TSTP Solution File: NUM924+8 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM924+8 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:49:00 EDT 2023
% Result : Theorem 17.64s 17.87s
% Output : Proof 17.64s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 1.20/1.23 % Problem : NUM924+8 : TPTP v8.1.2. Released v5.3.0.
% 1.20/1.24 % Command : do_cvc5 %s %d
% 1.25/1.45 % Computer : n001.cluster.edu
% 1.25/1.45 % Model : x86_64 x86_64
% 1.25/1.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 1.25/1.45 % Memory : 8042.1875MB
% 1.25/1.45 % OS : Linux 3.10.0-693.el7.x86_64
% 1.25/1.45 % CPULimit : 300
% 1.25/1.45 % WCLimit : 300
% 1.25/1.45 % DateTime : Fri Aug 25 15:58:45 EDT 2023
% 1.25/1.46 % CPUTime :
% 2.49/2.67 %----Proving TF0_NAR, FOF, or CNF
% 17.64/17.87 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.jEMb3BuPMv/cvc5---1.0.5_1718.p...
% 17.64/17.87 ------- get file name : TPTP file name is NUM924+8
% 17.64/17.87 ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_1718.smt2...
% 17.64/17.87 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 17.64/17.87 --- Run --no-e-matching --full-saturate-quant at 5...
% 17.64/17.87 % SZS status Theorem for NUM924+8
% 17.64/17.87 % SZS output start Proof for NUM924+8
% 17.64/17.87 (
% 17.64/17.87 (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_3))) (let ((_let_5 (tptp.number_number_of tptp.nat))) (let ((_let_6 (tptp.hAPP tptp.int tptp.nat _let_5 _let_4))) (let ((_let_7 (tptp.power_power tptp.int))) (let ((_let_8 (tptp.fun tptp.nat tptp.int))) (let ((_let_9 (tptp.hAPP tptp.int _let_8 _let_7 tptp.s))) (let ((_let_10 (tptp.hAPP tptp.nat tptp.int _let_9 _let_6))) (let ((_let_11 (tptp.plus_plus tptp.int))) (let ((_let_12 (tptp.fun tptp.int tptp.int))) (let ((_let_13 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_12 _let_11 _let_10) _let_2))) (let ((_let_14 (tptp.ord_less tptp.int))) (let ((_let_15 (tptp.fun tptp.int tptp.bool))) (let ((_let_16 (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_14 _let_13) _let_1))))) (let ((_let_17 (tptp.linord20386208strict tptp.int))) (let ((_let_18 (tptp.number_number_of tptp.int))) (let ((_let_19 (tptp.hAPP tptp.int tptp.int _let_18 _let_4))) (let ((_let_20 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_3))) (let ((_let_21 (tptp.hAPP tptp.int tptp.int _let_18 _let_20))) (let ((_let_22 (tptp.fun tptp.nat tptp.bool))) (let ((_let_23 (tptp.fun tptp.nat _let_22))) (let ((_let_24 (tptp.hAPP _let_23 _let_23 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.fequal tptp.nat)))) (let ((_let_25 (tptp.fun tptp.nat tptp.nat))) (let ((_let_26 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_27 (tptp.fun _let_26 tptp.bool))) (let ((_let_28 (= tptp.pred_nat (tptp.hAPP _let_27 _let_27 (tptp.collect _let_26) (tptp.hAPP _let_23 _let_27 (tptp.product_prod_case tptp.nat tptp.nat tptp.bool) (tptp.hAPP _let_25 _let_23 (tptp.hAPP _let_23 (tptp.fun _let_25 _let_23) (tptp.combb tptp.nat _let_22 tptp.nat) _let_24) tptp.suc)))))) (let ((_let_29 (tptp.filter tptp.nat))) (let ((_let_30 (tptp.number_number_of tptp.real))) (let ((_let_31 (tptp.hAPP