_real A B)) (tptp.has_fi5821293074295781190e_real G (tptp.aa_real_real G2 X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1222579329274155063t_real A B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real G2 X3))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real G A)) (tptp.aa_real_real G B))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (F3 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 F3 X3) (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))))) (exists ((Z3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) 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 F3 Z3)))))))) (forall ((A tptp.real) (B tptp.real) (V tptp.fun_real_real) (K tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (=> (not (= A B)) (=> (forall ((X3 tptp.real)) (tptp.has_fi5821293074295781190e_real V K (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))) (= (tptp.aa_real_real V (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real A) B)) _let_1)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real V A)) (tptp.aa_real_real V B))) _let_1)))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4))) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F X)) (tptp.aa_real_real F Y4))))) (= L tptp.zero_zero_real))))) (forall ((F tptp.fun_real_real) (L tptp.real) (X tptp.real) (D tptp.real)) (=> (tptp.has_fi5821293074295781190e_real F L (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Y4 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X) Y4))) D)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real F Y4)) (tptp.aa_real_real F X))))) (= L tptp.zero_zero_real))))) (forall ((N2 tptp.nat) (X tptp.real) (S2 tptp.set_real)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_acs N2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real N2)) (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 N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))) (tptp.topolo2177554685111907308n_real X S2))) (forall ((G tptp.fun_real_real) (M tptp.real) (X tptp.real) (N2 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_act G) N2) (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 N2)) (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 N2) tptp.one_one_nat)))) M) _let_1)))) (forall ((Z tptp.real) (R2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Z)) (tptp.has_fi5821293074295781190e_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_acu R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Z) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R2) tptp.one_one_real))) (tptp.topolo2177554685111907308n_real Z tptp.top_top_set_real)))) (forall ((F tptp.fun_re4238438383274954274t_real) (F3 tptp.fun_re4238438383274954274t_real) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 tptp.fun_nat_real)) (let ((_let_1 (tptp.aa_real_fun_nat_real F3 X0))) (=> (forall ((N tptp.nat)) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_jg F) N) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real F3 X0) N) (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 L5) (=> (forall ((N tptp.nat) (X3 tptp.real) (Y4 tptp.real)) (let ((_let_1 (tptp.set_or1633881224788618240n_real A B))) (=> (tptp.member_real X3 _let_1) (=> (tptp.member_real Y4 _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real F X3) N)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real F Y4) N)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real L5 N)) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real X3) Y4))))))))) (tptp.has_fi5821293074295781190e_real (tptp.aTP_Lamm_qo F) (tptp.suminf_real _let_1) (tptp.topolo2177554685111907308n_real X0 tptp.top_top_set_real)))))))))) (forall ((X tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.has_fi5821293074295781190e_real (tptp.aa_rea7340605660300375871l_real tptp.log B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real tptp.ln_ln_real B)) X)) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((G tptp.fun_real_real) (M tptp.real) (X tptp.real) (R2 tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (let ((_let_2 (tptp.aa_real_real G X))) (=> (tptp.has_fi5821293074295781190e_real G M _let_1) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (tptp.has_fi5821293074295781190e_real (tptp.aa_rea7340605660300375871l_real (tptp.aTP_Lamm_acv G) R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real _let_2) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real R2) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M) _let_1)))))) (forall ((G tptp.fun_real_real) (M tptp.real) (X tptp.real) (F tptp.fun_real_real) (R2 tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (let ((_let_2 (tptp.aa_real_real G X))) (let ((_let_3 (tptp.aa_real_real F X))) (=> (tptp.has_fi5821293074295781190e_real G M _let_1) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_2)) (=> (tptp.has_fi5821293074295781190e_real F R2 _let_1) (tptp.has_fi5821293074295781190e_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_acw G) F) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real _let_2) _let_3)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real R2) (tptp.aa_real_real tptp.ln_ln_real _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real M) _let_3)) _let_2))) _let_1)))))))) (forall ((X tptp.real) (A2 tptp.set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.abs_abs_real X)) tptp.one_one_real)) (tptp.has_fi5821293074295781190e_real tptp.artanh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.topolo2177554685111907308n_real X A2)))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (tptp.has_fi5821293074295781190e_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X))) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((X tptp.real)) (tptp.has_fi5821293074295781190e_real tptp.arctan (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real tptp.one_one_real) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))) (forall ((X tptp.real) (A2 tptp.set_real)) (tptp.has_fi5821293074295781190e_real tptp.arsinh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real))) (tptp.topolo2177554685111907308n_real X A2))) (forall ((X tptp.real) (D2 tptp.real)) (let ((_let_1 (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_real_real tptp.sqrt X)))) (=> (not (= X tptp.zero_zero_real)) (=> (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) X)) (= D2 (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)) (= D2 (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 D2 (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))))))) (forall ((X tptp.real) (A2 tptp.set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.has_fi5821293074295781190e_real tptp.arcosh_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_real_real tptp.sqrt (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_real))) (tptp.topolo2177554685111907308n_real X A2)))) (forall ((R tptp.real) (F tptp.fun_nat_real) (X0 tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real R) R)) (tptp.summable_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_acx F) X3)))) (=> (tptp.member_real X0 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real R) R)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R)) (tptp.has_fi5821293074295781190e_real (tptp.aTP_Lamm_acz F) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_acx F) X0)) (tptp.topolo2177554685111907308n_real X0 tptp.top_top_set_real)))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root 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_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 N2)) (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 N2) (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) (N2 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 ((T5 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 T5)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ada Diff) X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)))))))) (forall ((Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (X tptp.real) (N2 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 ((T5 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 T5)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ada Diff) X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2))))))))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root 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))) N2))) (=> (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 N2)) (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 N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))))) (forall ((H tptp.real) (N2 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) N2)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T5) (tptp.topolo2177554685111907308n_real T5 tptp.top_top_set_real)))) (exists ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5) H)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_ss H) Diff)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real H) N2))))))))))) (forall ((H tptp.real) (Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (N2 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) (T5 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T5) (tptp.topolo2177554685111907308n_real T5 tptp.top_top_set_real)))) (exists ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) H)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_ss H) Diff)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real H) N2)))))))))) (forall ((H tptp.real) (N2 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) N2)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real H) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) 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)) T5) (tptp.topolo2177554685111907308n_real T5 tptp.top_top_set_real)))) (exists ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real H) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5) tptp.zero_zero_real)) (= (tptp.aa_real_real F H) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_ss H) Diff)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real H) N2))))))))))) (forall ((Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (N2 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) N2)) (=> (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 ((T5 tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.abs_abs_real T5))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real _let_1) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ada Diff) X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2)))))))))))) (forall ((Diff tptp.fun_na6724076748692969250l_real) (F tptp.fun_real_real) (N2 tptp.nat) (X tptp.real)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real T5)) (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)) T5) (tptp.topolo2177554685111907308n_real T5 tptp.top_top_set_real)))) (exists ((T5 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 T5)) (tptp.aa_real_real tptp.abs_abs_real X))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ada Diff) X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) N2))))))))) (forall ((N2 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) N2)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) 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)) T5) (tptp.topolo2177554685111907308n_real T5 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 ((T5 tptp.real)) (let ((_let_1 (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5))) (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 T5)) (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) T5)) (tptp.pp (tptp.aa_real_bool _let_1 X)))) (= (tptp.aa_real_real F X) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_adb Diff) C) X)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (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)) N2))))))))))))))))))) (forall ((N2 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) N2)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) 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)) T5) (tptp.topolo2177554685111907308n_real T5 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 ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5) B)) (= (tptp.aa_real_real F B) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_adc Diff) B) C)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (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)) N2)))))))))))) (forall ((N2 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) N2)) (=> (= (tptp.aa_nat_fun_real_real Diff tptp.zero_zero_nat) F) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) 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)) T5) (tptp.topolo2177554685111907308n_real T5 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 ((T5 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real T5) C)) (= (tptp.aa_real_real F A) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_adc Diff) A) C)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat N2))) (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 N2) T5)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real N2))) (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)) N2)))))))))))) (forall ((N2 tptp.nat) (H tptp.real) (Diff tptp.fun_na6724076748692969250l_real) (K tptp.nat) (B3 tptp.real)) (=> (forall ((M2 tptp.nat) (T5 tptp.real)) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M2) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T5)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T5) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real Diff M2) (tptp.aa_real_real (tptp.aa_nat_fun_real_real Diff (tptp.aa_nat_nat tptp.suc M2)) T5) (tptp.topolo2177554685111907308n_real T5 tptp.top_top_set_real)))) (=> (= N2 (tptp.aa_nat_nat tptp.suc K)) (forall ((M3 tptp.nat) (T6 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 N2) _let_1))) (=> (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M3) N2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) T6)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real T6) H))) (tptp.has_fi5821293074295781190e_real (tptp.aa_nat_fun_real_real (tptp.aa_rea1103652080130114956l_real (tptp.aa_fun2567993205388704171l_real (tptp.aTP_Lamm_ade N2) Diff) B3) 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) T6)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_adf Diff) M3) T6)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_2))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real B3) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real T6) _let_2)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_2))))) (tptp.topolo2177554685111907308n_real T6 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_adg (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_adh X)) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real)))) (forall ((N2 tptp.nat) (X tptp.real)) (let ((_let_1 (tptp.aa_nat_fun_real_real tptp.root 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 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (=> (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 N2))) (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 N2) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))) (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat M))) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int tptp.bit_se2923211474154528505it_int _let_1) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_num_int tptp.numeral_numeral_int N2))) (tptp.case_option_int_num tptp.zero_zero_int (tptp.aTP_Lamm_adi M) (tptp.bit_take_bit_num _let_1 N2))))) (forall ((M tptp.num) (N2 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 N2)))) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num M (tptp.aa_num_num tptp.bitM N2))))) (forall ((M tptp.num)) (= (tptp.bit_take_bit_num tptp.zero_zero_nat M) tptp.none_num)) (forall ((N2 tptp.nat)) (= (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N2) tptp.one) (tptp.some_num tptp.one))) (forall ((R2 tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R2) tptp.one) (tptp.some_num tptp.one))) (forall ((N2 tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N2) (tptp.aa_num_num tptp.bit0 M)) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_adj (tptp.bit_take_bit_num N2 M)))) (forall ((N2 tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_nat_nat tptp.suc N2) (tptp.aa_num_num tptp.bit1 M)) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.bit_take_bit_num N2 M))))) (forall ((R2 tptp.num) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R2) (tptp.aa_num_num tptp.bit0 M)) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_adj (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.pred_numeral R2) M)))) (forall ((R2 tptp.num) (M tptp.num)) (= (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.numeral_numeral_nat R2) (tptp.aa_num_num tptp.bit1 M)) (tptp.some_num (tptp.case_option_num_num tptp.one tptp.bit1 (tptp.bit_take_bit_num (tptp.aa_num_nat tptp.pred_numeral R2) M))))) (forall ((N2 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 N2)))) (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 N2))))) (forall ((M tptp.num) (N2 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 N2)))) (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 N2))))) (forall ((N2 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 N2)))) (tptp.aa_num_int tptp.numeral_numeral_int M)) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num M (tptp.aa_num_num tptp.bitM N2))))) (forall ((N2 tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num N2 (tptp.aa_num_num tptp.bit0 M)) (tptp.case_nat_option_num tptp.none_num (tptp.aTP_Lamm_adk M) N2))) (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 ((N2 tptp.num)) (= (tptp.bit_and_not_num tptp.one (tptp.aa_num_num tptp.bit0 N2)) (tptp.some_num tptp.one))) (forall ((N2 tptp.num)) (= (tptp.bit_and_not_num tptp.one (tptp.aa_num_num tptp.bit1 N2)) tptp.none_num)) (= (tptp.bit_and_not_num tptp.one tptp.one) tptp.none_num) (forall ((N2 tptp.nat)) (= (tptp.bit_take_bit_num N2 tptp.one) (tptp.case_nat_option_num tptp.none_num tptp.aTP_Lamm_adl N2))) (forall ((N2 tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num N2 (tptp.aa_num_num tptp.bit1 M)) (tptp.case_nat_option_num tptp.none_num (tptp.aTP_Lamm_adm M) N2))) (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) (N2 tptp.num) (Q2 tptp.num)) (= (= (tptp.bit_and_not_num M N2) (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 N2))) (tptp.aa_num_int tptp.numeral_numeral_int Q2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (tptp.bit_and_not_num (tptp.aa_num_num tptp.bit1 M) (tptp.aa_num_num tptp.bit0 N2)) (tptp.case_o6005452278849405969um_num (tptp.some_num tptp.one) tptp.aTP_Lamm_adn (tptp.bit_and_not_num M N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (tptp.bit_and_not_num M N2) 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 N2))) tptp.zero_zero_int))) (forall ((M tptp.num) (N2 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 N2)) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num N2 M)))) (forall ((M tptp.num) (N2 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 N2))) (tptp.case_option_int_num tptp.zero_zero_int tptp.numeral_numeral_int (tptp.bit_and_not_num M N2)))) (forall ((N2 tptp.nat) (M tptp.num)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.bit_se2925701944663578781it_nat N2) (tptp.aa_num_nat tptp.numeral_numeral_nat M)))) (let ((_let_2 (tptp.bit_take_bit_num N2 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 ((N2 tptp.nat) (M tptp.num)) (= (tptp.bit_take_bit_num N2 M) (tptp.produc478579273971653890on_num tptp.aTP_Lamm_adr (tptp.product_Pair_nat_num N2 M)))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real) F))) (exists ((L6 tptp.real) (M8 tptp.real)) (and (forall ((X2 tptp.real)) (let ((_let_1 (tptp.aa_real_real F X2))) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X2) B))) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L6) _let_1)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real _let_1) M8)))))) (forall ((Y2 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L6) Y2)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Y2) M8))) (exists ((X3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (= (tptp.aa_real_real F X3) Y2)))))))))) (forall ((X tptp.real)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) tptp.sqrt)) (forall ((X tptp.real) (N2 tptp.nat)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) (tptp.aa_nat_fun_real_real tptp.root N2))) (forall ((A tptp.real) (X tptp.real) (B tptp.real) (G tptp.fun_real_real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) B)) (=> (forall ((Z3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z3) B)) (= (tptp.aa_real_real G (tptp.aa_real_real F Z3)) Z3)))) (=> (forall ((Z3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z3) B)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z3 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 ((B tptp.real) (X tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) X)) (=> (forall ((X3 tptp.real)) (=> (tptp.member_real X3 (tptp.set_or1633881224788618240n_real B X)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F X3))))) (=> (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X tptp.top_top_set_real) F) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) (tptp.aa_real_real F X))))))) (forall ((D tptp.real) (X tptp.real) (G tptp.fun_real_real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) D)) (=> (forall ((Z3 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 Z3) X))) D)) (= (tptp.aa_real_real G (tptp.aa_real_real F Z3)) Z3))) (=> (forall ((Z3 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 Z3) X))) D)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z3 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) (F3 tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((Z3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z3) B)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z3 tptp.top_top_set_real) F)))) (=> (forall ((Z3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) Z3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Z3) B)) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real Z3 tptp.top_top_set_real) G)))) (=> (forall ((Z3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) B)) (tptp.has_fi5821293074295781190e_real G (tptp.aa_real_real G2 Z3) (tptp.topolo2177554685111907308n_real Z3 tptp.top_top_set_real))))) (=> (forall ((Z3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) B)) (tptp.has_fi5821293074295781190e_real F (tptp.aa_real_real F3 Z3) (tptp.topolo2177554685111907308n_real Z3 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 F3 C3))))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (C tptp.real)) (=> (tptp.filterlim_real_real F (tptp.topolo2815343760600316023s_real L) (tptp.topolo2177554685111907308n_real C tptp.top_top_set_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) L)) (exists ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (forall ((X2 tptp.real)) (=> (and (not (= X2 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) X2))) R3))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_real_real F X2)))))))))) (forall ((F tptp.fun_real_real) (L tptp.real) (C tptp.real)) (=> (tptp.filterlim_real_real F (tptp.topolo2815343760600316023s_real L) (tptp.topolo2177554685111907308n_real C tptp.top_top_set_real)) (=> (not (= L tptp.zero_zero_real)) (exists ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (forall ((X2 tptp.real)) (=> (and (not (= X2 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) X2))) R3))) (not (= (tptp.aa_real_real F X2) 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 ((R3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) R3)) (forall ((X2 tptp.real)) (=> (and (not (= X2 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) X2))) R3))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real F X2)) tptp.zero_zero_real))))))))) (tptp.filterlim_real_real tptp.aTP_Lamm_ads _let_27 (tptp.topolo2177554685111907308n_real _let_25 tptp.top_top_set_real)) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) (tptp.aa_nat_real A tptp.zero_zero_nat))) (forall ((N8 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N8))) (let ((_let_2 (tptp.aTP_Lamm_adt A))) (let ((_let_3 (tptp.groups6591440286371151544t_real _let_2))) (tptp.member_real (tptp.suminf_real _let_2) (tptp.set_or1222579329274155063t_real (tptp.aa_set_nat_real _let_3 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)) (tptp.aa_set_nat_real _let_3 (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 ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_nat_real A tptp.zero_zero_nat)) tptp.zero_zero_real)) (forall ((N8 tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N8))) (let ((_let_2 (tptp.aTP_Lamm_adt A))) (let ((_let_3 (tptp.groups6591440286371151544t_real _let_2))) (tptp.member_real (tptp.suminf_real _let_2) (tptp.set_or1222579329274155063t_real (tptp.aa_set_nat_real _let_3 (tptp.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.aa_set_nat_real _let_3 (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat _let_1)))))))))))) (tptp.filterlim_nat_nat tptp.suc tptp.at_top_nat tptp.at_top_nat) (forall ((C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.filterlim_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ao C) tptp.at_top_nat tptp.at_top_nat))) (forall ((C tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) C)) (tptp.filterlim_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat C) tptp.at_top_nat tptp.at_top_nat))) (forall ((X6 tptp.fun_nat_real) (B3 tptp.real)) (=> (tptp.topolo6980174941875973593q_real X6) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real X6 I3))) B3))) (not (forall ((L6 tptp.real)) (not (tptp.filterlim_nat_real X6 (tptp.topolo2815343760600316023s_real L6) tptp.at_top_nat))))))) (tptp.filterlim_nat_real tptp.aTP_Lamm_adu (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (forall ((F tptp.fun_nat_real) (G tptp.fun_nat_real)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N)) (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N))))) (=> (forall ((N 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 N))) (tptp.aa_nat_real G N)))) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N)) (tptp.aa_nat_real G N)))) (=> (tptp.filterlim_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hr F) G) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (tptp.topolo2815343760600316023s_real L3))) (and (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N8)) L3))) (tptp.filterlim_nat_real F _let_1 tptp.at_top_nat) (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L3) (tptp.aa_nat_real G N8)))) (tptp.filterlim_nat_real G _let_1 tptp.at_top_nat))))))))) (forall ((X6 tptp.fun_nat_real)) (=> (forall ((R3 tptp.real)) (exists ((N6 tptp.nat)) (forall ((N tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N6) N)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real R3) (tptp.aa_nat_real X6 N))))))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_adv X6) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (tptp.filterlim_nat_real tptp.aTP_Lamm_adw _let_27 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_adx C) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat))) (tptp.filterlim_nat_real tptp.aTP_Lamm_ady _let_27 tptp.at_top_nat) (forall ((R2 tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_adz R2) (tptp.topolo2815343760600316023s_real R2) tptp.at_top_nat)) (forall ((F tptp.fun_nat_real) (L tptp.real)) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N)) (tptp.aa_nat_real F (tptp.aa_nat_nat tptp.suc N))))) (=> (forall ((N tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real F N)) L))) (=> (forall ((E2 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) E2)) (exists ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real F N8)) E2)))))) (tptp.filterlim_nat_real F (tptp.topolo2815343760600316023s_real L) tptp.at_top_nat))))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X) tptp.one_one_real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat)))) (forall ((X tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.one_one_real) X)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_aea 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_aeb X) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat))) (forall ((R2 tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_aec R2) (tptp.topolo2815343760600316023s_real R2) tptp.at_top_nat)) (forall ((X tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_aed X) (tptp.topolo2815343760600316023s_real (tptp.aa_real_real tptp.exp_real X)) tptp.at_top_nat)) (forall ((R2 tptp.real)) (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_aee R2) (tptp.topolo2815343760600316023s_real R2) tptp.at_top_nat)) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (tptp.summable_real (tptp.aTP_Lamm_adt A))))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (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 A N)))) (=> (forall ((N 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 N))) (tptp.aa_nat_real A N)))) (tptp.summable_real (tptp.aTP_Lamm_adt A)))))) (forall ((Theta tptp.fun_nat_real) (Theta2 tptp.real)) (=> (tptp.filterlim_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_aef Theta) Theta2) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (not (forall ((K2 tptp.fun_nat_int)) (not (tptp.filterlim_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_aeg Theta) K2) (tptp.topolo2815343760600316023s_real Theta2) tptp.at_top_nat)))))) (forall ((Theta tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real (tptp.aTP_Lamm_aeh Theta) (tptp.topolo2815343760600316023s_real tptp.one_one_real) tptp.at_top_nat) (exists ((K2 tptp.fun_nat_int)) (tptp.filterlim_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_aeg Theta) K2) (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat)))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (tptp.topolo6980174941875973593q_real A) (tptp.filterlim_nat_real (tptp.aTP_Lamm_aei A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_adt 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_nu X) (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) (=> (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 A N)))) (=> (forall ((N 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 N))) (tptp.aa_nat_real A N)))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_aei A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_adt A))) tptp.at_top_nat))))) (forall ((A tptp.fun_nat_real) (N2 tptp.nat)) (let ((_let_1 (tptp.aTP_Lamm_adt A))) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (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 A N)))) (=> (forall ((N 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 N))) (tptp.aa_nat_real A N)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_1) (tptp.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))) N2)))) (tptp.suminf_real _let_1)))))))) (forall ((A tptp.fun_nat_real)) (=> (forall ((N 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 N))) (tptp.aa_nat_real A 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 A N)))) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (exists ((L3 tptp.real)) (let ((_let_1 (tptp.topolo2815343760600316023s_real L3))) (and (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_adt 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))) N8)))) L3))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_aei A) _let_1 tptp.at_top_nat) (forall ((N8 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L3) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_adt 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))) N8)) tptp.one_one_nat)))))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_aej 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_aej A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_adt A))) tptp.at_top_nat)))) (forall ((A tptp.fun_nat_real) (N2 tptp.nat)) (let ((_let_1 (tptp.aTP_Lamm_adt A))) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (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 A N)))) (=> (forall ((N 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 N))) (tptp.aa_nat_real A N)))) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.suminf_real _let_1)) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real _let_1) (tptp.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))) N2)) tptp.one_one_nat)))))))))) (forall ((A tptp.fun_nat_real)) (=> (tptp.filterlim_nat_real A (tptp.topolo2815343760600316023s_real tptp.zero_zero_real) tptp.at_top_nat) (=> (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 A N)))) (=> (forall ((N 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 N))) (tptp.aa_nat_real A N)))) (tptp.filterlim_nat_real (tptp.aTP_Lamm_aej A) (tptp.topolo2815343760600316023s_real (tptp.suminf_real (tptp.aTP_Lamm_adt A))) tptp.at_top_nat))))) (forall ((F tptp.fun_real_real)) (= (tptp.real_V5970128139526366754l_real F) (exists ((C4 tptp.real)) (forall ((X4 tptp.real)) (= (tptp.aa_real_real F X4) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real X4) C4)))))) (forall ((X tptp.real)) (tptp.filterlim_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_aek 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)))) (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.aa_complex_real (tptp.real_V3694042436643373181omplex X) Y) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex X) Y)))) (= (tptp.comple7806235888213564991et_nat _let_21) tptp.bot_bot_set_nat) (= (tptp.aa_nat_set_nat tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) _let_29) (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.tan_real tptp.at_bot_real (tptp.topolo2177554685111907308n_real _let_28 (tptp.set_or5849166863359141190n_real _let_28))) (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))) (= (tptp.comple7399068483239264473et_nat (tptp.image_nat_set_nat tptp.set_ord_atLeast_nat tptp.top_top_set_nat)) tptp.top_top_set_nat) (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.filterlim_real_real tptp.ln_ln_real tptp.at_bot_real _let_26) (tptp.filterlim_real_real tptp.inverse_inverse_real tptp.at_bot_real (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5984915006950818249n_real tptp.zero_zero_real))) (forall ((B tptp.real) (F tptp.fun_real_real) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B)) (exists ((Y2 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y2 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real tptp.zero_zero_real) Y2)))))) (=> (tptp.filterlim_real_real F (tptp.topolo2815343760600316023s_real Flim) tptp.at_bot_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Flim) (tptp.aa_real_real F B)))))) (forall ((N2 tptp.nat) (F tptp.fun_real_real) (F4 tptp.filter_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.filterlim_real_real F tptp.at_bot_real F4) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2))) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_ael N2) F) tptp.at_bot_real F4))))) (tptp.filterlim_real_real tptp.arctan (tptp.topolo2815343760600316023s_real _let_28) tptp.at_bot_real) (forall ((M7 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat M7)) (=> (not (= M7 tptp.bot_bot_set_nat)) (=> (not (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat tptp.zero_zero_nat) M7))) (= (tptp.aa_set_nat_nat tptp.gcd_Gcd_nat M7) (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat (tptp.comple7806235888213564991et_nat (tptp.image_nat_set_nat tptp.aTP_Lamm_aem M7)))))))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (= (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_eu N2))) N2))) (tptp.ord_le4104064031414453916r_real tptp.at_bot_real tptp.at_infinity_real) (tptp.filterlim_real_real tptp.sqrt tptp.at_top_real tptp.at_top_real) (tptp.filterlim_real_real tptp.ln_ln_real tptp.at_top_real tptp.at_top_real) (tptp.filterlim_real_real tptp.exp_real tptp.at_top_real tptp.at_top_real) (tptp.filterlim_nat_real tptp.semiri5074537144036343181t_real tptp.at_top_real tptp.at_top_nat) (tptp.filterlim_real_real tptp.uminus_uminus_real tptp.at_top_real tptp.at_bot_real) (tptp.filterlim_real_real tptp.uminus_uminus_real tptp.at_bot_real tptp.at_top_real) (forall ((S3 tptp.set_nat)) (=> (tptp.pp (tptp.aa_set_nat_bool tptp.finite_finite_nat S3)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_set_nat_nat tptp.finite_card_nat S3)) (tptp.aa_nat_nat tptp.suc (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat S3)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat M) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aen N2) M))))))))) (forall ((N2 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) N2)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.gcd_gcd_nat M) N2) (tptp.aa_set_nat_nat tptp.lattic8265883725875713057ax_nat (tptp.collect_nat (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aeo N2) M)))))) (tptp.filterlim_real_real tptp.aTP_Lamm_aep _let_27 tptp.at_top_real) (tptp.filterlim_real_real tptp.inverse_inverse_real tptp.at_top_real _let_26) (tptp.filterlim_real_real tptp.inverse_inverse_real _let_26 tptp.at_top_real) (forall ((K tptp.nat)) (tptp.filterlim_real_real (tptp.aa_nat_fun_real_real tptp.aTP_Lamm_aeq 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_aer X) (tptp.topolo2815343760600316023s_real (tptp.aa_real_real tptp.exp_real X)) tptp.at_top_real)) (forall ((B tptp.real) (F tptp.fun_real_real) (Flim tptp.real)) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B) X3)) (exists ((Y2 tptp.real)) (and (tptp.has_fi5821293074295781190e_real F Y2 (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Y2) tptp.zero_zero_real)))))) (=> (tptp.filterlim_real_real F (tptp.topolo2815343760600316023s_real Flim) tptp.at_top_real) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Flim) (tptp.aa_real_real F B)))))) (tptp.filterlim_real_real tptp.arctan (tptp.topolo2815343760600316023s_real _let_25) tptp.at_top_real) (tptp.filterlim_real_real tptp.tan_real tptp.at_top_real (tptp.topolo2177554685111907308n_real _let_25 (tptp.set_or5984915006950818249n_real _let_25))) (forall ((N2 tptp.nat) (F tptp.fun_real_real) (F4 tptp.filter_real)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat tptp.zero_zero_nat) N2)) (=> (tptp.filterlim_real_real F tptp.at_bot_real F4) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) N2)) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_ael N2) F) tptp.at_top_real F4))))) (forall ((P tptp.fun_nat_bool)) (= (tptp.eventually_nat (tptp.aTP_Lamm_aes 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_aet P) K) tptp.at_top_nat) (tptp.eventually_nat P tptp.at_top_nat))) (forall ((N2 tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (tptp.lattic8263393255366662781ax_int (tptp.collect_int (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_ew N2))) (tptp.aa_int_int tptp.abs_abs_int N2)))) (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_aet P) K) tptp.at_top_nat))) (not (tptp.eventually_nat tptp.aTP_Lamm_az tptp.at_top_nat)) (tptp.ord_le4104064031414453916r_real tptp.at_top_real tptp.at_infinity_real) (forall ((F4 tptp.filter_nat)) (= (tptp.ord_le2510731241096832064er_nat F4 tptp.at_top_nat) (forall ((N9 tptp.nat)) (tptp.eventually_nat (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) F4)))) (forall ((P tptp.fun_nat_bool)) (= (tptp.eventually_nat P tptp.at_top_nat) (exists ((N9 tptp.nat)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) N5)) (tptp.pp (tptp.aa_nat_bool P N5))))))) (forall ((C tptp.nat) (P tptp.fun_nat_bool)) (=> (forall ((X3 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat C) X3)) (tptp.pp (tptp.aa_nat_bool P X3)))) (tptp.eventually_nat P tptp.at_top_nat))) (= tptp.topolo3078684682413903454n_bool (tptp.topolo2897919652413631970y_bool (tptp.sup_sup_set_set_bool (tptp.image_bool_set_bool tptp.set_or4454636193642143162n_bool tptp.top_top_set_bool) (tptp.image_bool_set_bool tptp.set_or5593231766841527037n_bool tptp.top_top_set_bool)))) (= tptp.topolo4325760605701065253en_int (tptp.topolo1611008123915946401gy_int (tptp.sup_sup_set_set_int (tptp.image_int_set_int tptp.set_ord_lessThan_int tptp.top_top_set_int) (tptp.image_int_set_int tptp.set_or1207661135979820486an_int tptp.top_top_set_int)))) (forall ((N2 tptp.int) (M tptp.int)) (=> (not (= N2 tptp.zero_zero_int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.gcd_gcd_int M) N2) (tptp.lattic8263393255366662781ax_int (tptp.collect_int (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_aeu N2) M)))))) (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_aev P) A) (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))) (forall ((P tptp.fun_real_bool)) (= (tptp.eventually_real P tptp.at_top_real) (tptp.eventually_real (tptp.aTP_Lamm_aew P) (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))) (forall ((P tptp.fun_real_bool)) (= (tptp.eventually_real P (tptp.topolo2177554685111907308n_real tptp.zero_zero_real (tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (tptp.eventually_real (tptp.aTP_Lamm_aew P) tptp.at_top_real))) (forall ((P tptp.fun_real_bool) (A tptp.real)) (let ((_let_1 (tptp.aa_real_real tptp.uminus_uminus_real A))) (= (tptp.eventually_real P (tptp.topolo2177554685111907308n_real A (tptp.set_or5984915006950818249n_real A))) (tptp.eventually_real (tptp.aTP_Lamm_aex P) (tptp.topolo2177554685111907308n_real _let_1 (tptp.set_or5849166863359141190n_real _let_1)))))) (forall ((A tptp.real) (B tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (tptp.eventually_real (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_aey A) B) (tptp.topolo2177554685111907308n_real A (tptp.set_or5849166863359141190n_real A))))) (forall ((B tptp.real) (A tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real B) A)) (tptp.eventually_real (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_aey B) A) (tptp.topolo2177554685111907308n_real A (tptp.set_or5984915006950818249n_real A))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F3 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_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F3) G2) tptp.at_top_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F) G) tptp.at_top_real _let_1)))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F3 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_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F3) G2) tptp.at_top_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F) G) tptp.at_top_real _let_1)))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F3 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_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F3) G2) tptp.at_bot_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F) G) tptp.at_bot_real _let_1)))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F3 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_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F3) G2) tptp.at_top_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa 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) (F3 tptp.fun_real_real) (F4 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_afb G) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_afb G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G2) F3) F4 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F) G) F4 _let_1))))))))))) (forall ((G tptp.fun_real_real) (X tptp.real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F3 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_afb G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G2) F3) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G) F) _let_2 _let_1))))))))) (forall ((G tptp.fun_real_real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F3 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_afb G2) tptp.at_top_real) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez F) F3) tptp.at_top_real) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) tptp.at_top_real) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G2) F3) _let_1 tptp.at_top_real) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G) F) _let_1 tptp.at_top_real)))))))) (= tptp.topolo4328251076210115529en_nat (tptp.topolo1613498594424996677gy_nat (tptp.sup_sup_set_set_nat _let_22 _let_21))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F3 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_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F3) G2) tptp.at_bot_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F) G) tptp.at_bot_real _let_1)))))))) (forall ((F tptp.fun_real_real) (A tptp.real) (G tptp.fun_real_real) (F3 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_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F3) G2) tptp.at_bot_real _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F) G) tptp.at_bot_real _let_1)))))))) (forall ((F tptp.fun_real_real) (X tptp.real) (G tptp.fun_real_real) (G2 tptp.fun_real_real) (F3 tptp.fun_real_real) (F4 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_afb G) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_afb G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G2) F3) F4 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F) G) F4 _let_1))))))))))) (forall ((F0 tptp.fun_real_real) (G0 tptp.fun_real_real) (G2 tptp.fun_real_real) (F3 tptp.fun_real_real) (F4 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_afb G0) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_afb G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez F0) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G0) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G2) F3) F4 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F0) G0) F4 _let_1))))))))))) (forall ((G tptp.fun_real_real) (X tptp.real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F3 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_afb G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G2) F3) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G) F) _let_2 _let_1))))))))) (forall ((G tptp.fun_real_real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F3 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_afb G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G2) F3) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc 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) (F3 tptp.fun_real_real) (F4 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_afb G) _let_1) (=> (tptp.eventually_real (tptp.aTP_Lamm_afb G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G2) F3) F4 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa F) G) F4 _let_1))))))))))) (forall ((G tptp.fun_real_real) (X tptp.real) (G2 tptp.fun_real_real) (F tptp.fun_real_real) (F3 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_afb G2) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez F) F3) _let_1) (=> (tptp.eventually_real (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_aez G) G2) _let_1) (=> (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G2) F3) _let_2 _let_1) (tptp.filterlim_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afc G) F) _let_2 _let_1))))))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((Y4 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P Y4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Y4) B)))) (tptp.pp (tptp.aa_nat_bool P (tptp.order_Greatest_nat P)))))) (forall ((P tptp.fun_nat_bool) (K tptp.nat) (B tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool P K)) (=> (forall ((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) B)))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat K) (tptp.order_Greatest_nat P)))))) (forall ((P tptp.fun_nat_bool) (B tptp.nat)) (=> (exists ((X_13 tptp.nat)) (tptp.pp (tptp.aa_nat_bool P X_13))) (=> (forall ((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) B)))) (tptp.pp (tptp.aa_nat_bool P (tptp.order_Greatest_nat P)))))) (forall ((F tptp.fun_nat_real) (A tptp.real) (B tptp.real)) (=> (tptp.ord_less_eq_set_real (tptp.image_nat_real F tptp.top_top_set_nat) (tptp.set_or1222579329274155063t_real A B)) (tptp.bfun_nat_real F tptp.at_top_nat))) (forall ((X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) tptp.one_one_real)) (tptp.bfun_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real X) tptp.at_top_nat)))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2))) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (= Xa2 tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_afd Deg2) TreeList2) Summary2))) Mima))))))))))) (forall ((X6 tptp.fun_nat_real) (B3 tptp.real)) (=> (tptp.order_9091379641038594480t_real X6) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B3) (tptp.aa_nat_real X6 I3)))) (tptp.bfun_nat_real X6 tptp.at_top_nat)))) (forall ((X6 tptp.fun_nat_real) (B3 tptp.real)) (=> (tptp.order_9091379641038594480t_real X6) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real B3) (tptp.aa_nat_real X6 I3)))) (not (forall ((L6 tptp.real)) (=> (tptp.filterlim_nat_real X6 (tptp.topolo2815343760600316023s_real L6) tptp.at_top_nat) (not (forall ((I tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real L6) (tptp.aa_nat_real X6 I))))))))))) (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg) _let_1)))) (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid (tptp.vEBT_Node Mima2 Deg TreeList Summary)) Deg4)) (and (= Deg Deg4) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_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 TreeList) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_afd Deg) TreeList) Summary))) Mima2))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (let ((_let_1 (tptp.pp Y))) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2)) _let_1) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (= _let_1 (not (= Xa2 tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2)) (= (tptp.pp Y) (not (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_afd Deg2) TreeList2) Summary2))) Mima)))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2)) (=> (=> (exists ((Uu2 tptp.bool) (Uv2 tptp.bool)) (= X (tptp.vEBT_Leaf Uu2 Uv2))) (not (= Xa2 tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2)) (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_afd Deg2) TreeList2) Summary2))) Mima)))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2))) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)) (= Xa2 tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (and (= Deg2 Xa2) (forall ((X3 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X3) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X3) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_afd Deg2) TreeList2) Summary2))) Mima)))))))))))))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)) (not (= Xa2 tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_1)))) (let ((_let_3 (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2))) (=> (= X _let_3) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_3 Xa2)) (not (and (= Deg2 Xa2) (forall ((X2 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X2) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_2)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) _let_2)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_afd Deg2) TreeList2) Summary2))) Mima))))))))))))))) (forall ((X6 tptp.set_int)) (= (tptp.complete_Sup_Sup_int X6) (tptp.the_int (tptp.aTP_Lamm_afe X6)))) (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.bool)) (=> (= (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X) Xa2)) (tptp.pp Y)) (=> (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat X Xa2)) (=> (forall ((Uu2 tptp.bool) (Uv2 tptp.bool)) (let ((_let_1 (tptp.vEBT_Leaf Uu2 Uv2))) (=> (= X _let_1) (=> (= (tptp.pp Y) (= Xa2 tptp.one_one_nat)) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (tptp.vEBT_Node Mima Deg2 TreeList2 Summary2))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_3 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Deg2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X _let_1) (=> (= (tptp.pp Y) (and (= Deg2 Xa2) (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid X4) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Deg2) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))))) (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_VEBT_valid Summary2) _let_3)) (= (tptp.size_s6755466524823107622T_VEBT TreeList2) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_2) _let_3)) (tptp.pp (tptp.aa_opt6800557945374683724t_bool (tptp.case_o7912701867834613557at_nat (tptp.aa_bool_bool (tptp.fconj (tptp.aa_bool_bool tptp.fNot (tptp.aa_fun_nat_bool_bool tptp.fEx_nat (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Summary2)))) (tptp.fAll_VEBT_VEBT (tptp.cOMBS_6222329278419335549l_bool (tptp.cOMBB_3438363824644082366T_VEBT tptp.fimplies (tptp.cOMBC_771164880915498576T_bool tptp.member_VEBT_VEBT (tptp.set_VEBT_VEBT2 TreeList2))) (tptp.cOMBB_3745307990312268622T_VEBT tptp.fNot (tptp.cOMBB_2885587777813823575T_VEBT tptp.fEx_nat tptp.vEBT_V8194947554948674370ptions))))) (tptp.produc8955392012077580105t_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_afd Deg2) TreeList2) Summary2))) Mima)))) (not (tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel (tptp.produc738532404422230701BT_nat _let_1 Xa2)))))))))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (G tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real) F))) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B))) (tptp.differ6690327859849518006l_real F (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)))) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X3) B))) (tptp.topolo4422821103128117721l_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real) G))) (=> (forall ((X3 tptp.real)) (=> (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B))) (tptp.differ6690327859849518006l_real G (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C3 tptp.real)) (let ((_let_1 (tptp.topolo2177554685111907308n_real C3 tptp.top_top_set_real))) (and (tptp.has_fi5821293074295781190e_real G G_c _let_1) (tptp.has_fi5821293074295781190e_real F F_c _let_1) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) C3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real C3) B)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real F B)) (tptp.aa_real_real F A))) G_c) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real G B)) (tptp.aa_real_real G A))) F_c))))))))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (tptp.differ6690327859849518006l_real F (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))))) (exists ((L3 tptp.real) (Z3 tptp.real)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) Z3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Z3) B)) (tptp.has_fi5821293074295781190e_real F L3 (tptp.topolo2177554685111907308n_real Z3 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)) L3)))))))) (forall ((A2 tptp.set_real) (F tptp.fun_real_real)) (=> (tptp.topolo5044208981011980120l_real A2 F) (tptp.topolo5044208981011980120l_real A2 (tptp.aTP_Lamm_aff F)))) (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_afg F))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (exists ((C3 tptp.real) (D3 tptp.real)) (and (= (tptp.image_real_real F (tptp.set_or1222579329274155063t_real A B)) (tptp.set_or1222579329274155063t_real C3 D3)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real C3) D3))))))) (forall ((A2 tptp.set_real)) (=> (tptp.ord_less_eq_set_real A2 (tptp.set_ord_atLeast_real tptp.one_one_real)) (tptp.topolo5044208981011980120l_real A2 tptp.arcosh_real))) (forall ((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_afh F))))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (F3 tptp.fun_re7681423839302404990l_real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) 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 F3 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 F3 Xi) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real B) A)))))))))))) (forall ((A2 tptp.set_real)) (=> (tptp.ord_less_eq_set_real A2 (tptp.set_or1633881224788618240n_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real) tptp.one_one_real)) (tptp.topolo5044208981011980120l_real A2 tptp.artanh_real))) (forall ((A tptp.real) (B tptp.real) (F tptp.fun_real_real) (X tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) B)) (=> (tptp.topolo5044208981011980120l_real (tptp.set_or1222579329274155063t_real A B) F) (=> (forall ((X3 tptp.real)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real A) X3)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real X3) B)) (tptp.has_fi5821293074295781190e_real F tptp.zero_zero_real (tptp.topolo2177554685111907308n_real X3 tptp.top_top_set_real))))) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real A) X)) (=> (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real X) B)) (= (tptp.aa_real_real F X) (tptp.aa_real_real F A)))))))) (= tptp.topolo1511823702728130853y_real (tptp.comple2936214249959783750l_real (tptp.image_2178119161166701260l_real tptp.aTP_Lamm_afj _let_20))) (= tptp.topolo896644834953643431omplex (tptp.comple8358262395181532106omplex (tptp.image_5971271580939081552omplex tptp.aTP_Lamm_afl _let_20))) (forall ((U3 tptp.set_complex)) (= (tptp.topolo4110288021797289639omplex U3) (forall ((X4 tptp.complex)) (=> (tptp.member_complex X4 U3) (tptp.eventu5826381225784669381omplex (tptp.produc9214369023355538061x_bool (tptp.aa_com1326194769588742913x_bool (tptp.aTP_Lamm_afm U3) X4)) tptp.topolo896644834953643431omplex))))) (forall ((U3 tptp.set_real)) (= (tptp.topolo4860482606490270245n_real U3) (forall ((X4 tptp.real)) (=> (tptp.member_real X4 U3) (tptp.eventu3244425730907250241l_real (tptp.produc5257810830037637649l_bool (tptp.aa_rea2091369211473463559l_bool (tptp.aTP_Lamm_afn U3) X4)) tptp.topolo1511823702728130853y_real))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat M) N2) (tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat M) N2)))) (forall ((P tptp.fun_Pr7757163693017731481t_bool)) (= (tptp.eventu1038000079068216329at_nat P (tptp.prod_filter_nat_nat tptp.at_top_nat tptp.at_top_nat)) (exists ((N9 tptp.nat)) (forall ((M6 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) M6)) (forall ((N5 tptp.nat)) (=> (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat N9) N5)) (tptp.pp (tptp.aa_Pro2232559814647311250t_bool P (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat N5) M6)))))))))) (forall ((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.order_mono_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat N2)))) (tptp.order_mono_nat_nat tptp.suc) (forall ((X6 tptp.fun_nat_real) (B3 tptp.real)) (=> (tptp.order_mono_nat_real X6) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 I3)) B3))) (tptp.bfun_nat_real X6 tptp.at_top_nat)))) (forall ((X6 tptp.fun_nat_real) (B3 tptp.real)) (=> (tptp.order_mono_nat_real X6) (=> (forall ((I3 tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 I3)) B3))) (not (forall ((L6 tptp.real)) (=> (tptp.filterlim_nat_real X6 (tptp.topolo2815343760600316023s_real L6) tptp.at_top_nat) (not (forall ((I tptp.nat)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_nat_real X6 I)) L6)))))))))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_oc 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_tn Uu) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_aaf Uu)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Uu)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Uu) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_real_real tptp.cos_real Uu) tptp.zero_zero_real)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_sk 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_ads 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_aep 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_adu 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.code_integer)) (= (tptp.aa_Cod1783974652533396728nteger tptp.aTP_Lamm_ya Uu) (tptp.plus_p5714425477246183910nteger Uu tptp.one_one_Code_integer))) (forall ((Uu tptp.complex)) (= (tptp.aa_complex_complex tptp.aTP_Lamm_xv Uu) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uu) tptp.one_one_complex))) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_xy Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) tptp.one_one_real))) (forall ((Uu tptp.rat)) (= (tptp.aa_rat_rat tptp.aTP_Lamm_xw Uu) (tptp.aa_rat_rat (tptp.plus_plus_rat Uu) tptp.one_one_rat))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_xz Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) tptp.one_one_nat))) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_xx Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) tptp.one_one_int))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_adw Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uu)))) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_adg Uu) (tptp.suminf_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nw Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_set_nat tptp.aTP_Lamm_aem Uu) (tptp.collect_nat (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_eu Uu)))) (forall ((Uu tptp.real)) (= (tptp.aa_rea5117059003799598681omplex tptp.aTP_Lamm_afl Uu) (tptp.princi3496590319149328850omplex (tptp.collec8663557070575231912omplex (tptp.produc9214369023355538061x_bool (tptp.aTP_Lamm_afk Uu)))))) (forall ((Uu tptp.real)) (= (tptp.aa_rea5428163979925208277l_real tptp.aTP_Lamm_afj Uu) (tptp.princi6114159922880469582l_real (tptp.collec3799799289383736868l_real (tptp.produc5257810830037637649l_bool (tptp.aTP_Lamm_afi Uu)))))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_ady 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_adn Uu) (tptp.some_num (tptp.aa_num_num tptp.bit1 Uu)))) (forall ((Uu tptp.num)) (= (tptp.aa_num_option_num tptp.aTP_Lamm_adj Uu) (tptp.some_num (tptp.aa_num_num tptp.bit0 Uu)))) (forall ((Uu tptp.int)) (= (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_aal Uu) (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.uminus_uminus_int Uu)))) (forall ((Uu tptp.int)) (= (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_aak Uu) (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int tptp.abs_abs_int Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_km Uu) (tptp.product_Pair_nat_nat (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.int)) (= (tptp.aa_int_nat tptp.aTP_Lamm_acd Uu) (tptp.aa_int_nat tptp.nat2 (tptp.aa_int_int tptp.abs_abs_int Uu)))) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_option_num tptp.aTP_Lamm_adl Uu) (tptp.some_num tptp.one))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_adq Uu) Uua) (tptp.case_num_option_num (tptp.some_num tptp.one) (tptp.aTP_Lamm_ado Uua) (tptp.aTP_Lamm_adp Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_uk Uu) Uua) (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_uh Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_complex))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_ul Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_real))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ui Uu) Uua) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_rat))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_uj Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_int))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aTP_Lamm_to Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) Uua)) tptp.zero_zero_real) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat)) _let_1)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.code_int_of_integer Uu)))) (= (tptp.aa_Code_integer_int (tptp.aa_Cod1242632294114111009er_int tptp.aTP_Lamm_abh Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uu)))) (= (tptp.aa_nat_Code_integer (tptp.aa_nat2010205248571845816nteger tptp.aTP_Lamm_nt Uu) Uua) (tptp.if_Code_integer (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat) _let_1 (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uu)))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_no Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat)) _let_1) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uu)))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_nr Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat)) _let_1) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uu)))) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat tptp.aTP_Lamm_np Uu) Uua) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat) _let_1) (tptp.aa_rat_rat (tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uu)))) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ns Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat)) _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uu)))) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int tptp.aTP_Lamm_nq Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uua) tptp.zero_zero_nat)) _let_1) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.code_num_of_integer Uu))) (let ((_let_2 (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num _let_1) _let_1))) (= (tptp.aa_Code_integer_num (tptp.aa_Cod6128727250572145423er_num tptp.aTP_Lamm_abi Uu) Uua) (tptp.aa_num_num (tptp.aa_num_fun_num_num (tptp.if_num (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uua) tptp.zero_z3403309356797280102nteger)) _let_2) (tptp.aa_num_num (tptp.aa_num_fun_num_num tptp.plus_plus_num _let_2) tptp.one)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (let ((_let_1 (tptp.code_nat_of_integer Uu))) (let ((_let_2 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) _let_1))) (= (tptp.aa_Code_integer_nat (tptp.aa_Cod5420483313623307717er_nat tptp.aTP_Lamm_abk 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_aaj Uu) Uua) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) tptp.zero_zero_int) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int tptp.sgn_sgn_int Uu)) Uua)) (tptp.aa_int_int tptp.abs_abs_int Uu))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_uf Uu) Uua) (tptp.if_Code_integer (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua)) tptp.zero_z3403309356797280102nteger))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_uc Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_complex))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_ug Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_real))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ud Uu) Uua) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_rat))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_ue Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))) tptp.zero_zero_int))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aa_nat3713591252005393295on_num tptp.aTP_Lamm_adr Uu) Uua) (tptp.case_nat_option_num tptp.none_num (tptp.aTP_Lamm_adq Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aTP_Lamm_ado Uu) Uua) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_adj (tptp.bit_take_bit_num Uu Uua)))) (forall ((Uu tptp.num) (Uua tptp.nat)) (= (tptp.aa_nat_option_num (tptp.aTP_Lamm_adk Uu) Uua) (tptp.case_o6005452278849405969um_num tptp.none_num tptp.aTP_Lamm_adj (tptp.bit_take_bit_num Uua Uu)))) (forall ((Uu tptp.fun_nat_fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_va Uu) Uua) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_uz Uu) Uua)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_uy Uu) Uua) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_ux Uu) Uua)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nv 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_sz 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_tq Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) _let_1))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_wu Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Uua)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uua))) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_wr Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Uua)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_wv Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ws Uu) Uua) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Uua)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_wt Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) Uua)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_za Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua))) Uua)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_zc Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua))) Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_zb Uu) Uua) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua))) Uua)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.real) (Uua tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_aac Uu) Uua)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Uua) _let_1)) (= (tptp.aa_real_real tptp.sin_real Uua) Uu))))) (forall ((Uu tptp.real) (Uua tptp.real)) (let ((_let_1 (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.pi) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))))) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_aab Uu) Uua)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real _let_1)) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Uua) _let_1)) (= (tptp.aa_real_real tptp.tan_real Uua) Uu))))) (forall ((Uu tptp.complex) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_aai Uu) Uua)) (and (= (tptp.aa_complex_complex tptp.sgn_sgn_complex Uu) (tptp.aa_real_complex tptp.cis Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.pi)) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Uua) tptp.pi))))) (forall ((Uu tptp.real) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_real_fun_int_bool tptp.aTP_Lamm_aag Uu) Uua)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real (tptp.aa_int_real tptp.ring_1_of_int_real Uua)) Uu)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Uu) (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uua) tptp.one_one_int))))))) (forall ((Uu tptp.rat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_aah Uu) Uua)) (and (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat (tptp.aa_int_rat tptp.ring_1_of_int_rat Uua)) Uu)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Uu) (tptp.aa_int_rat tptp.ring_1_of_int_rat (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uua) tptp.one_one_int))))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) tptp.one_one_nat))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_nw 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_adh 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_adt Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_xi Uu) Uua) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Uua)) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_xf Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Uua)) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_xj Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_xg Uu) Uua) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Uua)) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_xh Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) Uua)) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua))))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_yb Uu) Uua) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uu) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))) Uua))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_yd Uu) Uua) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))) Uua))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_yc Uu) Uua) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))) Uua))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_xs Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex Uu) Uua)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex Uu) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_xu Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real Uu) Uua)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Uu) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_xt Uu) Uua) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat Uu) Uua)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.divide_divide_rat Uu) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_ye Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex Uu) Uua)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_yg Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real Uu) Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real tptp.one_one_real)) Uua)))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_yf Uu) Uua) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat Uu) Uua)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat tptp.one_one_rat)) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_abo 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_wb Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uu) Uua)) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))))) (forall ((Uu tptp.set_int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_afe Uu) Uua)) (and (tptp.member_int Uua Uu) (forall ((X4 tptp.int)) (=> (tptp.member_int X4 Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int X4) Uua))))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_sy 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_aeq 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_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_uv 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_uu 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.aa_nat5545486172511849908x_bool tptp.aTP_Lamm_cf Uu) Uua)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) Uu) tptp.one_one_complex))) (forall ((Uu tptp.nat) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_ce Uu) Uua)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uu) tptp.one_one_real))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_aed 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_aek 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_aer 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_nu Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real tptp.one_one_real) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real _let_1))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) _let_1))))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_aae Uu) Uua)) (and (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real tptp.zero_zero_real) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_eq_real Uua) tptp.pi)) (= (tptp.aa_real_real tptp.cos_real Uua) Uu)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_real (tptp.aTP_Lamm_my Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real Uu _let_1)) (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_mv Uu) Uua) (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat Uu _let_1)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_mx Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uu _let_1)) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (= (tptp.aa_nat_int (tptp.aTP_Lamm_mw Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int Uu _let_1)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc _let_1)))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_mc Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ma Uu) Uua) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_mb Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_kp Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu Uua)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.zero_zero_complex) Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_kr Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uua)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_kq Uu) Uua) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_qx Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int tptp.zero_zero_int) Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_mu Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uua)) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ms Uu) Uua) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_mt Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_mo Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex Uu Uua)) (tptp.aa_nat_complex Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_mr Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uua)) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_mp Uu) Uua) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_mq Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_rh Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uua)) (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_rf Uu) Uua) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uua)) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_rg Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uua)) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_us Uu) Uua) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real Uu Uua)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_uq Uu) Uua) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat Uu Uua)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Uua)))) (forall ((Uu tptp.fun_complex_real) (Uua tptp.complex)) (= (tptp.aa_complex_complex (tptp.aTP_Lamm_tm Uu) Uua) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_complex_real Uu Uua)) tptp.zero_zero_real))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_tl Uu) Uua) (tptp.aa_real_complex (tptp.complex2 (tptp.aa_nat_real Uu Uua)) tptp.zero_zero_real))) (forall ((Uu tptp.fun_complex_real) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_kb Uu) Uua)) (= (tptp.aa_complex_real Uu Uua) tptp.zero_zero_real))) (forall ((Uu tptp.fun_complex_rat) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_kd Uu) Uua)) (= (tptp.aa_complex_rat Uu Uua) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_complex_nat) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_kf Uu) Uua)) (= (tptp.aa_complex_nat Uu Uua) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_complex_int) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_kg Uu) Uua)) (= (tptp.aa_complex_int Uu Uua) tptp.zero_zero_int))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_kh Uu) Uua)) (= (tptp.aa_nat_complex Uu Uua) tptp.zero_zero_complex))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_ki Uu) Uua)) (= (tptp.aa_nat_rat Uu Uua) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_int_complex) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_jz Uu) Uua)) (= (tptp.aa_int_complex Uu Uua) tptp.zero_zero_complex))) (forall ((Uu tptp.fun_int_real) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_ka Uu) Uua)) (= (tptp.aa_int_real Uu Uua) tptp.zero_zero_real))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_kc Uu) Uua)) (= (tptp.aa_int_rat Uu Uua) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_ke Uu) Uua)) (= (tptp.aa_int_nat Uu Uua) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_aej Uu) Uua) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_adt 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_aei Uu) Uua) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aTP_Lamm_adt 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.code_integer) (Uua tptp.bool)) (= (tptp.aa_bool_char (tptp.aa_Cod6370812454140447392l_char tptp.aTP_Lamm_acq Uu) Uua) (tptp.produc7257819798349884575l_char (tptp.aTP_Lamm_acp Uua) (tptp.code_bit_cut_integer Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_aca Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat tptp.nat_triangle (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) Uua))) Uu))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_ts Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu) Uua)))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_tr Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc Uua))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uua)))) (forall ((Uu tptp.num) (Uua tptp.num)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat Uu))) (= (tptp.aa_num_int (tptp.aTP_Lamm_adi Uu) Uua) (tptp.aa_int_int (tptp.aa_nat_fun_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.aa_int_fun_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_ach 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_sx 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_sq 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.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_yr Uu) Uua) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua)) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real tptp.aTP_Lamm_yt Uu) Uua) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua)) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ys Uu) Uua) (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)) Uu))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_aad Uu) Uua)) (= (tptp.aa_real_real tptp.exp_real Uua) Uu))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger tptp.aTP_Lamm_kx Uu) Uua) (tptp.produc1086072967326762835nteger Uu (tptp.plus_p5714425477246183910nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua) tptp.one_one_Code_integer)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_kw Uu) Uua) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_nat)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_kv Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)) tptp.one_one_int)))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger tptp.aTP_Lamm_kl Uu) Uua) (tptp.produc1086072967326762835nteger Uu (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat tptp.aTP_Lamm_kk Uu) Uua) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.aTP_Lamm_kj Uu) Uua) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_zj Uu) Uua) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uu) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua)) (tptp.numera6690914467698888265omplex (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_zl Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua)) (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_zk Uu) Uua) (tptp.aa_rat_rat (tptp.plus_plus_rat Uu) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua)) (tptp.aa_num_rat tptp.numeral_numeral_rat (tptp.aa_num_num tptp.bit0 tptp.one)))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_xe 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_aee 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_md 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_aec 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_adz Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat tptp.suc Uua)))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_acg Uu) Uua) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real Uu) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_acb Uu) Uua)) (= Uua (tptp.aa_nat_nat tptp.suc Uu)))) (forall ((Uu tptp.set_complex) (Uua tptp.set_complex)) (= (tptp.pp (tptp.aa_set_complex_bool (tptp.aTP_Lamm_cc Uu) Uua)) (tptp.ord_le211207098394363844omplex Uua Uu))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_cb Uu) Uua)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat Uua) Uu)))) (forall ((Uu tptp.set_int) (Uua tptp.set_int)) (= (tptp.pp (tptp.aa_set_int_bool (tptp.aTP_Lamm_cd Uu) Uua)) (tptp.ord_less_eq_set_int Uua Uu))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_um Uu) Uua)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_eq_rat Uua) Uu)))) (forall ((Uu tptp.num) (Uua tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_un Uu) Uua)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_eq_num Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_bz Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat Uua) Uu)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_uo Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_acf Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat Uua) Uu))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.aTP_Lamm_qh Uu) Uua)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real Uua) Uu)))) (forall ((Uu tptp.bool) (Uua tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aTP_Lamm_qi Uu) Uua)) (tptp.pp (tptp.aa_bool_bool (tptp.ord_less_bool Uua) Uu)))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_qd Uu) Uua)) (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_set_nat Uua) Uu)))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.aTP_Lamm_qe Uu) Uua)) (tptp.pp (tptp.aa_rat_bool (tptp.aa_rat_fun_rat_bool tptp.ord_less_rat Uua) Uu)))) (forall ((Uu tptp.num) (Uua tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.aTP_Lamm_qf Uu) Uua)) (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool tptp.ord_less_num Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_ca Uu) Uua)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uua) Uu)))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_qg Uu) Uua)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_int Uua) Uu)))) (forall ((Uu tptp.real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.aTP_Lamm_am Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Uua) Uu))) (forall ((Uu tptp.rat) (Uua tptp.rat)) (= (tptp.aa_rat_rat (tptp.aTP_Lamm_an Uu) Uua) (tptp.aa_rat_rat (tptp.times_times_rat Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_ao Uu) Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua) Uu))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ap Uu) Uua) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uu))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_acc 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_acs Uu) Uua) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uu))) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.aTP_Lamm_ace 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_acu Uu) Uua) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real Uua) Uu))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer)) (= (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.aTP_Lamm_ev Uu) Uua)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.dvd_dvd_Code_integer Uua) Uu)))) (forall ((Uu tptp.complex) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.aTP_Lamm_et Uu) Uua)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.dvd_dvd_complex Uua) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.aTP_Lamm_eu 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_ew 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_abr 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_up 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_adx Uu) Uua) (tptp.aa_real_real (tptp.aa_nat_fun_real_real tptp.root Uua) Uu))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aTP_Lamm_aa Uu) Uua)) (tptp.member5262025264175285858nt_int Uua Uu))) (forall ((Uu tptp.set_complex) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_ab Uu) Uua)) (tptp.member_complex Uua Uu))) (forall ((Uu tptp.set_real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_a Uu) Uua)) (tptp.member_real 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_sj 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_si Uu) Uua) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua)))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_aew Uu) Uua)) (tptp.pp (tptp.aa_real_bool Uu (tptp.aa_real_real tptp.inverse_inverse_real Uua))))) (forall ((Uu tptp.fun_real_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_acr Uu) Uua) (tptp.aa_real_real Uu (tptp.aa_real_real tptp.uminus_uminus_real Uua)))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_aex Uu) Uua)) (tptp.pp (tptp.aa_real_bool Uu (tptp.aa_real_real tptp.uminus_uminus_real Uua))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_pk Uu) Uua) (tptp.aa_nat_complex Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_lp Uu) Uua) (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_aes Uu) Uua)) (tptp.pp (tptp.aa_nat_bool Uu (tptp.aa_nat_nat tptp.suc Uua))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ly Uu) Uua) (tptp.aa_nat_rat Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_lo Uu) Uua) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_lz Uu) Uua) (tptp.aa_nat_int Uu (tptp.aa_nat_nat tptp.suc Uua)))) (forall ((Uu tptp.nat) (Uua tptp.num)) (= (tptp.aa_num_option_num (tptp.aTP_Lamm_adp 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_adm 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_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_abz Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_aby Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_abx Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_abw Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_abv Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_abu Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool tptp.aTP_Lamm_abt Uu) Uua) (tptp.produc8955392012077580105t_bool (tptp.aa_nat8637530788439456283t_bool (tptp.aTP_Lamm_abs Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat tptp.aTP_Lamm_abq Uu) Uua) (tptp.produc2626176000494625587at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_abp Uu) Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_acz Uu) Uua) (tptp.suminf_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_acy Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex tptp.aTP_Lamm_zw Uu) Uua) (tptp.aa_real_complex tptp.cis (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi)) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uu))))) (forall ((Uu tptp.fun_real_real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_afb 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_ex Uu) Uua)) (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat _let_1) Uua)))))))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat3829984526574172007omplex (tptp.aTP_Lamm_zg Uu) Uua) (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex Uu) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_zi Uu) Uua) (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_zh Uu) Uua) (tptp.times_times_rat (tptp.aa_rat_rat (tptp.minus_minus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))))) (forall ((Uu tptp.code_integer) (Uua tptp.nat)) (= (tptp.aa_nat6383147911832638789nteger (tptp.aTP_Lamm_yy Uu) Uua) (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.plus_p5714425477246183910nteger Uu (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uua))))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat3829984526574172007omplex (tptp.aTP_Lamm_yu Uu) Uua) (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uu) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uua))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_yx Uu) Uua) (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uua))))) (forall ((Uu tptp.rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_yv Uu) Uua) (tptp.times_times_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Uu) (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_yz Uu) Uua) (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uua))))) (forall ((Uu tptp.int) (Uua tptp.nat)) (= (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_yw Uu) Uua) (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uua))))) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_aeb Uu) Uua) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.aTP_Lamm_abg 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_abf 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.set_Pr958786334691620121nt_int) (Uua tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aTP_Lamm_le Uu) Uua)) (not (tptp.member5262025264175285858nt_int Uua Uu)))) (forall ((Uu tptp.set_complex) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_lf Uu) Uua)) (not (tptp.member_complex Uua Uu)))) (forall ((Uu tptp.set_real) (Uua tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aTP_Lamm_ld Uu) Uua)) (not (tptp.member_real Uua Uu)))) (forall ((Uu tptp.set_set_nat) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_lg Uu) Uua)) (not (tptp.member_set_nat Uua Uu)))) (forall ((Uu tptp.set_nat) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_lh Uu) Uua)) (not (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_li Uu) Uua)) (not (tptp.member_int Uua Uu)))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.complex)) (= (tptp.aa_complex_real (tptp.aTP_Lamm_oa Uu) Uua) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_nz Uu) Uua) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_ob Uu) Uua) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_adv Uu) Uua) (tptp.aa_real_real tptp.inverse_inverse_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_complex_nat) (Uua tptp.complex)) (= (tptp.aa_complex_complex (tptp.aTP_Lamm_nc Uu) Uua) (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_complex_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_ne Uu) Uua) (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_ng Uu) Uua) (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_nf Uu) Uua) (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_nd Uu) Uua) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_nb Uu) Uua) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_int_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_zx Uu) Uua) (tptp.aa_real_complex tptp.real_V4546457046886955230omplex (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.complex)) (= (tptp.aa_complex_complex (tptp.aTP_Lamm_fx Uu) Uua) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_complex_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aTP_Lamm_tz Uu) Uua) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger (tptp.aa_nat_Code_integer Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_pl Uu) Uua) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_fy Uu) Uua) (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_rat (tptp.aTP_Lamm_ty Uu) Uua) (tptp.aa_rat_rat tptp.uminus_uminus_rat (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_int (tptp.aTP_Lamm_tx Uu) Uua) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_fw Uu) Uua) (tptp.aa_int_int tptp.uminus_uminus_int (tptp.aa_int_int Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat3829984526574172007omplex (tptp.aTP_Lamm_sl Uu) Uua) (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_sp Uu) Uua) (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_rat_rat (tptp.aTP_Lamm_sm Uu) Uua) (tptp.plus_plus_rat (tptp.aa_nat_rat Uu Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_so Uu) Uua) (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.nat)) (= (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_sn Uu) Uua) (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int Uu Uua)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_afh 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_aff Uu) Uua) (tptp.aa_real_real tptp.arsinh_real (tptp.aa_real_real Uu Uua)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_afg 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_ko Uu) Uua) (tptp.aa_real_real tptp.abs_abs_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_kn Uu) Uua) (tptp.aa_int_int tptp.abs_abs_int (tptp.aa_int_int Uu Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_aeh Uu) Uua) (tptp.aa_real_real tptp.cos_real (tptp.aa_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_aaz Uu) Uua) (tptp.aa_complex_real tptp.re (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_aba Uu) Uua) (tptp.aa_complex_real tptp.im (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_co3258106519541737638omplex) (Uua tptp.complex)) (= (tptp.aa_complex_complex (tptp.aTP_Lamm_qu Uu) Uua) (tptp.suminf_complex (tptp.aa_com8181001469867462503omplex Uu Uua)))) (forall ((Uu tptp.fun_co8378349014452122532t_real) (Uua tptp.complex)) (= (tptp.aa_complex_real (tptp.aTP_Lamm_qn Uu) Uua) (tptp.suminf_real (tptp.aa_com20334259897932645t_real Uu Uua)))) (forall ((Uu tptp.fun_re2084383175013312036omplex) (Uua tptp.real)) (= (tptp.aa_real_complex (tptp.aTP_Lamm_qq Uu) Uua) (tptp.suminf_complex (tptp.aa_rea1531280491672885477omplex Uu Uua)))) (forall ((Uu tptp.fun_re4238438383274954274t_real) (Uua tptp.real)) (= (tptp.aa_real_real (tptp.aTP_Lamm_qo Uu) Uua) (tptp.suminf_real (tptp.aa_real_fun_nat_real Uu Uua)))) (forall ((Uu tptp.fun_na1142814060743658952omplex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_qr Uu) Uua) (tptp.suminf_complex (tptp.aa_nat6454746962644518025omplex Uu Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aTP_Lamm_qw Uu) Uua) (tptp.suminf_real (tptp.aa_nat_fun_nat_real Uu Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat)) (= (tptp.aa_nat_nat (tptp.aTP_Lamm_qv Uu) Uua) (tptp.suminf_nat (tptp.aa_nat_fun_nat_nat Uu Uua)))) (forall ((Uu tptp.fun_in8056368165505483812omplex) (Uua tptp.int)) (= (tptp.aa_int_complex (tptp.aTP_Lamm_qs Uu) Uua) (tptp.suminf_complex (tptp.aa_int4144929030551567077omplex Uu Uua)))) (forall ((Uu tptp.fun_int_fun_nat_real) (Uua tptp.int)) (= (tptp.aa_int_real (tptp.aTP_Lamm_qp Uu) Uua) (tptp.suminf_real (tptp.aa_int_fun_nat_real Uu Uua)))) (forall ((Uu tptp.fun_int_fun_nat_int) (Uua tptp.int)) (= (tptp.aa_int_int (tptp.aTP_Lamm_qt Uu) Uua) (tptp.suminf_int (tptp.aa_int_fun_nat_int Uu Uua)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aTP_Lamm_abb Uu) Uua) (tptp.aa_complex_complex tptp.cnj (tptp.aa_nat_complex Uu Uua)))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aTP_Lamm_ky Uu) Uua)) (not (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu Uua))))) (forall ((Uu tptp.fun_complex_bool) (Uua tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aTP_Lamm_kz Uu) Uua)) (not (tptp.pp (tptp.aa_complex_bool Uu Uua))))) (forall ((Uu tptp.fun_set_nat_bool) (Uua tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aTP_Lamm_la Uu) Uua)) (not (tptp.pp (tptp.aa_set_nat_bool Uu Uua))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aTP_Lamm_lb Uu) Uua)) (not (tptp.pp (tptp.aa_nat_bool Uu Uua))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aTP_Lamm_lc Uu) Uua)) (not (tptp.pp (tptp.aa_int_bool Uu Uua))))) (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_tp 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_sh Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uub)) (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real Uua Uub)))) (forall ((Uu tptp.num) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.aa_num_Code_integer tptp.numera6620942414471956472nteger Uu))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_fa Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le3102999989581377725nteger _let_2) Uub) (tptp.produc1086072967326762835nteger (tptp.plus_p5714425477246183910nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger Uub _let_2)) (tptp.produc1086072967326762835nteger _let_1 Uub)))))) (forall ((Uu tptp.num) (Uua tptp.nat) (Uub tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.aa_num_nat tptp.numeral_numeral_nat Uu))) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aTP_Lamm_ey Uu) Uua) Uub) (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.if_Pro6206227464963214023at_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat _let_2) Uub)) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) _let_2))) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat _let_1) Uub)))))) (forall ((Uu tptp.num) (Uua tptp.int) (Uub tptp.int)) (let ((_let_1 (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_num_int tptp.numeral_numeral_int (tptp.aa_num_num tptp.bit0 tptp.one))) Uua))) (let ((_let_2 (tptp.aa_num_int tptp.numeral_numeral_int Uu))) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_ez Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.ord_less_eq_int _let_2) Uub) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int _let_1) tptp.one_one_int)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int Uub) _let_2))) (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int _let_1) Uub)))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_oy Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.aa_nat_complex Uua Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_oz Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.aa_nat_real Uua Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_pa Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.aa_nat_nat Uua Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_pb Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.aa_nat_int Uua Uub)) tptp.zero_zero_int))) (forall ((Uu tptp.complex) (Uua tptp.fun_complex_real) (Uub tptp.complex)) (= (tptp.aa_complex_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_fh Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.fequal_complex Uu) Uub)) (tptp.aa_complex_real Uua Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.complex) (Uua tptp.fun_complex_rat) (Uub tptp.complex)) (= (tptp.aa_complex_rat (tptp.aa_fun7622890401989837636ex_rat (tptp.aTP_Lamm_fl Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.fequal_complex Uu) Uub) (tptp.aa_complex_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.real) (Uua tptp.fun_real_complex) (Uub tptp.real)) (= (tptp.aa_real_complex (tptp.aa_fun2233226938935547116omplex (tptp.aTP_Lamm_fc Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real Uu) Uub)) (tptp.aa_real_complex Uua Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_ff Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real Uu) Uub)) (tptp.aa_real_real Uua Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.real) (Uua tptp.fun_real_rat) (Uub tptp.real)) (= (tptp.aa_real_rat (tptp.aa_fun2468082234287226944al_rat (tptp.aTP_Lamm_fi Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real Uu) Uub) (tptp.aa_real_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_fd Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uu) Uub)) (tptp.aa_nat_complex Uua Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_fj Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uu) Uub) (tptp.aa_nat_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.int) (Uua tptp.fun_int_complex) (Uub tptp.int)) (= (tptp.aa_int_complex (tptp.aa_fun3088484340408535532omplex (tptp.aTP_Lamm_fe Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) Uub)) (tptp.aa_int_complex Uua Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.int) (Uua tptp.fun_int_real) (Uub tptp.int)) (= (tptp.aa_int_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_fg Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) Uub)) (tptp.aa_int_real Uua Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.int) (Uua tptp.fun_int_rat) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_fk Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uu) Uub) (tptp.aa_int_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.complex) (Uua tptp.fun_complex_real) (Uub tptp.complex)) (= (tptp.aa_complex_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_fr Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.fequal_complex Uub) Uu)) (tptp.aa_complex_real Uua Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.complex) (Uua tptp.fun_complex_rat) (Uub tptp.complex)) (= (tptp.aa_complex_rat (tptp.aa_fun7622890401989837636ex_rat (tptp.aTP_Lamm_fv Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.fequal_complex Uub) Uu) (tptp.aa_complex_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.real) (Uua tptp.fun_real_complex) (Uub tptp.real)) (= (tptp.aa_real_complex (tptp.aa_fun2233226938935547116omplex (tptp.aTP_Lamm_fm Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real Uub) Uu)) (tptp.aa_real_complex Uua Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_fp Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real Uub) Uu)) (tptp.aa_real_real Uua Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.real) (Uua tptp.fun_real_rat) (Uub tptp.real)) (= (tptp.aa_real_rat (tptp.aa_fun2468082234287226944al_rat (tptp.aTP_Lamm_fs Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real Uub) Uu) (tptp.aa_real_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_fn Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu)) (tptp.aa_nat_complex Uua Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_oo 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.fequal_nat Uub) Uu)) (tptp.aa_nat_real Uua Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_ft Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu) (tptp.aa_nat_rat Uua Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_op Uu) Uua) Uub) (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 Uub) Uu)) (tptp.aa_nat_nat Uua Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_oq Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu)) (tptp.aa_nat_int Uua Uub)) tptp.zero_zero_int))) (forall ((Uu tptp.int) (Uua tptp.fun_int_complex) (Uub tptp.int)) (= (tptp.aa_int_complex (tptp.aa_fun3088484340408535532omplex (tptp.aTP_Lamm_fo Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uub) Uu)) (tptp.aa_int_complex Uua Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.int) (Uua tptp.fun_int_real) (Uub tptp.int)) (= (tptp.aa_int_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_fq Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uub) Uu)) (tptp.aa_int_real Uua Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.int) (Uua tptp.fun_int_rat) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun1481061427733998144nt_rat (tptp.aTP_Lamm_fu Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int Uub) Uu) (tptp.aa_int_rat Uua Uub)) tptp.zero_zero_rat))) (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_abm Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger _let_1 tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger (tptp.minus_8373710615458151222nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uu) Uub)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_aci Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger _let_1 tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger (tptp.minus_8373710615458151222nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger (tptp.abs_abs_Code_integer Uu) Uub)))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (let ((_let_1 (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua))) (= (tptp.aa_Cod6977894654539884864nteger (tptp.aa_Cod8380929501330563836nteger (tptp.aTP_Lamm_abl Uu) Uua) Uub) (tptp.if_Pro6119634080678213985nteger (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger _let_1 tptp.zero_z3403309356797280102nteger) (tptp.produc1086072967326762835nteger (tptp.minus_8373710615458151222nteger _let_1 tptp.one_one_Code_integer) (tptp.minus_8373710615458151222nteger Uu Uub)))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ou Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool Uu Uub)) (tptp.aa_nat_complex Uua Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ov Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool Uu Uub)) (tptp.aa_nat_real Uua Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_ow Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool Uu Uub)) (tptp.aa_nat_nat Uua Uub)) tptp.zero_zero_nat))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_ox Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool Uu Uub)) (tptp.aa_nat_int Uua Uub)) tptp.zero_zero_int))) (forall ((Uu tptp.fun_complex_real) (Uua tptp.fun_complex_bool) (Uub tptp.complex)) (= (tptp.aa_complex_real (tptp.aa_fun2902006202505214429x_real (tptp.aTP_Lamm_ju Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_complex_bool Uua Uub)) (tptp.aa_complex_real Uu Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.fun_complex_rat) (Uua tptp.fun_complex_bool) (Uub tptp.complex)) (= (tptp.aa_complex_rat (tptp.aa_fun5529999419959482889ex_rat (tptp.aTP_Lamm_jy Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_complex_bool Uua Uub) (tptp.aa_complex_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_real_complex) (Uua tptp.fun_real_bool) (Uub tptp.real)) (= (tptp.aa_real_complex (tptp.aa_fun6813637976755515871omplex (tptp.aTP_Lamm_jp Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_real_bool Uua Uub)) (tptp.aa_real_complex Uu Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.fun_real_real) (Uua tptp.fun_real_bool) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6348708079608492509l_real (tptp.aTP_Lamm_js Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_real_bool Uua Uub)) (tptp.aa_real_real Uu Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.fun_real_rat) (Uua tptp.fun_real_bool) (Uub tptp.real)) (= (tptp.aa_real_rat (tptp.aa_fun7219699593533116937al_rat (tptp.aTP_Lamm_jv Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_real_bool Uua Uub) (tptp.aa_real_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun8588439219086927967omplex (tptp.aTP_Lamm_jq Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool Uua Uub)) (tptp.aa_nat_complex Uu Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun5656162108953708681at_rat (tptp.aTP_Lamm_jw Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool Uua Uub) (tptp.aa_nat_rat Uu Uub)) tptp.zero_zero_rat))) (forall ((Uu tptp.fun_int_complex) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_complex (tptp.aa_fun3606824691168040799omplex (tptp.aTP_Lamm_jr Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_int_bool Uua Uub)) (tptp.aa_int_complex Uu Uub)) tptp.zero_zero_complex))) (forall ((Uu tptp.fun_int_real) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_real (tptp.aa_fun6974987029372589917t_real (tptp.aTP_Lamm_jt Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_int_bool Uua Uub)) (tptp.aa_int_real Uu Uub)) tptp.zero_zero_real))) (forall ((Uu tptp.fun_int_rat) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.aa_int_rat (tptp.aa_fun4400602662665189257nt_rat (tptp.aTP_Lamm_jx Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_int_bool Uua Uub) (tptp.aa_int_rat Uu Uub)) tptp.zero_zero_rat))) (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_aez 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_nat_fun_nat_real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_uz Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real Uu Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_ux Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat Uu Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uub)))) (forall ((Uu tptp.fun_co7673397065115134084omplex) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_gd Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex Uu Uub) Uua))) (forall ((Uu tptp.fun_co3258106519541737638omplex) (Uua tptp.nat) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_nat3829984526574172007omplex (tptp.aTP_Lamm_pz Uu) Uua) Uub) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex Uu Uub) Uua))) (forall ((Uu tptp.fun_co8378349014452122532t_real) (Uua tptp.nat) (Uub tptp.complex)) (= (tptp.aa_complex_real (tptp.aa_nat480766339200631653x_real (tptp.aTP_Lamm_pm Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_com20334259897932645t_real Uu Uub) Uua))) (forall ((Uu tptp.fun_co636942507509095880at_nat) (Uua tptp.nat) (Uub tptp.complex)) (= (tptp.aa_complex_nat (tptp.aa_nat3391284541783913865ex_nat (tptp.aTP_Lamm_jd Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_com6383720667567721865at_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_co333780937270390912nt_int) (Uua tptp.int) (Uub tptp.complex)) (= (tptp.aa_complex_int (tptp.aa_int6126987627036542017ex_int (tptp.aTP_Lamm_ie Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_com3205223359959579713nt_int Uu Uub) Uua))) (forall ((Uu tptp.fun_re7208826350674946562omplex) (Uua tptp.complex) (Uub tptp.real)) (= (tptp.aa_real_complex (tptp.aa_com4766338864777664963omplex (tptp.aTP_Lamm_ij Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_rea2618301233319580611omplex Uu Uub) Uua))) (forall ((Uu tptp.fun_re2084383175013312036omplex) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.aa_real_complex (tptp.aa_nat7791439356240649701omplex (tptp.aTP_Lamm_pr Uu) Uua) Uub) (tptp.aa_nat_complex (tptp.aa_rea1531280491672885477omplex Uu Uub) Uua))) (forall ((Uu tptp.fun_re4238438383274954274t_real) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_jg Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real Uu Uub) Uua))) (forall ((Uu tptp.fun_real_fun_nat_nat) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.aa_real_nat (tptp.aa_nat_fun_real_nat (tptp.aTP_Lamm_iv Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_real_fun_nat_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_real_fun_int_int) (Uua tptp.int) (Uub tptp.real)) (= (tptp.aa_real_int (tptp.aa_int_fun_real_int (tptp.aTP_Lamm_hw Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_real_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.fun_na1591161823130732966omplex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_in Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_nat3829984526574172007omplex Uu Uub) Uua))) (forall ((Uu tptp.fun_na1142814060743658952omplex) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_pt Uu) Uua) Uub) (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_gj Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_gg Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_int_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_ia Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_nat_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.fun_in1307110748760623106omplex) (Uua tptp.complex) (Uub tptp.int)) (= (tptp.aa_int_complex (tptp.aa_com9156536935073639875omplex (tptp.aTP_Lamm_ir Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_int3545933452204062147omplex Uu Uub) Uua))) (forall ((Uu tptp.fun_in8056368165505483812omplex) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.aa_int_complex (tptp.aa_nat7430282427850695397omplex (tptp.aTP_Lamm_pv Uu) Uua) Uub) (tptp.aa_nat_complex (tptp.aa_int4144929030551567077omplex Uu Uub) Uua))) (forall ((Uu tptp.fun_int_fun_nat_real) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.aa_int_real (tptp.aa_nat_fun_int_real (tptp.aTP_Lamm_pp Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_int_fun_nat_real Uu Uub) Uua))) (forall ((Uu tptp.fun_int_fun_nat_nat) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_nat_fun_int_nat (tptp.aTP_Lamm_iz Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_int_fun_nat_nat Uu Uub) Uua))) (forall ((Uu tptp.fun_int_fun_nat_int) (Uua tptp.nat) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_px Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int Uu Uub) Uua))) (forall ((Uu tptp.fun_int_fun_int_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_ga Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_zt Uu) Uua) Uub) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_zs Uu) Uua) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_zr Uu) Uua) Uub) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_zq Uu) Uua) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_zp Uu) Uua) Uub) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_zo Uu) Uua) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_zn Uu) Uua) Uub) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_zm Uu) Uua) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_vl Uu) Uua) Uub) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_vk Uu) Uua) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_vj Uu) Uua) Uub) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_fun5379041630539201665omplex (tptp.aTP_Lamm_vi Uu) Uua) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uub)))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_te Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu)) tptp.one_one_complex) tptp.zero_zero_complex)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_tf Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu)) tptp.one_one_real) tptp.zero_zero_real)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_tg Uu) Uua) Uub) (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.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uub) Uu)) tptp.one_one_int) tptp.zero_zero_int)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uua) Uub)))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.code_integer)) (= (tptp.aa_Cod2825494507867081354r_bool (tptp.aa_Cod4981436349852597092r_bool (tptp.aTP_Lamm_abj Uu) Uua) Uub) (tptp.produc5135875973608410785r_bool (tptp.if_Code_integer (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) Uu) Uua (tptp.minus_8373710615458151222nteger (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uua) Uub)) (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer Uub) tptp.one_one_Code_integer)))) (forall ((Uu tptp.fun_nat_fun_nat_real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_ut Uu) Uua) Uub) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_gj Uu) Uub)) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uub) Uua)))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_ur Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_gg Uu) Uub)) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uub) Uua)))) (forall ((Uu tptp.bool) (Uua tptp.code_integer) (Uub tptp.bool)) (= (tptp.aa_bool_char (tptp.aa_Cod6370812454140447392l_char (tptp.aTP_Lamm_acp Uu) Uua) Uub) (tptp.produc7257819798349884575l_char (tptp.aa_boo1160955832611998748l_char (tptp.aTP_Lamm_aco Uu) Uub) (tptp.code_bit_cut_integer Uua)))) (forall ((Uu tptp.rat) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_aax Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aaw 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_aav Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aau 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_aat Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aas 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_aar Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int (tptp.produc4245557441103728435nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aaq 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_aap Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_aao 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_aan Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.produc8560705615207772305t_bool (tptp.aa_int2327297053056786951t_bool (tptp.aTP_Lamm_aam Uua) Uub)) (tptp.quotient_of Uu))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_co3258106519541737638omplex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun5003373910569599327omplex (tptp.aTP_Lamm_qa Uu) Uua) Uub) (tptp.groups7754918857620584856omplex (tptp.aa_nat3829984526574172007omplex (tptp.aTP_Lamm_pz Uua) Uub) Uu))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun8710705519803144921at_int (tptp.aTP_Lamm_py Uu) Uua) Uub) (tptp.groups4538972089207619220nt_int (tptp.aa_nat_fun_int_int (tptp.aTP_Lamm_px Uua) Uub) Uu))) (forall ((Uu tptp.set_int) (Uua tptp.fun_in8056368165505483812omplex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun3543561798013398749omplex (tptp.aTP_Lamm_pw Uu) Uua) Uub) (tptp.groups3049146728041665814omplex (tptp.aa_nat7430282427850695397omplex (tptp.aTP_Lamm_pv Uua) Uub) Uu))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_na1142814060743658952omplex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun4886358607025424513omplex (tptp.aTP_Lamm_pu Uu) Uua) Uub) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_pt Uua) Uub)) Uu))) (forall ((Uu tptp.set_real) (Uua tptp.fun_re2084383175013312036omplex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun7632768522510439005omplex (tptp.aTP_Lamm_ps Uu) Uua) Uub) (tptp.groups5754745047067104278omplex (tptp.aa_nat7791439356240649701omplex (tptp.aTP_Lamm_pr Uua) Uub) Uu))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun2842512154077127769t_real (tptp.aTP_Lamm_pq Uu) Uua) Uub) (tptp.groups8778361861064173332t_real (tptp.aa_nat_fun_int_real (tptp.aTP_Lamm_pp Uua) Uub) Uu))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_co8378349014452122532t_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun471735231769099483t_real (tptp.aTP_Lamm_pn Uu) Uua) Uub) (tptp.groups5808333547571424918x_real (tptp.aa_nat480766339200631653x_real (tptp.aTP_Lamm_pm Uua) Uub) Uu))) (forall ((Uu tptp.set_real) (Uua tptp.fun_re4238438383274954274t_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun628238740774635481t_real (tptp.aTP_Lamm_po Uu) Uua) Uub) (tptp.groups8097168146408367636l_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_jg Uua) Uub) Uu))) (forall ((Uu tptp.fun_nat_fun_nat_real) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_set1166323925324055613t_real (tptp.aTP_Lamm_gk Uu) Uua) Uub) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_gj Uu) Uub)) Uua))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun7039663905532832253t_real (tptp.aTP_Lamm_qc Uu) Uua) Uub) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_gj Uua) Uub)) Uu))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_gh Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_gg Uu) Uub)) Uua))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun8466562714962205125at_nat (tptp.aTP_Lamm_qb Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_gg Uua) Uub)) Uu))) (forall ((Uu tptp.fun_co7673397065115134084omplex) (Uua tptp.set_complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_set7743095458595710203omplex (tptp.aTP_Lamm_ge Uu) Uua) Uub) (tptp.groups7754918857620584856omplex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_gd Uu) Uub) Uua))) (forall ((Uu tptp.fun_int_fun_int_int) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_gb Uu) Uua) Uub) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_ga Uu) Uub) Uua))) (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_ada Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uu Uub) tptp.zero_zero_real)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_na5723442673449079972x_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun5746040925223427547t_real (tptp.aTP_Lamm_sr Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_complex_real (tptp.aa_nat480766339200631653x_real Uua Uub) tptp.zero_zero_complex)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_na6724076748692969250l_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1113820866546176217t_real (tptp.aTP_Lamm_ss Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uua Uub) tptp.zero_zero_real)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_fun_rat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun507281639146497029t_real (tptp.aTP_Lamm_st Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_rat_real (tptp.aa_nat_fun_rat_real Uua Uub) tptp.zero_zero_rat)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun7039663905532832253t_real (tptp.aTP_Lamm_su Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real Uua Uub) tptp.zero_zero_nat)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_fun_int_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun241848180832411225t_real (tptp.aTP_Lamm_sv Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real (tptp.aa_nat_fun_int_real Uua Uub) tptp.zero_zero_int)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_nat5545486172511849908x_bool (tptp.aTP_Lamm_vd Uu) Uua) Uub)) (= (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql Uu) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uua)) tptp.zero_zero_complex))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_nat_fun_real_bool (tptp.aTP_Lamm_ve Uu) Uua) Uub)) (= (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj Uu) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uua)) tptp.zero_zero_real))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ks Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex tptp.zero_zero_complex) Uub))) (tptp.aa_nat_complex Uua Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ku Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real tptp.zero_zero_real) Uub))) (tptp.aa_nat_real Uua Uub)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_kt Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.divide_divide_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat Uu Uub)) (tptp.aa_nat_rat (tptp.power_power_rat tptp.zero_zero_rat) Uub))) (tptp.aa_nat_rat Uua Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_acx 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_sw 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.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_tu Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uub)) (tptp.aa_nat_complex Uu Uub))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_tw Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uub)) (tptp.aa_nat_real Uu Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat)))))) (forall ((Uu tptp.set_VEBT_VEBT) (Uua tptp.nat) (Uub tptp.list_VEBT_VEBT)) (= (tptp.pp (tptp.aa_lis2822252094023462681T_bool (tptp.aa_nat1297483763028037422T_bool (tptp.aTP_Lamm_bw Uu) Uua) Uub)) (and (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 Uub) Uu) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s6755466524823107622T_VEBT Uub)) Uua))))) (forall ((Uu tptp.set_complex) (Uua tptp.nat) (Uub tptp.list_complex)) (= (tptp.pp (tptp.aa_list_complex_bool (tptp.aa_nat8039161444313734436x_bool (tptp.aTP_Lamm_bv Uu) Uua) Uub)) (and (tptp.ord_le211207098394363844omplex (tptp.set_complex2 Uub) Uu) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_s3451745648224563538omplex Uub)) Uua))))) (forall ((Uu tptp.set_bool) (Uua tptp.nat) (Uub tptp.list_bool)) (= (tptp.pp (tptp.aa_list_bool_bool (tptp.aa_nat4862889769322786699l_bool (tptp.aTP_Lamm_bx Uu) Uua) Uub)) (and (tptp.ord_less_eq_set_bool (tptp.set_bool2 Uub) Uu) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_bool Uub)) Uua))))) (forall ((Uu tptp.set_nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_bu Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 Uub)) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_nat Uub)) Uua))))) (forall ((Uu tptp.set_int) (Uua tptp.nat) (Uub tptp.list_int)) (= (tptp.pp (tptp.aa_list_int_bool (tptp.aa_nat1619170893822700070t_bool (tptp.aTP_Lamm_by Uu) Uua) Uub)) (and (tptp.ord_less_eq_set_int (tptp.set_int2 Uub) Uu) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.size_size_list_int Uub)) Uua))))) (forall ((Uu tptp.set_VEBT_VEBT) (Uua tptp.nat) (Uub tptp.list_VEBT_VEBT)) (= (tptp.pp (tptp.aa_lis2822252094023462681T_bool (tptp.aa_nat1297483763028037422T_bool (tptp.aTP_Lamm_br Uu) Uua) Uub)) (and (tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT2 Uub) Uu) (= (tptp.size_s6755466524823107622T_VEBT Uub) Uua)))) (forall ((Uu tptp.set_complex) (Uua tptp.nat) (Uub tptp.list_complex)) (= (tptp.pp (tptp.aa_list_complex_bool (tptp.aa_nat8039161444313734436x_bool (tptp.aTP_Lamm_bq Uu) Uua) Uub)) (and (tptp.ord_le211207098394363844omplex (tptp.set_complex2 Uub) Uu) (= (tptp.size_s3451745648224563538omplex Uub) Uua)))) (forall ((Uu tptp.set_bool) (Uua tptp.nat) (Uub tptp.list_bool)) (= (tptp.pp (tptp.aa_list_bool_bool (tptp.aa_nat4862889769322786699l_bool (tptp.aTP_Lamm_bs Uu) Uua) Uub)) (and (tptp.ord_less_eq_set_bool (tptp.set_bool2 Uub) Uu) (= (tptp.size_size_list_bool Uub) Uua)))) (forall ((Uu tptp.set_nat) (Uua tptp.nat) (Uub tptp.list_nat)) (= (tptp.pp (tptp.aa_list_nat_bool (tptp.aa_nat2079453845469346690t_bool (tptp.aTP_Lamm_bp Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.ord_less_eq_set_nat (tptp.set_nat2 Uub)) Uu)) (= (tptp.size_size_list_nat Uub) Uua)))) (forall ((Uu tptp.set_int) (Uua tptp.nat) (Uub tptp.list_int)) (= (tptp.pp (tptp.aa_list_int_bool (tptp.aa_nat1619170893822700070t_bool (tptp.aTP_Lamm_bt Uu) Uua) Uub)) (and (tptp.ord_less_eq_set_int (tptp.set_int2 Uub) Uu) (= (tptp.size_size_list_int 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_abd 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_abn Uu) Uua) Uub)) (and (tptp.member_set_nat Uub (tptp.pow_nat (tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat Uu))) (= (tptp.aa_set_nat_nat 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_abe Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) (tptp.aa_nat_nat tptp.suc Uua)))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_tt Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.diffs_complex Uu) Uub)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_tv Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.diffs_real Uu) Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ub Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.diffs_complex Uua) Uub)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu) Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ua Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.diffs_real Uua) Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_vb 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_zy 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_cq 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_zz 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_ct 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_cs 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_cr 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.vEBT_VEBT) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_ak Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member Uu) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uua) Uub))))) (forall ((Uu tptp.vEBT_VEBT) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_al Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_vebt_member Uu) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (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_aeo 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_aeu 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.set_Pr958786334691620121nt_int) (Uua tptp.fun_Pr803113274115125473t_bool) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_bd Uu) Uua) Uub)) (and (tptp.member5262025264175285858nt_int Uub Uu) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uua Uub))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_bool) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_be Uu) Uua) Uub)) (and (tptp.member_complex Uub Uu) (tptp.pp (tptp.aa_complex_bool Uua Uub))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_bool) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun6476784834714468668l_bool (tptp.aTP_Lamm_bc Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (tptp.pp (tptp.aa_real_bool Uua Uub))))) (forall ((Uu tptp.set_set_nat) (Uua tptp.fun_set_nat_bool) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_bf Uu) Uua) Uub)) (and (tptp.member_set_nat Uub Uu) (tptp.pp (tptp.aa_set_nat_bool Uua Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_bg Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (tptp.pp (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_bh Uu) Uua) Uub)) (and (tptp.member_int Uub Uu) (tptp.pp (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun9073502203726719595x_bool (tptp.aTP_Lamm_ef Uu) Uua) Uub)) (and (tptp.member_complex Uub Uu) (not (= (tptp.aa_complex_complex Uua Uub) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_real) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun2898354424061222765x_bool (tptp.aTP_Lamm_en Uu) Uua) Uub)) (and (tptp.member_complex Uub Uu) (not (= (tptp.aa_complex_real Uua Uub) tptp.zero_zero_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_complex) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun3813300650643916655l_bool (tptp.aTP_Lamm_dz Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_complex Uua Uub) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_eh Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_real Uua Uub) tptp.zero_zero_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_rat) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun8987621170725249221l_bool (tptp.aTP_Lamm_ep Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_rat Uua Uub) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8004580481347240231t_bool (tptp.aTP_Lamm_eb Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_complex Uua Uub) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1349230436907296553t_bool (tptp.aTP_Lamm_ej Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_real Uua Uub) tptp.zero_zero_real))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aTP_Lamm_er Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_rat Uua Uub) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_complex) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun8146511558608327279t_bool (tptp.aTP_Lamm_ed Uu) Uua) Uub)) (and (tptp.member_int Uub Uu) (not (= (tptp.aa_int_complex Uua Uub) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_real) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1262781554902806129t_bool (tptp.aTP_Lamm_el Uu) Uua) Uub)) (and (tptp.member_int Uub Uu) (not (= (tptp.aa_int_real Uua Uub) tptp.zero_zero_real))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun9073502203726719595x_bool (tptp.aTP_Lamm_dl Uu) Uua) Uub)) (and (tptp.member_complex Uub Uu) (not (= (tptp.aa_complex_complex Uua Uub) tptp.one_one_complex))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_real) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun2898354424061222765x_bool (tptp.aTP_Lamm_dt Uu) Uua) Uub)) (and (tptp.member_complex Uub Uu) (not (= (tptp.aa_complex_real Uua Uub) tptp.one_one_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_complex) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun3813300650643916655l_bool (tptp.aTP_Lamm_df Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_complex Uua Uub) tptp.one_one_complex))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aTP_Lamm_dn Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_real Uua Uub) tptp.one_one_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_rat) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun8987621170725249221l_bool (tptp.aTP_Lamm_dv Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (= (tptp.aa_real_rat Uua Uub) tptp.one_one_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8004580481347240231t_bool (tptp.aTP_Lamm_dh Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_complex Uua Uub) tptp.one_one_complex))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1349230436907296553t_bool (tptp.aTP_Lamm_dp Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_real Uua Uub) tptp.one_one_real))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aTP_Lamm_dx Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uub) Uu)) (not (= (tptp.aa_nat_rat Uua Uub) tptp.one_one_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_complex) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun8146511558608327279t_bool (tptp.aTP_Lamm_dj Uu) Uua) Uub)) (and (tptp.member_int Uub Uu) (not (= (tptp.aa_int_complex Uua Uub) tptp.one_one_complex))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_real) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1262781554902806129t_bool (tptp.aTP_Lamm_dr Uu) Uua) Uub)) (and (tptp.member_int Uub Uu) (not (= (tptp.aa_int_real Uua Uub) tptp.one_one_real))))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.set_Pr958786334691620121nt_int) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_set1381271197253378494t_bool (tptp.aTP_Lamm_ar Uu) Uua) Uub)) (and (tptp.member5262025264175285858nt_int Uub Uu) (not (tptp.member5262025264175285858nt_int Uub Uua))))) (forall ((Uu tptp.set_complex) (Uua tptp.set_complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_set3741564773079358752x_bool (tptp.aTP_Lamm_as Uu) Uua) Uub)) (and (tptp.member_complex Uub Uu) (not (tptp.member_complex Uub Uua))))) (forall ((Uu tptp.set_real) (Uua tptp.set_real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_set8565328311858951076l_bool (tptp.aTP_Lamm_aq Uu) Uua) Uub)) (and (tptp.member_real Uub Uu) (not (tptp.member_real Uub Uua))))) (forall ((Uu tptp.set_set_nat) (Uua tptp.set_set_nat) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_set9121396911425987952t_bool (tptp.aTP_Lamm_at Uu) Uua) Uub)) (and (tptp.member_set_nat Uub Uu) (not (tptp.member_set_nat Uub Uua))))) (forall ((Uu tptp.set_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (let ((_let_1 (tptp.member_nat Uub))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_set3744802623701456604t_bool (tptp.aTP_Lamm_av Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool _let_1 Uu)) (not (tptp.pp (tptp.aa_set_nat_bool _let_1 Uua))))))) (forall ((Uu tptp.set_int) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_set7012339369581096484t_bool (tptp.aTP_Lamm_au Uu) Uua) Uub)) (and (tptp.member_int Uub Uu) (not (tptp.member_int Uub Uua))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_aen 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_uw Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)) Uu)))) (forall ((Uu tptp.real) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_afk Uu) Uua) Uub)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_complex_real (tptp.real_V3694042436643373181omplex Uua) Uub)) Uu)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_afi Uu) Uua) Uub)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.ord_less_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V975177566351809787t_real Uua) Uub)) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_vh Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)) Uu)))) (forall ((Uu tptp.set_Pr9123050470547338789r_bool) (Uua tptp.code_integer) (Uub tptp.bool)) (= (tptp.pp (tptp.aa_bool_bool (tptp.aa_Cod8494480694608518558l_bool (tptp.aTP_Lamm_oj Uu) Uua) Uub)) (tptp.member7941544277139469958r_bool (tptp.produc5135875973608410785r_bool Uua Uub) Uu))) (forall ((Uu tptp.set_Pr8218934625190621173um_num) (Uua tptp.num) (Uub tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_num_fun_num_bool (tptp.aTP_Lamm_ok Uu) Uua) Uub)) (tptp.member7279096912039735102um_num (tptp.product_Pair_num_num Uua Uub) Uu))) (forall ((Uu tptp.set_Pr6200539531224447659at_num) (Uua tptp.nat) (Uub tptp.num)) (= (tptp.pp (tptp.aa_num_bool (tptp.aa_nat_fun_num_bool (tptp.aTP_Lamm_ol Uu) Uua) Uub)) (tptp.member9148766508732265716at_num (tptp.product_Pair_nat_num Uua Uub) Uu))) (forall ((Uu tptp.set_Pr1261947904930325089at_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_om Uu) Uua) Uub)) (tptp.member8440522571783428010at_nat (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uua) Uub) Uu))) (forall ((Uu tptp.set_Pr958786334691620121nt_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_on Uu) Uua) Uub)) (tptp.member5262025264175285858nt_int (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub) Uu))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool (tptp.aTP_Lamm_de Uu) Uua) Uub)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex 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_aaa Uu) Uua) Uub)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uub) Uua) Uu))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_qy Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu (tptp.aa_nat_nat tptp.suc Uub))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qz Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu (tptp.aa_nat_nat tptp.suc Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun4551936527957760560t_real (tptp.aTP_Lamm_aeg Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_nat_int Uua Uub))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_num_real tptp.numeral_numeral_real (tptp.aa_num_num tptp.bit0 tptp.one))) tptp.pi))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_acy Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ql Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qj Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_vf Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat Uu Uub)) (tptp.aa_nat_rat (tptp.power_power_rat Uua) Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_vy Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uua) Uub)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_vg Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uub)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uua) Uub)))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_bn Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool Uu Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uub) Uua))))) (forall ((Uu tptp.fun_real_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_afa 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_afc 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_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_aay 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_co8153928105989009288nteger) (Uua tptp.fun_co8153928105989009288nteger) (Uub tptp.complex)) (= (tptp.aa_com4217951221296830281nteger (tptp.aa_fun5267417455630836558nteger (tptp.aTP_Lamm_me Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_com4217951221296830281nteger Uua Uub)) (tptp.aa_com4217951221296830281nteger Uu Uub)))) (forall ((Uu tptp.fun_complex_real) (Uua tptp.fun_complex_real) (Uub tptp.complex)) (= (tptp.aa_complex_real (tptp.aa_fun8933909628229591020x_real (tptp.aTP_Lamm_mi Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real Uua Uub)) (tptp.aa_complex_real Uu Uub)))) (forall ((Uu tptp.fun_complex_rat) (Uua tptp.fun_complex_rat) (Uub tptp.complex)) (= (tptp.aa_complex_rat (tptp.aa_fun7622890401989837636ex_rat (tptp.aTP_Lamm_ml Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_complex_rat Uua Uub)) (tptp.aa_complex_rat Uu Uub)))) (forall ((Uu tptp.fun_re6978948838062957830nteger) (Uua tptp.fun_re6978948838062957830nteger) (Uub tptp.real)) (= (tptp.aa_real_Code_integer (tptp.aa_fun7923231501384339402nteger (tptp.aTP_Lamm_mf Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_real_Code_integer Uua Uub)) (tptp.aa_real_Code_integer Uu Uub)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_mj Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real Uua Uub)) (tptp.aa_real_real Uu Uub)))) (forall ((Uu tptp.fun_real_rat) (Uua tptp.fun_real_rat) (Uub tptp.real)) (= (tptp.aa_real_rat (tptp.aa_fun2468082234287226944al_rat (tptp.aTP_Lamm_mm Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_real_rat Uua Uub)) (tptp.aa_real_rat Uu Uub)))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.fun_nat_Code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_fun589076786913273746nteger (tptp.aTP_Lamm_mg Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer Uua Uub)) (tptp.aa_nat_Code_integer Uu Uub)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aTP_Lamm_mn Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat Uua Uub)) (tptp.aa_nat_rat Uu Uub)))) (forall ((Uu tptp.fun_int_Code_integer) (Uua tptp.fun_int_Code_integer) (Uub tptp.int)) (= (tptp.aa_int_Code_integer (tptp.aa_fun5304498221708291146nteger (tptp.aTP_Lamm_mh Uu) Uua) Uub) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_int_Code_integer Uua Uub)) (tptp.aa_int_Code_integer Uu Uub)))) (forall ((Uu tptp.fun_int_real) (Uua tptp.fun_int_real) (Uub tptp.int)) (= (tptp.aa_int_real (tptp.aa_fun3252798400008884712t_real (tptp.aTP_Lamm_mk Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real Uua Uub)) (tptp.aa_int_real Uu Uub)))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_hq Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex Uu Uub)) (tptp.aa_complex_complex Uua Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_pj Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex Uua Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hr 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_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_hp Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_complex_nat) (Uua tptp.fun_complex_nat) (Uub tptp.complex)) (= (tptp.aa_complex_nat (tptp.aa_fun2465681967280144180ex_nat (tptp.aTP_Lamm_lj Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_complex_nat Uua Uub)) (tptp.aa_complex_nat Uu Uub)))) (forall ((Uu tptp.fun_real_nat) (Uua tptp.fun_real_nat) (Uub tptp.real)) (= (tptp.aa_real_nat (tptp.aa_fun211602392931233840al_nat (tptp.aTP_Lamm_lk Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_real_nat Uua Uub)) (tptp.aa_real_nat Uu Uub)))) (forall ((Uu tptp.fun_bool_nat) (Uua tptp.fun_bool_nat) (Uub tptp.bool)) (= (tptp.aa_bool_nat (tptp.aa_fun9101744387563128124ol_nat (tptp.aTP_Lamm_re Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_bool_nat Uua Uub)) (tptp.aa_bool_nat Uu Uub)))) (forall ((Uu tptp.fun_set_nat_nat) (Uua tptp.fun_set_nat_nat) (Uub tptp.set_nat)) (= (tptp.aa_set_nat_nat (tptp.aa_fun3386010016858254564at_nat (tptp.aTP_Lamm_ll Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_set_nat_nat Uua Uub)) (tptp.aa_set_nat_nat Uu Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_th Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex Uua Uub)) (tptp.aa_nat_complex Uu Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_tj Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uua Uub)) (tptp.aa_nat_real Uu Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_ln Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat Uua Uub)) (tptp.aa_nat_nat Uu Uub)))) (forall ((Uu tptp.fun_int_nat) (Uua tptp.fun_int_nat) (Uub tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun6506752150744536624nt_nat (tptp.aTP_Lamm_lm Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_int_nat Uua Uub)) (tptp.aa_int_nat Uu Uub)))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_hm Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex Uu Uub)) (tptp.aa_complex_complex Uua Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ph Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex Uua Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_ho Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real Uua Uub)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hn Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aTP_Lamm_pi Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_nat_int Uu Uub)) (tptp.aa_nat_int Uua Uub)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_hl Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_real_real) (Uua tptp.fun_real_real) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun6946558556880649704l_real (tptp.aTP_Lamm_acw 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_Pr803113274115125473t_bool) (Uua tptp.fun_Pr803113274115125473t_bool) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_cg Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uua Uub))))) (forall ((Uu tptp.fun_complex_bool) (Uua tptp.fun_complex_bool) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_ck Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_complex_bool Uu Uub)) (tptp.pp (tptp.aa_complex_bool Uua Uub))))) (forall ((Uu tptp.fun_set_nat_bool) (Uua tptp.fun_set_nat_bool) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_ch Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_set_nat_bool Uu Uub)) (tptp.pp (tptp.aa_set_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_ci Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_nat_bool Uu Uub)) (tptp.pp (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_cj Uu) Uua) Uub)) (or (tptp.pp (tptp.aa_int_bool Uu Uub)) (tptp.pp (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.fun_Pr803113274115125473t_bool) (Uub tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool (tptp.aa_fun8917503761599146496t_bool (tptp.aTP_Lamm_cl Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uua Uub))))) (forall ((Uu tptp.fun_complex_bool) (Uua tptp.fun_complex_bool) (Uub tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun1096865461735438652x_bool (tptp.aTP_Lamm_cp Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_complex_bool Uu Uub)) (tptp.pp (tptp.aa_complex_bool Uua Uub))))) (forall ((Uu tptp.fun_set_nat_bool) (Uua tptp.fun_set_nat_bool) (Uub tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool (tptp.aa_fun3565389549526402364t_bool (tptp.aTP_Lamm_cm Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_set_nat_bool Uu Uub)) (tptp.pp (tptp.aa_set_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_nat_bool) (Uua tptp.fun_nat_bool) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun3878383735219268284t_bool (tptp.aTP_Lamm_cn Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_nat_bool Uu Uub)) (tptp.pp (tptp.aa_nat_bool Uua Uub))))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_bool) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun5146555767781538748t_bool (tptp.aTP_Lamm_co Uu) Uua) Uub)) (and (tptp.pp (tptp.aa_int_bool Uu Uub)) (tptp.pp (tptp.aa_int_bool Uua Uub))))) (forall ((Uu tptp.fun_co7673397065115134084omplex) (Uua tptp.set_complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_set7743095458595710203omplex (tptp.aTP_Lamm_gc Uu) Uua) Uub) (tptp.groups7754918857620584856omplex (tptp.aa_com3342990543769683525omplex Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_real) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_set1166323925324055613t_real (tptp.aTP_Lamm_gi Uu) Uua) Uub) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_fun_nat_nat) (Uua tptp.set_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_set6537093552120046177at_nat (tptp.aTP_Lamm_gf Uu) Uua) Uub) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_fun_int_int) (Uua tptp.set_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_set7310040872927613301nt_int (tptp.aTP_Lamm_fz Uu) Uua) Uub) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aTP_Lamm_bo Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat (tptp.aa_nat_nat Uu Uub)) Uua)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_jj Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.modulo_modulo_nat (tptp.aa_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_ji Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.modulo_modulo_int (tptp.aa_int_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_hs Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_complex_complex Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ot Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.divide1717551699836669952omplex (tptp.aa_nat_complex Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_ht Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_nat_real Uu Uub)) Uua))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.aTP_Lamm_he Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_pe Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_hg Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_hf Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) Uua))) (forall ((Uu tptp.fun_int_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_hd Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uu Uub)) Uua))) (forall ((Uu tptp.complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_ta Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uua Uub)) Uu))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_tb Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uua Uub)) Uu))) (forall ((Uu tptp.fun_nat_Code_integer) (Uua tptp.code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_rk Uu) Uua) Uub) (tptp.minus_8373710615458151222nteger (tptp.aa_nat_Code_integer Uu Uub) Uua))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_rl Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_ri Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat Uu Uub)) Uua))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_rj Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int Uu Uub)) Uua))) (forall ((Uu tptp.fun_real_real) (Uua tptp.nat) (Uub tptp.real)) (= (tptp.aa_real_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_act 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_ael 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_acv Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.powr_real (tptp.aa_real_real Uu Uub)) Uua))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun7054779078796324018t_real (tptp.aTP_Lamm_rm Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_nat_complex Uua Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_Cod1578151519121547077nteger (tptp.aTP_Lamm_nl Uu) Uua) Uub) (tptp.plus_p5714425477246183910nteger Uu (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger Uub)) Uua)))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_ni Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uu) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uub)) Uua)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_nn Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uub)) Uua)))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aTP_Lamm_nj Uu) Uua) Uub) (tptp.aa_rat_rat (tptp.plus_plus_rat Uu) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uub)) Uua)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_nm Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat Uub)) Uua)))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_nk Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int Uub)) Uua)))) (forall ((Uu tptp.complex) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_sd Uu) Uua) Uub) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_sg Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_se Uu) Uua) Uub) (tptp.aa_nat_rat (tptp.power_power_rat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_sf Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_aea Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real Uua) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uub)))) (forall ((Uu tptp.complex) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_ls Uu) Uua) Uub) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lv Uu) Uua) Uub) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aTP_Lamm_lt Uu) Uua) Uub) (tptp.aa_nat_rat (tptp.power_power_rat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aTP_Lamm_lu Uu) Uua) Uub) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_mz Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uu) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uub) Uua)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_aey Uu) Uua) Uub)) (tptp.member_real Uub (tptp.set_or1633881224788618240n_real Uu Uua)))) (forall ((Uu tptp.complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_fun3187328805393345264omplex (tptp.aTP_Lamm_hi Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Uu) (tptp.aa_complex_complex Uua Uub)))) (forall ((Uu tptp.complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_os Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Uu) (tptp.aa_nat_complex Uua Uub)))) (forall ((Uu tptp.real) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_hk Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Uu) (tptp.aa_nat_real Uua Uub)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aTP_Lamm_hj Uu) Uua) Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uu) (tptp.aa_nat_nat Uua Uub)))) (forall ((Uu tptp.int) (Uua tptp.fun_int_int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun6280345759651049192nt_int (tptp.aTP_Lamm_hh Uu) Uua) Uub) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) (tptp.aa_int_int Uua Uub)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_pf Uu) Uua) Uub) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex Uua) (tptp.aa_nat_complex 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_pg Uu) Uua) Uub) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real Uua) (tptp.aa_nat_real Uu Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_rd Uu) Uua) Uub) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_rc Uu) Uua) Uub) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uub))))) (forall ((Uu tptp.fun_real_bool) (Uua tptp.real) (Uub tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool (tptp.aTP_Lamm_aev 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_complex) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aTP_Lamm_or Uu) Uua) Uub) (tptp.aa_nat_complex Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aTP_Lamm_lr 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_aet Uu) Uua) Uub)) (tptp.pp (tptp.aa_nat_bool Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aTP_Lamm_lq Uu) Uua) Uub) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)))) (forall ((Uu tptp.fun_Pr2477239776880934807at_nat) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat7997280740862404369at_nat (tptp.aa_nat5682243440470347102at_nat (tptp.aTP_Lamm_jk Uu) Uua) Uub) (tptp.aa_Pro8023792847356852296at_nat Uu (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uua) Uub)))) (forall ((Uu tptp.fun_Pr248683899324676269t_bool) (Uua tptp.nat) (Uub tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool (tptp.aTP_Lamm_jl Uu) Uua) Uub) (tptp.aa_Pro595088089689268830t_bool Uu (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat Uua) Uub)))) (forall ((Uu tptp.fun_Pr2478283820680522243nt_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aTP_Lamm_jm Uu) Uua) Uub) (tptp.aa_Pro6970504127699319548nt_int Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub)))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.int) (Uub tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aTP_Lamm_jn Uu) Uua) Uub)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub))))) (forall ((Uu tptp.fun_Pr982841511892225912nt_int) (Uua tptp.int) (Uub tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aTP_Lamm_jo Uu) Uua) Uub) (tptp.aa_Pro6799258434465214121nt_int Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int Uua) Uub)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aTP_Lamm_tc Uu) Uua) Uub) (tptp.aa_nat_complex Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uu)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aTP_Lamm_td Uu) Uua) Uub) (tptp.aa_nat_real Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uu)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_com20334259897932645t_real (tptp.aTP_Lamm_qm Uu) Uua) Uub) (tptp.aa_complex_real tptp.real_V1022390504157884413omplex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu Uub)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) Uub))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_qk Uu) Uua) Uub) (tptp.aa_real_real tptp.real_V7735802525324610683m_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uub))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aTP_Lamm_aef 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.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_zo Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool _let_2 Uub)) (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 Uuc)))) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uub) _let_1))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub)))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu) Uuc))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc)))) tptp.zero_zero_complex))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_zm Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_bool_bool (tptp.fconj (tptp.aa_nat_bool _let_2 Uub)) (tptp.aa_bool_bool tptp.fNot (tptp.aa_nat_bool _let_2 Uuc)))) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real tptp.uminus_uminus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uub) _let_1))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc)))) tptp.zero_zero_real))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_zs Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) Uub)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_rea2618301233319580611omplex tptp.real_V2046097035970521341omplex (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uub) _let_1))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu) Uuc))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc)))) tptp.zero_zero_complex)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_zq Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.dvd_dvd_nat _let_1) Uub)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.real_V1485227260804924795R_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_int_real tptp.ring_1_of_int_real (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int tptp.uminus_uminus_int tptp.one_one_int)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uub) _let_1))) (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))))) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uub))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc)))) tptp.zero_zero_real)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_wc Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_complex Uua Uuc)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.zero_zero_complex) (tptp.aa_nat_complex Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_wk Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_real Uua Uuc)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.zero_zero_real) (tptp.aa_nat_real Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_we Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu) tptp.zero_zero_rat) (tptp.aa_nat_rat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_wi Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.zero_zero_nat) (tptp.aa_nat_nat Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_wg Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_int Uua Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc) Uu)) tptp.zero_zero_int) (tptp.aa_nat_int Uub (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aa_fun7497765718855568684omplex (tptp.aTP_Lamm_wd Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_complex Uua Uuc)) (tptp.aa_nat_complex Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_fun8674848580393814182t_real (tptp.aTP_Lamm_wl Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_real Uua Uuc)) (tptp.aa_nat_real Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_fun765758790203053448at_rat (tptp.aa_fun3638354034882855594at_rat (tptp.aTP_Lamm_wf Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu) (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_nat) (Uub tptp.fun_nat_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5791449513213591928at_nat (tptp.aa_fun6854695580826382482at_nat (tptp.aTP_Lamm_wj Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_nat Uua Uuc)) (tptp.aa_nat_nat Uub Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.fun_nat_int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun5565043122120104496at_int (tptp.aa_fun5140708168904641446at_int (tptp.aTP_Lamm_wh Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) Uu)) (tptp.aa_nat_int Uua Uuc)) (tptp.aa_nat_int Uub Uuc)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.set_nat) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2955221450537884980omplex (tptp.aa_set5115289136882354743omplex (tptp.aTP_Lamm_ti Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uua)) (tptp.aa_nat_complex Uub Uuc)) (tptp.aa_nat_complex Uu Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.set_nat) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun1839206346889086768t_real (tptp.aa_set1316517696749040435t_real (tptp.aTP_Lamm_tk Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uua)) (tptp.aa_nat_real Uub Uuc)) (tptp.aa_nat_real Uu Uuc)))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_oi Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_oh Uu) Uua) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_og Uu) Uua) Uub) Uuc) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_of Uu) Uua) Uub) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) Uuc))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_oe Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_od Uu) Uua) Uub)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_nat_nat tptp.suc tptp.zero_zero_nat))) Uuc))))) (forall ((Uu tptp.bool) (Uua tptp.bool) (Uub tptp.code_integer) (Uuc tptp.bool)) (= (tptp.aa_bool_char (tptp.aa_Cod6370812454140447392l_char (tptp.aa_boo1160955832611998748l_char (tptp.aTP_Lamm_aco Uu) Uua) Uub) Uuc) (tptp.produc7257819798349884575l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aTP_Lamm_acn Uu) Uua) Uuc) (tptp.code_bit_cut_integer Uub)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.set_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_set1166323925324055613t_real (tptp.aa_fun1400677770452585267t_real (tptp.aTP_Lamm_hc Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_hb Uu) Uua) Uuc)) Uub))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.set_nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_set6537093552120046177at_nat (tptp.aa_fun4561837934398617467at_nat (tptp.aTP_Lamm_ha Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_gz Uu) Uua) Uuc)) Uub))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.fun_complex_complex) (Uub tptp.set_complex) (Uuc tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_set7743095458595710203omplex (tptp.aa_fun1583801116089702097omplex (tptp.aTP_Lamm_gy Uu) Uua) Uub) Uuc) (tptp.groups7754918857620584856omplex (tptp.aa_com3342990543769683525omplex (tptp.aa_fun6995112137416684571omplex (tptp.aTP_Lamm_gx Uu) Uua) Uuc) Uub))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.set_int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_set7310040872927613301nt_int (tptp.aa_fun8076508010538293575nt_int (tptp.aTP_Lamm_gw Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int (tptp.aa_int_fun_int_int (tptp.aa_fun5911324870756489105nt_int (tptp.aTP_Lamm_gv Uu) Uua) Uuc) Uub))) (forall ((Uu tptp.nat) (Uua tptp.code_integer) (Uub tptp.code_integer) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_Code_integer (tptp.aa_Cod1578151519121547077nteger (tptp.aa_Cod6397266357770349983nteger (tptp.aTP_Lamm_wp Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.if_Code_integer (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat) (tptp.aa_Cod1783974652533396728nteger tptp.uminus1351360451143612070nteger Uub) (tptp.if_Code_integer (tptp.aa_nat_bool _let_1 Uu) tptp.one_one_Code_integer tptp.zero_z3403309356797280102nteger))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aTP_Lamm_wn Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat)) (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Uub)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex (tptp.aa_nat_bool _let_1 Uu)) tptp.one_one_complex) tptp.zero_zero_complex))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aTP_Lamm_wq Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat)) (tptp.aa_real_real tptp.uminus_uminus_real Uub)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real (tptp.aa_nat_bool _let_1 Uu)) tptp.one_one_real) tptp.zero_zero_real))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aTP_Lamm_wo Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat) (tptp.aa_rat_rat tptp.uminus_uminus_rat Uub)) (tptp.aa_rat_rat (tptp.if_rat (tptp.aa_nat_bool _let_1 Uu) tptp.one_one_rat) tptp.zero_zero_rat))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_bool tptp.fequal_nat Uuc))) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aTP_Lamm_wm Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool _let_1 tptp.zero_zero_nat)) (tptp.aa_int_int tptp.uminus_uminus_int Uub)) (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int (tptp.aa_nat_bool _let_1 Uu)) tptp.one_one_int) tptp.zero_zero_int))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uua) Uuc))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_re4238438383274954274t_real) (Uub tptp.fun_re9121486324101951821t_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_fun555827300007793674t_real (tptp.aa_fun8353879187736340217t_real (tptp.aTP_Lamm_jh Uu) Uua) Uub) Uuc) (tptp.groups8097168146408367636l_real (tptp.aa_nat_fun_real_real (tptp.aTP_Lamm_jg Uua) Uuc) (tptp.collect_real (tptp.aa_nat_fun_real_bool (tptp.aa_fun3382945097342017788l_bool (tptp.aTP_Lamm_cu Uu) Uub) Uuc))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_co636942507509095880at_nat) (Uub tptp.fun_co2841405903858895691t_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun996456248398975532at_nat (tptp.aa_fun8754082201773474805at_nat (tptp.aTP_Lamm_je Uu) Uua) Uub) Uuc) (tptp.groups5693394587270226106ex_nat (tptp.aa_nat3391284541783913865ex_nat (tptp.aTP_Lamm_jd Uua) Uuc) (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aa_fun5091585579174883964x_bool (tptp.aTP_Lamm_dd Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_nat_nat) (Uub tptp.fun_int_fun_nat_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun4133023758092209198at_nat (tptp.aa_fun7384697781603784697at_nat (tptp.aTP_Lamm_ja Uu) Uua) Uub) Uuc) (tptp.groups4541462559716669496nt_nat (tptp.aa_nat_fun_int_nat (tptp.aTP_Lamm_iz Uua) Uuc) (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun3035398748895483388t_bool (tptp.aTP_Lamm_da Uu) Uub) Uuc))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_fun_nat_nat) (Uub tptp.fun_re9121486324101951821t_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_fun5672750458368166062at_nat (tptp.aa_fun6824837968375615225at_nat (tptp.aTP_Lamm_iw Uu) Uua) Uub) Uuc) (tptp.groups1935376822645274424al_nat (tptp.aa_nat_fun_real_nat (tptp.aTP_Lamm_iv Uua) Uuc) (tptp.collect_real (tptp.aa_nat_fun_real_bool (tptp.aa_fun3382945097342017788l_bool (tptp.aTP_Lamm_cu Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_in1307110748760623106omplex) (Uub tptp.fun_in5750378413879446255x_bool) (Uuc tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_fun2686559102040213132omplex (tptp.aa_fun5422379709423809691omplex (tptp.aTP_Lamm_is Uu) Uua) Uub) Uuc) (tptp.groups3049146728041665814omplex (tptp.aa_com9156536935073639875omplex (tptp.aTP_Lamm_ir Uua) Uuc) (tptp.collect_int (tptp.aa_com2211550117870696024t_bool (tptp.aa_fun3087709329828230012t_bool (tptp.aTP_Lamm_dc Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_na1591161823130732966omplex) (Uub tptp.fun_na5941084329111710283x_bool) (Uuc tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_fun1613615970879741416omplex (tptp.aa_fun7586814990830484307omplex (tptp.aTP_Lamm_io Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_com8181001469867462503omplex (tptp.aTP_Lamm_in Uua) Uuc)) (tptp.collect_nat (tptp.aa_com5335841084339320244t_bool (tptp.aa_fun8674784841953735804t_bool (tptp.aTP_Lamm_cz Uu) Uub) Uuc))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_re7208826350674946562omplex) (Uub tptp.fun_re3010880487650781423x_bool) (Uuc tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_fun8128191506076533516omplex (tptp.aa_fun840110154952133019omplex (tptp.aTP_Lamm_ik Uu) Uua) Uub) Uuc) (tptp.groups5754745047067104278omplex (tptp.aa_com4766338864777664963omplex (tptp.aTP_Lamm_ij Uua) Uuc) (tptp.collect_real (tptp.aa_com8943241093633526360l_bool (tptp.aa_fun8455611678790336124l_bool (tptp.aTP_Lamm_cw Uu) Uub) Uuc))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_co333780937270390912nt_int) (Uub tptp.fun_co2381122952212249071t_bool) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun855801025254967176nt_int (tptp.aa_fun315996177946036377nt_int (tptp.aTP_Lamm_ig Uu) Uua) Uub) Uuc) (tptp.groups5690904116761175830ex_int (tptp.aa_int6126987627036542017ex_int (tptp.aTP_Lamm_ie Uua) Uuc) (tptp.collect_complex (tptp.aa_int5354780257279585880x_bool (tptp.aa_fun2352441141717865852x_bool (tptp.aTP_Lamm_if Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_int_int) (Uub tptp.fun_nat_fun_int_bool) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun4504283173926863078nt_int (tptp.aa_fun5512849559334105941nt_int (tptp.aTP_Lamm_ib Uu) Uua) Uub) Uuc) (tptp.groups3539618377306564664at_int (tptp.aa_int_fun_nat_int (tptp.aTP_Lamm_ia Uua) Uuc) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun8184653438340336124t_bool (tptp.aTP_Lamm_cy Uu) Uub) Uuc))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_fun_int_int) (Uub tptp.fun_re8661203372455305201t_bool) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_fun5532095235224157706nt_int (tptp.aa_fun4786959800906006429nt_int (tptp.aTP_Lamm_hx Uu) Uua) Uub) Uuc) (tptp.groups1932886352136224148al_int (tptp.aa_int_fun_real_int (tptp.aTP_Lamm_hw Uua) Uuc) (tptp.collect_real (tptp.aa_int_fun_real_bool (tptp.aa_fun1536421850685375484l_bool (tptp.aTP_Lamm_cv Uu) Uub) Uuc))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_wa 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_vz 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_nat_int) (Uua tptp.fun_nat_int) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_fun2315716387381795033at_int (tptp.aTP_Lamm_vr Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_fun6128006242533108349at_int (tptp.aTP_Lamm_vq Uu) Uua) Uuc) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uub) Uuc)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_fun5559679822142647773at_rat (tptp.aTP_Lamm_vp Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_fun2663889555218712533at_rat (tptp.aTP_Lamm_vo Uu) Uua) Uuc) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_fun4732485501138722137t_real (tptp.aTP_Lamm_vs Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_vk Uu) Uua) Uuc)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uuc)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_fun3721018923249493343omplex (tptp.aTP_Lamm_vn Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_fun5379041630539201665omplex (tptp.aTP_Lamm_vi Uu) Uua) Uuc)) (tptp.aa_nat_set_nat tptp.set_ord_atMost_nat Uuc))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uub) Uuc)))) (forall ((Uu tptp.fun_na6724076748692969250l_real) (Uua tptp.nat) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_adf 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_add 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_adb 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_adc Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.divide_divide_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uu Uuc) Uub)) (tptp.aa_nat_real tptp.semiri2265585572941072030t_real Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real Uua) Uub)) Uuc)))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_rn Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uu) Uua)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (tptp.aa_nat_complex _let_1 Uuc))) (tptp.aa_nat_complex _let_1 Uub))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_real_fun_nat_real tptp.power_power_real Uu))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_rt Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) Uua)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (tptp.aa_nat_real _let_1 Uuc))) (tptp.aa_nat_real _let_1 Uub))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.power_power_rat Uu))) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_rp Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Uu) Uua)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (tptp.aa_nat_rat _let_1 Uuc))) (tptp.aa_nat_rat _let_1 Uub))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_int_fun_nat_int tptp.power_power_int Uu))) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_rr Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) Uua)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (tptp.aa_nat_int _let_1 Uuc))) (tptp.aa_nat_int _let_1 Uub))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uua))) (let ((_let_2 (tptp.aa_nat_fun_nat_nat tptp.times_times_nat Uu))) (= (tptp.aa_nat7603221163087113075at_nat (tptp.aa_nat8803788312118491388at_nat (tptp.aa_nat4158579785191972357at_nat (tptp.aTP_Lamm_abp Uu) Uua) Uub) Uuc) (tptp.aa_nat7603221163087113075at_nat (tptp.product_Pair_nat_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Uub)) (tptp.aa_nat_nat _let_1 Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat _let_2 Uuc)) (tptp.aa_nat_nat _let_1 Uub))))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_od Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uua) Uu)) Uuc)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Uuc))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_oh Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uua) Uu)) Uuc)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_of Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Uua) Uu)) Uuc)) (tptp.aa_nat_rat (tptp.power_power_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) Uuc))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_nat2010205248571845816nteger (tptp.aa_Cod3140087502949435154nteger (tptp.aTP_Lamm_yj Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger Uu) Uuc))) (tptp.aa_nat_Code_integer (tptp.comm_s8582702949713902594nteger Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_yk Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Uu) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.comm_s7457072308508201937r_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_yh Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Uu) Uuc))) (tptp.aa_nat_rat (tptp.comm_s4028243227959126397er_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_yi Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int Uu) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.comm_s4660882817536571857er_int Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.code_integer) (Uua tptp.code_integer) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_Code_integer (tptp.aa_nat2010205248571845816nteger (tptp.aa_Cod3140087502949435154nteger (tptp.aTP_Lamm_vw Uu) Uua) Uub) Uuc) (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_Cod1783974652533396728nteger (tptp.aa_Cod4161879620478718930nteger tptp.times_3573771949741848930nteger (tptp.aa_nat_Code_integer tptp.semiri4939895301339042750nteger (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uu) Uuc))) (tptp.aa_nat_Code_integer (tptp.power_8256067586552552935nteger Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_vt Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu) Uuc))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_vx Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_vu Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uu) Uuc))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_vm Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat tptp.semiri1316708129612266289at_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uu) Uuc))) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.power_power_nat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_vv Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int tptp.semiri1314217659103216013at_int (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.binomial Uub) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) Uuc))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.complex) (Uua tptp.nat) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_rz Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu) Uuc)))) (forall ((Uu tptp.real) (Uua tptp.nat) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_sc Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc)))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_sa Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_rat (tptp.power_power_rat Uu) Uuc)))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_sb Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) (tptp.aa_nat_nat tptp.suc Uuc)))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) Uuc)))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_re3010880487650781423x_bool) (Uub tptp.real) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_rea5887071448072802392x_bool (tptp.aa_fun9179849694055305084x_bool (tptp.aTP_Lamm_ih Uu) Uua) Uub) Uuc)) (and (tptp.member_complex Uuc Uu) (tptp.pp (tptp.aa_complex_bool (tptp.aa_rea5887071448072802392x_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_na5941084329111710283x_bool) (Uub tptp.nat) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_nat5545486172511849908x_bool (tptp.aa_fun2551091230351774588x_bool (tptp.aTP_Lamm_il Uu) Uua) Uub) Uuc)) (and (tptp.member_complex Uuc Uu) (tptp.pp (tptp.aa_complex_bool (tptp.aa_nat5545486172511849908x_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_in5750378413879446255x_bool) (Uub tptp.int) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_int5354780257279585880x_bool (tptp.aa_fun6456964791495427196x_bool (tptp.aTP_Lamm_ip Uu) Uua) Uub) Uuc)) (and (tptp.member_complex Uuc Uu) (tptp.pp (tptp.aa_complex_bool (tptp.aa_int5354780257279585880x_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_co2841405903858895691t_bool) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_com5335841084339320244t_bool (tptp.aa_fun1991907153922069372t_bool (tptp.aTP_Lamm_jb Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_com5335841084339320244t_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_re9121486324101951821t_bool) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_real_fun_nat_bool (tptp.aa_fun5702564393759107580t_bool (tptp.aTP_Lamm_it Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_real_fun_nat_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_int_fun_nat_bool) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool (tptp.aa_fun3602880909931171836t_bool (tptp.aTP_Lamm_ix Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_co2381122952212249071t_bool) (Uub tptp.complex) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_com2211550117870696024t_bool (tptp.aa_fun8206557716905444476t_bool (tptp.aTP_Lamm_ic Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_com2211550117870696024t_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_re8661203372455305201t_bool) (Uub tptp.real) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_real_fun_int_bool (tptp.aa_fun6227302519962330364t_bool (tptp.aTP_Lamm_hu Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_real_fun_int_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_nat_fun_int_bool) (Uub tptp.nat) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool (tptp.aa_fun7617171277304647676t_bool (tptp.aTP_Lamm_hy Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool Uua Uub) Uuc))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_co2841405903858895691t_bool) (Uub tptp.nat) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_nat5545486172511849908x_bool (tptp.aa_fun5091585579174883964x_bool (tptp.aTP_Lamm_dd Uu) Uua) Uub) Uuc)) (and (tptp.member_complex Uuc Uu) (tptp.pp (tptp.aa_nat_bool (tptp.aa_com5335841084339320244t_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_co2381122952212249071t_bool) (Uub tptp.int) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_int5354780257279585880x_bool (tptp.aa_fun2352441141717865852x_bool (tptp.aTP_Lamm_if Uu) Uua) Uub) Uuc)) (and (tptp.member_complex Uuc Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_com2211550117870696024t_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_re3010880487650781423x_bool) (Uub tptp.complex) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_com8943241093633526360l_bool (tptp.aa_fun8455611678790336124l_bool (tptp.aTP_Lamm_cw Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (tptp.pp (tptp.aa_complex_bool (tptp.aa_rea5887071448072802392x_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_re9121486324101951821t_bool) (Uub tptp.nat) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_nat_fun_real_bool (tptp.aa_fun3382945097342017788l_bool (tptp.aTP_Lamm_cu Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (tptp.pp (tptp.aa_nat_bool (tptp.aa_real_fun_nat_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_re8661203372455305201t_bool) (Uub tptp.int) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_int_fun_real_bool (tptp.aa_fun1536421850685375484l_bool (tptp.aTP_Lamm_cv Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_real_fun_int_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_na5941084329111710283x_bool) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_com5335841084339320244t_bool (tptp.aa_fun8674784841953735804t_bool (tptp.aTP_Lamm_cz Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_nat5545486172511849908x_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_nat_bool) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_fun3051233943552222972t_bool (tptp.aTP_Lamm_cx Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_fun_int_bool) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool (tptp.aa_fun8184653438340336124t_bool (tptp.aTP_Lamm_cy Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_in5750378413879446255x_bool) (Uub tptp.complex) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_com2211550117870696024t_bool (tptp.aa_fun3087709329828230012t_bool (tptp.aTP_Lamm_dc Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (tptp.pp (tptp.aa_complex_bool (tptp.aa_int5354780257279585880x_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_nat_bool) (Uub tptp.nat) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_nat_fun_int_bool (tptp.aa_fun3035398748895483388t_bool (tptp.aTP_Lamm_da Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (tptp.pp (tptp.aa_nat_bool (tptp.aa_int_fun_nat_bool Uua Uuc) Uub))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_db Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uuc) Uub))))) (forall ((Uu tptp.complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (let ((_let_2 (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu))) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_ro Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex _let_2 Uuc)) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uu) Uua)) _let_1)) (tptp.aa_nat_complex _let_2 _let_1))))))) (forall ((Uu tptp.real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (let ((_let_2 (tptp.aa_real_fun_nat_real tptp.power_power_real Uu))) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_ru Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real _let_2 Uuc)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uu) Uua)) _let_1)) (tptp.aa_nat_real _let_2 _let_1))))))) (forall ((Uu tptp.rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (let ((_let_2 (tptp.power_power_rat Uu))) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_rq Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat _let_2 Uuc)) (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Uu) Uua)) _let_1)) (tptp.aa_nat_rat _let_2 _let_1))))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (let ((_let_1 (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))) (let ((_let_2 (tptp.aa_int_fun_nat_int tptp.power_power_int Uu))) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_rs Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int _let_2 Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int Uu) Uua)) _let_1)) (tptp.aa_nat_int _let_2 _let_1))))))) (forall ((Uu tptp.complex) (Uua tptp.nat) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_rv Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uu) Uuc)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.real) (Uua tptp.nat) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_ry Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uu) Uuc)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.rat) (Uua tptp.nat) (Uub tptp.rat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_nat298952458717073160at_rat (tptp.aTP_Lamm_rw Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.power_power_rat Uu) Uuc)) (tptp.aa_nat_rat (tptp.power_power_rat Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.nat) (Uub tptp.int) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_nat6704147566042551216at_int (tptp.aTP_Lamm_rx Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uu) Uuc)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uub) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uua) Uuc))))) (forall ((Uu tptp.nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_vc 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_aao 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_abu 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_aam 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_abs 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_abw 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_aby 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.set_complex) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool (tptp.aa_com1326194769588742913x_bool (tptp.aTP_Lamm_afm Uu) Uua) Uub) Uuc)) (=> (= Uub Uua) (tptp.member_complex Uuc Uu)))) (forall ((Uu tptp.set_real) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool (tptp.aa_rea2091369211473463559l_bool (tptp.aTP_Lamm_afn Uu) Uua) Uub) Uuc)) (=> (= Uub Uua) (tptp.member_real Uuc Uu)))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_complex) (Uub tptp.fun_complex_complex) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun9073502203726719595x_bool (tptp.aa_fun6641798613628721963x_bool (tptp.aTP_Lamm_dm Uu) Uua) Uub) Uuc)) (and (tptp.member_complex Uuc Uu) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex Uua Uuc)) (tptp.aa_complex_complex Uub Uuc)) tptp.one_one_complex))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_real) (Uub tptp.fun_complex_real) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun2898354424061222765x_bool (tptp.aa_fun2094807616088678831x_bool (tptp.aTP_Lamm_du Uu) Uua) Uub) Uuc)) (and (tptp.member_complex Uuc Uu) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_complex_real Uua Uuc)) (tptp.aa_complex_real Uub Uuc)) tptp.one_one_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_complex) (Uub tptp.fun_real_complex) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun3813300650643916655l_bool (tptp.aa_fun5520078544946397361l_bool (tptp.aTP_Lamm_dg Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_real_complex Uua Uuc)) (tptp.aa_real_complex Uub Uuc)) tptp.one_one_complex))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_real) (Uub tptp.fun_real_real) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aa_fun334843040499603765l_bool (tptp.aTP_Lamm_do Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real Uua Uuc)) (tptp.aa_real_real Uub Uuc)) tptp.one_one_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_rat) (Uub tptp.fun_real_rat) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun8987621170725249221l_bool (tptp.aa_fun8530242357055030877l_bool (tptp.aTP_Lamm_dw Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_real_rat Uua Uuc)) (tptp.aa_real_rat Uub Uuc)) tptp.one_one_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_complex) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8004580481347240231t_bool (tptp.aa_fun5430245816583273541t_bool (tptp.aTP_Lamm_di Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uua Uuc)) (tptp.aa_nat_complex Uub Uuc)) tptp.one_one_complex))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_real) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1349230436907296553t_bool (tptp.aa_fun849216055071118793t_bool (tptp.aTP_Lamm_dq Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uua Uuc)) (tptp.aa_nat_real Uub Uuc)) tptp.one_one_real))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_dy Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)) tptp.one_one_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_complex) (Uub tptp.fun_int_complex) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun8146511558608327279t_bool (tptp.aa_fun3850298374753145905t_bool (tptp.aTP_Lamm_dk Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_int_complex Uua Uuc)) (tptp.aa_int_complex Uub Uuc)) tptp.one_one_complex))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_real) (Uub tptp.fun_int_real) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1262781554902806129t_bool (tptp.aa_fun6205147705862377397t_bool (tptp.aTP_Lamm_ds Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_int_real Uua Uuc)) (tptp.aa_int_real Uub Uuc)) tptp.one_one_real))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_complex) (Uub tptp.fun_complex_complex) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun9073502203726719595x_bool (tptp.aa_fun6641798613628721963x_bool (tptp.aTP_Lamm_eg Uu) Uua) Uub) Uuc)) (and (tptp.member_complex Uuc Uu) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_complex_complex Uua Uuc)) (tptp.aa_complex_complex Uub Uuc)) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_complex_real) (Uub tptp.fun_complex_real) (Uuc tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool (tptp.aa_fun2898354424061222765x_bool (tptp.aa_fun2094807616088678831x_bool (tptp.aTP_Lamm_eo Uu) Uua) Uub) Uuc)) (and (tptp.member_complex Uuc Uu) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_complex_real Uua Uuc)) (tptp.aa_complex_real Uub Uuc)) tptp.zero_zero_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_complex) (Uub tptp.fun_real_complex) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun3813300650643916655l_bool (tptp.aa_fun5520078544946397361l_bool (tptp.aTP_Lamm_ea Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_real_complex Uua Uuc)) (tptp.aa_real_complex Uub Uuc)) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_real) (Uub tptp.fun_real_real) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun9137271176455094897l_bool (tptp.aa_fun334843040499603765l_bool (tptp.aTP_Lamm_ei Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_real_real Uua Uuc)) (tptp.aa_real_real Uub Uuc)) tptp.zero_zero_real))))) (forall ((Uu tptp.set_real) (Uua tptp.fun_real_rat) (Uub tptp.fun_real_rat) (Uuc tptp.real)) (= (tptp.pp (tptp.aa_real_bool (tptp.aa_fun8987621170725249221l_bool (tptp.aa_fun8530242357055030877l_bool (tptp.aTP_Lamm_eq Uu) Uua) Uub) Uuc)) (and (tptp.member_real Uuc Uu) (not (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_real_rat Uua Uuc)) (tptp.aa_real_rat Uub Uuc)) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_complex) (Uub tptp.fun_nat_complex) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun8004580481347240231t_bool (tptp.aa_fun5430245816583273541t_bool (tptp.aTP_Lamm_ec Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex Uua Uuc)) (tptp.aa_nat_complex Uub Uuc)) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_real) (Uub tptp.fun_nat_real) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun1349230436907296553t_bool (tptp.aa_fun849216055071118793t_bool (tptp.aTP_Lamm_ek Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real Uua Uuc)) (tptp.aa_nat_real Uub Uuc)) tptp.zero_zero_real))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_nat_rat) (Uub tptp.fun_nat_rat) (Uuc tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_fun5637262893798792573t_bool (tptp.aa_fun2107527232086395633t_bool (tptp.aTP_Lamm_es Uu) Uua) Uub) Uuc)) (and (tptp.pp (tptp.aa_set_nat_bool (tptp.member_nat Uuc) Uu)) (not (= (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat Uua Uuc)) (tptp.aa_nat_rat Uub Uuc)) tptp.zero_zero_rat))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_complex) (Uub tptp.fun_int_complex) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun8146511558608327279t_bool (tptp.aa_fun3850298374753145905t_bool (tptp.aTP_Lamm_ee Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (not (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_int_complex Uua Uuc)) (tptp.aa_int_complex Uub Uuc)) tptp.zero_zero_complex))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_int_real) (Uub tptp.fun_int_real) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_fun1262781554902806129t_bool (tptp.aa_fun6205147705862377397t_bool (tptp.aTP_Lamm_em Uu) Uua) Uub) Uuc)) (and (tptp.member_int Uuc Uu) (not (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_int_real Uua Uuc)) (tptp.aa_int_real Uub Uuc)) tptp.zero_zero_real))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.nat) (Uub tptp.complex) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_nat2301396582920332468omplex (tptp.aTP_Lamm_ra Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uua))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uub) Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.real) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_rb Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uua))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uuc)))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_xk Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu Uuc)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) Uub)) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_xq Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uuc)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) Uub)) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_xm Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat Uu Uuc)) (tptp.aa_nat_rat (tptp.power_power_rat Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) Uub)) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_xo Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uuc)) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uua) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uuc) Uub)) tptp.one_one_nat))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.fun_nat_complex) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_fun5379041630539201665omplex (tptp.aTP_Lamm_vi Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu Uuc)) (tptp.aa_nat_complex Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_vk Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uuc)) (tptp.aa_nat_real Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.fun_nat_rat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_fun2663889555218712533at_rat (tptp.aTP_Lamm_vo Uu) Uua) Uub) Uuc) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat Uu Uuc)) (tptp.aa_nat_rat Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_vz Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uuc)) (tptp.aa_nat_nat Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.fun_nat_int) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_fun6128006242533108349at_int (tptp.aTP_Lamm_vq Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu Uuc)) (tptp.aa_nat_int Uua (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uub) Uuc))))) (forall ((Uu tptp.fun_complex_complex) (Uua tptp.fun_complex_complex) (Uub tptp.complex) (Uuc tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.aa_fun6995112137416684571omplex (tptp.aTP_Lamm_gx Uu) Uua) Uub) Uuc) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex Uu Uub)) (tptp.aa_complex_complex Uua Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.fun_nat_real) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_fun3023522663955195517t_real (tptp.aTP_Lamm_hb Uu) Uua) Uub) Uuc) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu Uub)) (tptp.aa_nat_real Uua Uuc)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.fun_nat_nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_fun6650658898577385413at_nat (tptp.aTP_Lamm_gz Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.times_times_nat (tptp.aa_nat_nat Uu Uub)) (tptp.aa_nat_nat Uua Uuc)))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aa_fun5911324870756489105nt_int (tptp.aTP_Lamm_gv Uu) Uua) Uub) Uuc) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int Uu Uub)) (tptp.aa_int_int Uua Uuc)))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_co636942507509095880at_nat) (Uub tptp.fun_co2841405903858895691t_bool) (Uuc tptp.complex)) (= (tptp.aa_complex_nat (tptp.aa_fun9050545535516344074ex_nat (tptp.aa_fun2757644259618170323ex_nat (tptp.aTP_Lamm_jc Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_com6383720667567721865at_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_com5335841084339320244t_bool (tptp.aa_fun1991907153922069372t_bool (tptp.aTP_Lamm_jb Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_int_fun_nat_nat) (Uub tptp.fun_int_fun_nat_bool) (Uuc tptp.int)) (= (tptp.aa_int_nat (tptp.aa_fun5132377469993263754nt_nat (tptp.aa_fun348247319442030677nt_nat (tptp.aTP_Lamm_iy Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_int_fun_nat_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_int_fun_nat_bool (tptp.aa_fun3602880909931171836t_bool (tptp.aTP_Lamm_ix Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_re4238438383274954274t_real) (Uub tptp.fun_re9121486324101951821t_bool) (Uuc tptp.real)) (= (tptp.aa_real_real (tptp.aa_fun7981600115099051494l_real (tptp.aa_fun2847282595593119957l_real (tptp.aTP_Lamm_jf Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real Uua Uuc)) (tptp.collect_nat (tptp.aa_real_fun_nat_bool (tptp.aa_fun5702564393759107580t_bool (tptp.aTP_Lamm_it Uu) Uub) Uuc))))) (forall ((Uu tptp.set_nat) (Uua tptp.fun_real_fun_nat_nat) (Uub tptp.fun_re9121486324101951821t_bool) (Uuc tptp.real)) (= (tptp.aa_real_nat (tptp.aa_fun5804151645385689226al_nat (tptp.aa_fun8436216498351771861al_nat (tptp.aTP_Lamm_iu Uu) Uua) Uub) Uuc) (tptp.aa_set_nat_nat (tptp.groups3542108847815614940at_nat (tptp.aa_real_fun_nat_nat Uua Uuc)) (tptp.collect_nat (tptp.aa_real_fun_nat_bool (tptp.aa_fun5702564393759107580t_bool (tptp.aTP_Lamm_it Uu) Uub) Uuc))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_in1307110748760623106omplex) (Uub tptp.fun_in5750378413879446255x_bool) (Uuc tptp.int)) (= (tptp.aa_int_complex (tptp.aa_fun751309451324587018omplex (tptp.aa_fun3438240386181387033omplex (tptp.aTP_Lamm_iq Uu) Uua) Uub) Uuc) (tptp.groups7754918857620584856omplex (tptp.aa_int3545933452204062147omplex Uua Uuc) (tptp.collect_complex (tptp.aa_int5354780257279585880x_bool (tptp.aa_fun6456964791495427196x_bool (tptp.aTP_Lamm_ip Uu) Uub) Uuc))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_na1591161823130732966omplex) (Uub tptp.fun_na5941084329111710283x_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_fun2700696402887535882omplex (tptp.aa_fun8019143150332516725omplex (tptp.aTP_Lamm_im Uu) Uua) Uub) Uuc) (tptp.groups7754918857620584856omplex (tptp.aa_nat3829984526574172007omplex Uua Uuc) (tptp.collect_complex (tptp.aa_nat5545486172511849908x_bool (tptp.aa_fun2551091230351774588x_bool (tptp.aTP_Lamm_il Uu) Uub) Uuc))))) (forall ((Uu tptp.set_complex) (Uua tptp.fun_re7208826350674946562omplex) (Uub tptp.fun_re3010880487650781423x_bool) (Uuc tptp.real)) (= (tptp.aa_real_complex (tptp.aa_fun4873726854752153866omplex (tptp.aa_fun883667864959905433omplex (tptp.aTP_Lamm_ii Uu) Uua) Uub) Uuc) (tptp.groups7754918857620584856omplex (tptp.aa_rea2618301233319580611omplex Uua Uuc) (tptp.collect_complex (tptp.aa_rea5887071448072802392x_bool (tptp.aa_fun9179849694055305084x_bool (tptp.aTP_Lamm_ih Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_co333780937270390912nt_int) (Uub tptp.fun_co2381122952212249071t_bool) (Uuc tptp.complex)) (= (tptp.aa_complex_int (tptp.aa_fun3700423334941611530ex_int (tptp.aa_fun3520494530470439451ex_int (tptp.aTP_Lamm_id Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int (tptp.aa_com3205223359959579713nt_int Uua Uuc) (tptp.collect_int (tptp.aa_com2211550117870696024t_bool (tptp.aa_fun8206557716905444476t_bool (tptp.aTP_Lamm_ic Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_nat_fun_int_int) (Uub tptp.fun_nat_fun_int_bool) (Uuc tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_fun3504929462025808522at_int (tptp.aa_fun3325927984641084153at_int (tptp.aTP_Lamm_hz Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int (tptp.aa_nat_fun_int_int Uua Uuc) (tptp.collect_int (tptp.aa_nat_fun_int_bool (tptp.aa_fun7617171277304647676t_bool (tptp.aTP_Lamm_hy Uu) Uub) Uuc))))) (forall ((Uu tptp.set_int) (Uua tptp.fun_real_fun_int_int) (Uub tptp.fun_re8661203372455305201t_bool) (Uuc tptp.real)) (= (tptp.aa_real_int (tptp.aa_fun529217645232493962al_int (tptp.aa_fun5832317237790237469al_int (tptp.aTP_Lamm_hv Uu) Uua) Uub) Uuc) (tptp.groups4538972089207619220nt_int (tptp.aa_real_fun_int_int Uua Uuc) (tptp.collect_int (tptp.aa_real_fun_int_bool (tptp.aa_fun6227302519962330364t_bool (tptp.aTP_Lamm_hu Uu) Uub) Uuc))))) (forall ((Uu tptp.bool) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_na Uu) Uua) Uub) Uuc)) (and (tptp.pp Uu) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uub) Uuc))))) (forall ((Uu tptp.fun_Pr2478283820680522243nt_int) (Uua tptp.fun_in1696471567231710611nt_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_fun4152872853588681340nt_int (tptp.aTP_Lamm_gt Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int Uua Uub) Uuc)))) (forall ((Uu tptp.fun_Pr803113274115125473t_bool) (Uua tptp.fun_in1696471567231710611nt_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun395975271853239642t_bool (tptp.aTP_Lamm_gp Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_Pro4501881432599481050t_bool Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int Uua Uub) Uuc))))) (forall ((Uu tptp.fun_Pr982841511892225912nt_int) (Uua tptp.fun_in1696471567231710611nt_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aa_fun7461304428735181397nt_int (tptp.aTP_Lamm_gq Uu) Uua) Uub) Uuc) (tptp.aa_Pro6799258434465214121nt_int Uu (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int Uua Uub) Uuc)))) (forall ((Uu tptp.fun_bo7720638723722887333nt_int) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_fun9101259627203045662nt_int (tptp.aTP_Lamm_gr Uu) Uua) Uub) Uuc) (tptp.aa_boo6976928504896087454nt_int Uu (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uub) Uuc)))) (forall ((Uu tptp.fun_bool_bool) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun8168818243683596540t_bool (tptp.aTP_Lamm_gl Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_bool_bool Uu (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uub) Uuc))))) (forall ((Uu tptp.fun_bool_int) (Uua tptp.fun_int_fun_int_bool) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aa_fun5341983444565040691nt_int (tptp.aTP_Lamm_gm Uu) Uua) Uub) Uuc) (tptp.aa_bool_int Uu (tptp.aa_int_bool (tptp.aa_int_fun_int_bool Uua Uub) Uuc)))) (forall ((Uu tptp.fun_in4211310926729683942nt_int) (Uua tptp.fun_int_fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_fun1034830265760468567nt_int (tptp.aTP_Lamm_gs Uu) Uua) Uub) Uuc) (tptp.aa_int7462565939943104719nt_int Uu (tptp.aa_int_int (tptp.aa_int_fun_int_int Uua Uub) Uuc)))) (forall ((Uu tptp.fun_int_bool) (Uua tptp.fun_int_fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool (tptp.aa_fun980369494830392501t_bool (tptp.aTP_Lamm_gn Uu) Uua) Uub) Uuc)) (tptp.pp (tptp.aa_int_bool Uu (tptp.aa_int_int (tptp.aa_int_fun_int_int Uua Uub) Uuc))))) (forall ((Uu tptp.fun_int_int) (Uua tptp.fun_int_fun_int_int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.aa_fun6119123525526402106nt_int (tptp.aTP_Lamm_go Uu) Uua) Uub) Uuc) (tptp.aa_int_int Uu (tptp.aa_int_int (tptp.aa_int_fun_int_int Uua Uub) Uuc)))) (forall ((Uu tptp.fun_fu6897202038601531823t_bool) (Uua tptp.fun_na4786964484885125043t_bool) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool (tptp.aa_fun3491305611276047780t_bool (tptp.aTP_Lamm_gu Uu) Uua) Uub) Uuc) (tptp.aa_fun830836278467416944t_bool Uu (tptp.aa_nat4401263874371387303t_bool (tptp.aa_nat4909001760120733684t_bool Uua Uub) Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_nat4085805313368488148t_real (tptp.aTP_Lamm_lx Uu) Uua) Uub) Uuc) (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)) Uuc)))) (forall ((Uu tptp.fun_nat_nat) (Uua tptp.nat) (Uub tptp.nat) (Uuc tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.aa_nat3783148529270815480at_nat (tptp.aTP_Lamm_lw Uu) Uua) Uub) Uuc) (tptp.aa_nat_nat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uub) Uua)) Uuc)))) (forall ((Uu tptp.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_aaq Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.minus_minus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uub) Uua))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aas Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.plus_plus_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uub) Uua))) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aau Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uub)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uuc))))) (forall ((Uu tptp.int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.int)) (= (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int (tptp.aa_int1966403025003302569nt_int (tptp.aTP_Lamm_aaw Uu) Uua) Uub) Uuc) (tptp.aa_Pro6970504127699319548nt_int tptp.normalize (tptp.aa_int7462565939943104719nt_int (tptp.aa_int2565445551602696444nt_int tptp.product_Pair_int_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uu) Uuc)) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int Uua) Uub))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_fun2548873334967081986t_real (tptp.aTP_Lamm_xd Uu) Uua) Uub) Uuc) Uud) (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aa_rea6454571821648764761t_real (tptp.aTP_Lamm_xc Uua) Uub) Uuc) Uud)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.int) (Uuc tptp.int) (Uud tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aa_fun7421131748584218370at_int (tptp.aTP_Lamm_xb Uu) Uua) Uub) Uuc) Uud) (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aa_int6823550873765277145at_int (tptp.aTP_Lamm_xa Uua) Uub) Uuc) Uud) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_fun8528462509625601970at_rat (tptp.aTP_Lamm_wz Uu) Uua) Uub) Uuc) Uud) (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aa_rat8984911954100663005at_rat (tptp.aTP_Lamm_wy Uua) Uub) Uuc) Uud) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_fun5031706661949900810omplex (tptp.aTP_Lamm_wx Uu) Uua) Uub) Uuc) Uud) (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aa_com7713930848417683039omplex (tptp.aTP_Lamm_ww Uua) Uub) Uuc) Uud)) (tptp.aa_nat_set_nat tptp.set_ord_lessThan_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.bool) (Uua tptp.bool) (Uub tptp.bool) (Uuc tptp.code_integer) (Uud tptp.bool)) (= (tptp.aa_bool_char (tptp.aa_Cod6370812454140447392l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aTP_Lamm_acn Uu) Uua) Uub) Uuc) Uud) (tptp.produc7257819798349884575l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aa_boo3984127200019211826l_char (tptp.aTP_Lamm_acm Uu) Uua) Uub) Uud) (tptp.code_bit_cut_integer Uuc)))) (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_ade Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_nat_fun_real_real Uua Uuc) Uud)) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_real_fun_nat_real (tptp.aa_nat1308781354268537904t_real (tptp.aTP_Lamm_add 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.fun_nat_real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_fun2548873334967081986t_real (tptp.aTP_Lamm_xr Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_set_nat_real (tptp.groups6591440286371151544t_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aTP_Lamm_xq Uua) Uuc) Uud)) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uud) Uu))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uud)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_int) (Uub tptp.int) (Uuc tptp.int) (Uud tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_int_fun_nat_int (tptp.aa_int5842867502692063756at_int (tptp.aa_fun7421131748584218370at_int (tptp.aTP_Lamm_xp Uu) Uua) Uub) Uuc) Uud) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.groups3539618377306564664at_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aTP_Lamm_xo Uua) Uuc) Uud) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uud) Uu))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uub) Uud)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_fun8528462509625601970at_rat (tptp.aTP_Lamm_xn Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.groups2906978787729119204at_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aTP_Lamm_xm Uua) Uuc) Uud) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uud) Uu))) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud)))) (forall ((Uu tptp.nat) (Uua tptp.fun_nat_complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_fun5031706661949900810omplex (tptp.aTP_Lamm_xl Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_set_nat_complex (tptp.groups2073611262835488442omplex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aTP_Lamm_xk Uua) Uuc) Uud)) (tptp.set_or1269000886237332187st_nat (tptp.aa_nat_nat tptp.suc Uud) Uu))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uub) Uud)))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_zd Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.minus_minus_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uud)) Uua)) tptp.one_one_complex)) Uud)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uub) Uud))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_zf Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.minus_minus_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uud)) Uua)) tptp.one_one_real)) Uud)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uud))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_ze Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.minus_minus_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uud)) Uua)) tptp.one_one_rat)) Uud)) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_yl Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex (tptp.aa_nat_complex tptp.semiri8010041392384452111omplex Uu)) Uua)) Uud)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uub) Uud))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_yp Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real (tptp.aa_nat_real tptp.semiri5074537144036343181t_real Uu)) Uua)) Uud)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uud))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_yn Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat (tptp.plus_plus_rat (tptp.aa_nat_rat tptp.semiri681578069525770553at_rat Uu)) Uua)) Uud)) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat Uuc) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.complex) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex (tptp.aa_com8177640530696437650omplex (tptp.aa_com177695874307951165omplex (tptp.aTP_Lamm_ym Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.gbinomial_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Uua)) Uud)) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex tptp.uminus1482373934393186551omplex Uub)) Uud))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.plus_plus_complex Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.real) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real (tptp.aa_rea7841385751566875788t_real (tptp.aa_rea1729780184207679413t_real (tptp.aTP_Lamm_yq Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.gbinomial_real (tptp.aa_real_real tptp.uminus_uminus_real Uua)) Uud)) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real tptp.uminus_uminus_real Uub)) Uud))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.plus_plus_real Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.nat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.rat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_rat_fun_nat_rat (tptp.aa_rat3146053865535587600at_rat (tptp.aa_rat7467449789483521253at_rat (tptp.aTP_Lamm_yo Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat (tptp.gbinomial_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat Uua)) Uud)) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat tptp.uminus_uminus_rat Uub)) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat (tptp.aa_rat_rat (tptp.plus_plus_rat Uub) Uuc)) (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.minus_minus_nat Uu) Uud))))) (forall ((Uu tptp.fun_nat_complex) (Uua tptp.complex) (Uub tptp.complex) (Uuc tptp.nat) (Uud tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_nat6454746962644518025omplex (tptp.aa_com4347742694490471604omplex (tptp.aa_com7713930848417683039omplex (tptp.aTP_Lamm_ww Uu) Uua) Uub) Uuc) Uud) (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex tptp.times_times_complex (tptp.aa_nat_complex Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uud)) tptp.one_one_nat))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uub) Uud))) (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.power_power_complex Uua) Uuc)))) (forall ((Uu tptp.fun_nat_real) (Uua tptp.real) (Uub tptp.real) (Uuc tptp.nat) (Uud tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_nat_fun_nat_real (tptp.aa_rea6853821027689443120t_real (tptp.aa_rea6454571821648764761t_real (tptp.aTP_Lamm_xc Uu) Uua) Uub) Uuc) Uud) (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real tptp.times_times_real (tptp.aa_nat_real Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uud)) tptp.one_one_nat))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uub) Uud))) (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.power_power_real Uua) Uuc)))) (forall ((Uu tptp.fun_nat_rat) (Uua tptp.rat) (Uub tptp.rat) (Uuc tptp.nat) (Uud tptp.nat)) (= (tptp.aa_nat_rat (tptp.aa_nat_fun_nat_rat (tptp.aa_rat250263598611652360at_rat (tptp.aa_rat8984911954100663005at_rat (tptp.aTP_Lamm_wy Uu) Uua) Uub) Uuc) Uud) (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_rat_rat (tptp.times_times_rat (tptp.aa_nat_rat Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uud)) tptp.one_one_nat))) (tptp.aa_nat_rat (tptp.power_power_rat Uub) Uud))) (tptp.aa_nat_rat (tptp.power_power_rat Uua) Uuc)))) (forall ((Uu tptp.fun_nat_int) (Uua tptp.int) (Uub tptp.int) (Uuc tptp.nat) (Uud tptp.nat)) (= (tptp.aa_nat_int (tptp.aa_nat_fun_nat_int (tptp.aa_int431785320988601264at_int (tptp.aa_int6823550873765277145at_int (tptp.aTP_Lamm_xa Uu) Uua) Uub) Uuc) Uud) (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_int_int (tptp.aa_int_fun_int_int tptp.times_times_int (tptp.aa_nat_int Uu (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.plus_plus_nat Uuc) Uud)) tptp.one_one_nat))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uub) Uud))) (tptp.aa_nat_int (tptp.aa_int_fun_nat_int tptp.power_power_int Uua) Uuc)))) (forall ((Uu tptp.nat) (Uua tptp.list_VEBT_VEBT) (Uub tptp.vEBT_VEBT) (Uuc tptp.nat) (Uud tptp.nat)) (let ((_let_1 (tptp.aa_num_nat tptp.numeral_numeral_nat (tptp.aa_num_num tptp.bit0 tptp.one)))) (let ((_let_2 (= Uuc Uud))) (= (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool (tptp.aa_VEB1917483692448707121t_bool (tptp.aa_lis1179741779018426550t_bool (tptp.aTP_Lamm_afd 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 ((I5 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 I5) (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_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions (tptp.nth_VEBT_VEBT Uua I5)) X_12))) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions Uub) I5)))))) (=> _let_2 (forall ((X4 tptp.vEBT_VEBT)) (=> (tptp.pp (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool tptp.member_VEBT_VEBT X4) (tptp.set_VEBT_VEBT2 Uua))) (not (exists ((X_12 tptp.nat)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_VEB4832260192069861672t_bool tptp.vEBT_V8194947554948674370ptions X4) X_12))))))) (=> (not _let_2) (and (tptp.pp (tptp.aa_nat_bool (tptp.vEBT_V5917875025757280293ildren (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat tptp.divide_divide_nat Uu) _let_1) Uua) Uud)) (forall ((X4 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 X4) (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) X4)) (and (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_nat Uuc) X4)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.ord_less_eq_nat X4) Uud)))))))))))))) (forall ((Uu tptp.bool) (Uua tptp.bool) (Uub tptp.bool) (Uuc tptp.bool) (Uud tptp.code_integer) (Uue tptp.bool)) (= (tptp.aa_bool_char (tptp.aa_Cod6370812454140447392l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aa_boo3984127200019211826l_char (tptp.aTP_Lamm_acm Uu) Uua) Uub) Uuc) Uud) Uue) (tptp.produc7257819798349884575l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aa_boo3984127200019211826l_char (tptp.aa_boo5194212545117631380l_char (tptp.aTP_Lamm_acl Uu) Uua) Uub) Uuc) Uue) (tptp.code_bit_cut_integer Uud)))) (forall ((Uu tptp.bool) (Uua tptp.bool) (Uub tptp.bool) (Uuc tptp.bool) (Uud tptp.bool) (Uue tptp.code_integer) (Uuf tptp.bool)) (= (tptp.aa_bool_char (tptp.aa_Cod6370812454140447392l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aa_boo3984127200019211826l_char (tptp.aa_boo5194212545117631380l_char (tptp.aTP_Lamm_acl Uu) Uua) Uub) Uuc) Uud) Uue) Uuf) (tptp.produc7257819798349884575l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aa_boo3984127200019211826l_char (tptp.aa_boo5194212545117631380l_char (tptp.aa_boo2023203282872912456l_char (tptp.aTP_Lamm_ack Uu) Uua) Uub) Uuc) Uud) Uuf) (tptp.code_bit_cut_integer Uue)))) (forall ((Uu tptp.bool) (Uua tptp.bool) (Uub tptp.bool) (Uuc tptp.bool) (Uud tptp.bool) (Uue tptp.bool) (Uuf tptp.bool) (Uug tptp.code_integer)) (= (tptp.aa_Cod6370812454140447392l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aa_boo3984127200019211826l_char (tptp.aa_boo5194212545117631380l_char (tptp.aa_boo2023203282872912456l_char (tptp.aa_boo9094958794169052458l_char (tptp.aTP_Lamm_acj Uu) Uua) Uub) Uuc) Uud) Uue) Uuf) Uug) (tptp.char2 Uu Uua Uub Uuc Uud Uue Uuf))) (forall ((Uu tptp.bool) (Uua tptp.bool) (Uub tptp.bool) (Uuc tptp.bool) (Uud tptp.bool) (Uue tptp.bool) (Uuf tptp.code_integer) (Uug tptp.bool)) (= (tptp.aa_bool_char (tptp.aa_Cod6370812454140447392l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aa_boo3984127200019211826l_char (tptp.aa_boo5194212545117631380l_char (tptp.aa_boo2023203282872912456l_char (tptp.aTP_Lamm_ack Uu) Uua) Uub) Uuc) Uud) Uue) Uuf) Uug) (tptp.produc7257819798349884575l_char (tptp.aa_boo1160955832611998748l_char (tptp.aa_boo3826374251381081086l_char (tptp.aa_boo3984127200019211826l_char (tptp.aa_boo5194212545117631380l_char (tptp.aa_boo2023203282872912456l_char (tptp.aa_boo9094958794169052458l_char (tptp.aTP_Lamm_acj Uu) Uua) Uub) Uuc) Uud) Uue) Uug) (tptp.code_bit_cut_integer Uuf)))) (forall ((Uu tptp.complex) (Uua tptp.nat)) (= (tptp.aa_nat_complex (tptp.aa_com8181001469867462503omplex tptp.aTP_Lamm_pc Uu) Uua) Uu)) (forall ((Uu tptp.real) (Uua tptp.nat)) (= (tptp.aa_nat_real (tptp.aa_real_fun_nat_real tptp.aTP_Lamm_pd Uu) Uua) Uu)) (forall ((Uu tptp.int) (Uua tptp.int)) (= (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.aTP_Lamm_nh Uu) Uua)) true)) (forall ((Uu tptp.complex)) (= (tptp.aa_complex_complex tptp.aTP_Lamm_af Uu) Uu)) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_ag Uu) Uu)) (forall ((Uu tptp.rat)) (= (tptp.aa_rat_rat tptp.aTP_Lamm_ah Uu) Uu)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_ai Uu) Uu)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_aj Uu) Uu)) (forall ((Uu tptp.complex)) (= (tptp.aa_complex_complex tptp.aTP_Lamm_bi Uu) tptp.zero_zero_complex)) (forall ((Uu tptp.real)) (= (tptp.aa_real_real tptp.aTP_Lamm_bj Uu) tptp.zero_zero_real)) (forall ((Uu tptp.rat)) (= (tptp.aa_rat_rat tptp.aTP_Lamm_bk Uu) tptp.zero_zero_rat)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_complex tptp.aTP_Lamm_nx Uu) tptp.zero_zero_complex)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_real tptp.aTP_Lamm_fb Uu) tptp.zero_zero_real)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_nat tptp.aTP_Lamm_bl Uu) tptp.zero_zero_nat)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_int tptp.aTP_Lamm_ny Uu) tptp.zero_zero_int)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_bm Uu) tptp.zero_zero_int)) (forall ((Uu tptp.nat)) (= (tptp.aa_nat_int tptp.aTP_Lamm_zu Uu) tptp.one_one_int)) (forall ((Uu tptp.int)) (= (tptp.aa_int_int tptp.aTP_Lamm_zv Uu) tptp.one_one_int)) (forall ((Uu tptp.product_prod_int_int)) (= (tptp.pp (tptp.aa_Pro4501881432599481050t_bool tptp.aTP_Lamm_aw Uu)) false)) (forall ((Uu tptp.complex)) (= (tptp.pp (tptp.aa_complex_bool tptp.aTP_Lamm_ax Uu)) false)) (forall ((Uu tptp.real)) (= (tptp.pp (tptp.aa_real_bool tptp.aTP_Lamm_bb Uu)) false)) (forall ((Uu tptp.set_nat)) (= (tptp.pp (tptp.aa_set_nat_bool tptp.aTP_Lamm_ay Uu)) false)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_az Uu)) false)) (forall ((Uu tptp.int)) (= (tptp.pp (tptp.aa_int_bool tptp.aTP_Lamm_ba Uu)) false)) (forall ((Uu tptp.nat)) (= (tptp.pp (tptp.aa_nat_bool tptp.aTP_Lamm_abc Uu)) true)) (forall ((P tptp.bool)) (or (tptp.pp P) (tptp.pp (tptp.aa_bool_bool tptp.fNot P)))) (forall ((P tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool tptp.fNot P))) (not (tptp.pp P)))) (tptp.pp tptp.fTrue) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fconj P) Q))) (tptp.pp Q))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fconj P) Q))) (tptp.pp P))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp P)) (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.fconj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fdisj P) Q))) (tptp.pp P) (tptp.pp Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.fdisj P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp P)) (tptp.pp (tptp.aa_bool_bool (tptp.fdisj P) Q)))) (not (tptp.pp tptp.fFalse)) (forall ((P tptp.bool) (Q tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies P) Q))) (not (tptp.pp P)) (tptp.pp Q))) (forall ((Q tptp.bool) (P tptp.bool)) (or (not (tptp.pp Q)) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies P) Q)))) (forall ((P tptp.bool) (Q tptp.bool)) (or (tptp.pp P) (tptp.pp (tptp.aa_bool_bool (tptp.aa_boo8970175072276269406l_bool tptp.fimplies P) Q)))) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int tptp.fFalse) X) Y) Y)) (forall ((X tptp.int) (Y tptp.int)) (= (tptp.aa_int_int (tptp.aa_int_fun_int_int (tptp.if_int tptp.fTrue) X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat tptp.fFalse) X) Y) Y)) (forall ((X tptp.nat) (Y tptp.nat)) (= (tptp.aa_nat_nat (tptp.aa_nat_fun_nat_nat (tptp.if_nat tptp.fTrue) X) Y) X)) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num (tptp.if_num tptp.fFalse) X) Y) Y)) (forall ((X tptp.num) (Y tptp.num)) (= (tptp.aa_num_num (tptp.aa_num_fun_num_num (tptp.if_num tptp.fTrue) X) Y) X)) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.if_rat tptp.fFalse X) Y) Y)) (forall ((X tptp.rat) (Y tptp.rat)) (= (tptp.aa_rat_rat (tptp.if_rat tptp.fTrue X) Y) X)) (forall ((P tptp.fun_nat_bool) (X tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool P X))) (tptp.pp (tptp.aa_fun_nat_bool_bool tptp.fEx_nat P)))) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real tptp.fFalse) X) Y) Y)) (forall ((X tptp.real) (Y tptp.real)) (= (tptp.aa_real_real (tptp.aa_rea7340605660300375871l_real (tptp.if_real tptp.fTrue) X) Y) X)) (forall ((X tptp.int) (Y tptp.int)) (or (not (= X Y)) (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y)))) (forall ((X tptp.int) (Y tptp.int)) (or (not (tptp.pp (tptp.aa_int_bool (tptp.aa_int_fun_int_bool tptp.fequal_int X) Y))) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (or (not (tptp.pp (tptp.aa_nat_bool (tptp.aa_nat_fun_nat_bool tptp.fequal_nat X) Y))) (= X Y))) (forall ((X tptp.bool) (Y tptp.bool)) (or (not (= X Y)) (tptp.pp (tptp.aa_bool_bool (tptp.fequal_bool X) Y)))) (forall ((X tptp.bool) (Y tptp.bool)) (or (not (tptp.pp (tptp.aa_bool_bool (tptp.fequal_bool X) Y))) (= X Y))) (forall ((X tptp.real) (Y tptp.real)) (or (not (= X Y)) (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real X) Y)))) (forall ((X tptp.real) (Y tptp.real)) (or (not (tptp.pp (tptp.aa_real_bool (tptp.aa_rea7809428808904475482l_bool tptp.fequal_real X) Y))) (= X Y))) (forall ((P tptp.fun_real_bool)) (= (tptp.aa_real_bool P (tptp.fChoice_real P)) (tptp.aa_fun3352386287069783311l_bool tptp.fEx_real P))) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex tptp.fFalse) X) Y) Y)) (forall ((X tptp.complex) (Y tptp.complex)) (= (tptp.aa_complex_complex (tptp.aa_com3342990543769683525omplex (tptp.if_complex tptp.fTrue) X) Y) X)) (forall ((X tptp.complex) (Y tptp.complex)) (or (not (= X Y)) (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.fequal_complex X) Y)))) (forall ((X tptp.complex) (Y tptp.complex)) (or (not (tptp.pp (tptp.aa_complex_bool (tptp.aa_com1553036987509291606x_bool tptp.fequal_complex X) Y))) (= X Y))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.if_Code_integer tptp.fFalse X Y) Y)) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (tptp.if_Code_integer tptp.fTrue X Y) X)) (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (tptp.if_VEBT_VEBT tptp.fFalse X Y) Y)) (forall ((X tptp.vEBT_VEBT) (Y tptp.vEBT_VEBT)) (= (tptp.if_VEBT_VEBT tptp.fTrue X Y) X)) (forall ((P tptp.fun_VEBT_VEBT_bool) (X tptp.vEBT_VEBT)) (or (not (tptp.pp (tptp.fAll_VEBT_VEBT P))) (tptp.pp (tptp.aa_VEBT_VEBT_bool P X)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (not (= X Y)) (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y)))) (forall ((X tptp.code_integer) (Y tptp.code_integer)) (or (not (tptp.pp (tptp.aa_Code_integer_bool (tptp.aa_Cod7250484176784686200r_bool tptp.fequal_Code_integer X) Y))) (= X Y))) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (tptp.if_option_nat tptp.fFalse X Y) Y)) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (= (tptp.if_option_nat tptp.fTrue X Y) X)) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (or (not (= X Y)) (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat X) Y)))) (forall ((X tptp.option_nat) (Y tptp.option_nat)) (or (not (tptp.pp (tptp.aa_option_nat_bool (tptp.aa_opt7943525813896274546t_bool tptp.fequal_option_nat X) Y))) (= X Y))) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int tptp.fFalse X) Y) Y)) (forall ((X tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (tptp.aa_Pro6970504127699319548nt_int (tptp.if_Pro3027730157355071871nt_int tptp.fTrue X) Y) X)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.if_Pro6206227464963214023at_nat tptp.fFalse) X) Y) Y)) (forall ((X tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (tptp.aa_Pro262675715343573244at_nat (tptp.aa_Pro8023792847356852296at_nat (tptp.if_Pro6206227464963214023at_nat tptp.fTrue) X) Y) X)) (forall ((P tptp.fun_bool_bool) (Q tptp.fun_VEBT_VEBT_bool) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBB_3745307990312268622T_VEBT P Q) R) (tptp.aa_bool_bool P (tptp.aa_VEBT_VEBT_bool Q R)))) (forall ((P tptp.fun_VE2066785035971159626l_bool) (Q tptp.fun_VEBT_VEBT_bool) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBS_6222329278419335549l_bool P Q) R) (tptp.aa_bool_bool (tptp.aa_VEB8047906998784800507l_bool P R) (tptp.aa_VEBT_VEBT_bool Q R)))) (forall ((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) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBB_2885587777813823575T_VEBT P Q) R) (tptp.aa_fun_nat_bool_bool P (tptp.aa_VEB4832260192069861672t_bool Q R)))) (forall ((P tptp.fun_bo1841576699660343469l_bool) (Q tptp.fun_VEBT_VEBT_bool) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEB8047906998784800507l_bool (tptp.cOMBB_3438363824644082366T_VEBT P Q) R) (tptp.aa_boo8970175072276269406l_bool P (tptp.aa_VEBT_VEBT_bool Q R)))) (forall ((P tptp.fun_VE7346385682144900493T_bool) (Q tptp.set_VEBT_VEBT) (R tptp.vEBT_VEBT)) (= (tptp.aa_VEBT_VEBT_bool (tptp.cOMBC_771164880915498576T_bool P Q) R) (tptp.aa_set8260762808118238015T_bool (tptp.aa_VEB289770264548726718T_bool P R) Q))) _let_19 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 26.75/26.92 )
% 26.75/26.92 % SZS output end Proof for ITP268_1
% 26.75/26.92 % cvc5---1.0.5 exiting
% 26.75/26.92 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------