tptp.int tptp.real _let_30 _let_4))) (let ((_let_32 (tptp.inverse_divide tptp.real))) (let ((_let_33 (tptp.fun tptp.real tptp.real))) (let ((_let_34 (tptp.hAPP tptp.real _let_33 _let_32 tptp.pi))) (let ((_let_35 (tptp.hAPP tptp.real tptp.real _let_34 _let_31))) (let ((_let_36 (tptp.filter tptp.real))) (let ((_let_37 (tptp.zero_zero tptp.real))) (let ((_let_38 (tptp.fun tptp.real _let_33))) (let ((_let_39 (tptp.fun _let_36 tptp.bool))) (let ((_let_40 (tptp.zero_zero tptp.nat))) (let ((_let_41 (tptp.fun _let_22 _let_22))) (let ((_let_42 (tptp.fun tptp.bool tptp.bool))) (let ((_let_43 (tptp.real_1 tptp.nat))) (let ((_let_44 (tptp.real_1 tptp.int))) (let ((_let_45 (tptp.fun tptp.int _let_33))) (let ((_let_46 (tptp.fun tptp.int tptp.real))) (let ((_let_47 (tptp.hAPP _let_46 _let_45 (tptp.hAPP _let_38 (tptp.fun _let_46 _let_45) (tptp.combb tptp.real _let_33 tptp.int) _let_32) _let_44))) (let ((_let_48 (tptp.combb tptp.real tptp.real tptp.nat))) (let ((_let_49 (tptp.fun tptp.nat tptp.real))) (let ((_let_50 (tptp.fun _let_49 _let_49))) (let ((_let_51 (tptp.fun tptp.int _let_50))) (let ((_let_52 (tptp.fun tptp.int _let_49))) (let ((_let_53 (tptp.fequal tptp.real))) (let ((_let_54 (tptp.fun _let_49 _let_22))) (let ((_let_55 (tptp.fun tptp.real tptp.bool))) (let ((_let_56 (tptp.fun tptp.real _let_54))) (let ((_let_57 (tptp.fun tptp.real _let_55))) (let ((_let_58 (tptp.fun tptp.int _let_22))) (let ((_let_59 (tptp.fun _let_52 _let_58))) (let ((_let_60 (tptp.fun tptp.real _let_59))) (let ((_let_61 (tptp.fun tptp.real _let_58))) (let ((_let_62 (tptp.fun tptp.nat _let_42))) (let ((_let_63 (tptp.fun _let_22 _let_62))) (let ((_let_64 (tptp.fun tptp.bool _let_42))) (let ((_let_65 (tptp.fun tptp.int _let_62))) (let ((_let_66 (tptp.fun _let_58 _let_65))) (let ((_let_67 (tptp.fun tptp.real _let_65))) (let ((_let_68 (tptp.fun tptp.int _let_41))) (let ((_let_69 (tptp.fun _let_65 _let_68))) (let ((_let_70 (tptp.fun tptp.real _let_68))) (let ((_let_71 (tptp.fun _let_22 _let_58))) (let ((_let_72 (tptp.fun tptp.real _let_71))) (let ((_let_73 (tptp.fun _let_58 _let_15))) (let ((_let_74 (tptp.fun _let_22 tptp.bool))) (let ((_let_75 (tptp.fun tptp.real _let_15))) (let ((_let_76 (tptp.fEx tptp.int))) (let ((_let_77 (tptp.fun _let_15 tptp.bool))) (let ((_let_78 (tptp.hAPP _let_77 (tptp.fun _let_75 _let_55) (tptp.combb _let_15 tptp.bool tptp.real) _let_76))) (let ((_let_79 (tptp.collect tptp.real))) (let ((_let_80 (tptp.field_char_0_Rats tptp.real))) (let ((_let_81 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_82 (tptp.fun _let_25 _let_49))) (let ((_let_83 (tptp.hAPP _let_49 _let_82 _let_81 _let_43))) (let ((_let_84 (tptp.inverse_inverse tptp.real))) (let ((_let_85 (tptp.fun _let_29 tptp.bool))) (let ((_let_86 (tptp.times_times tptp.int))) (let ((_let_87 (tptp.hAPP tptp.int _let_12 _let_86 _let_19))) (let ((_let_88 (tptp.fequal tptp.int))) (let ((_let_89 (tptp.fun _let_12 _let_15))) (let ((_let_90 (tptp.fun tptp.int _let_89))) (let ((_let_91 (tptp.fun tptp.int _let_15))) (let ((_let_92 (tptp.fun _let_12 _let_91))) (let ((_let_93 (tptp.hAPP _let_90 _let_92 (tptp.combc tptp.int _let_12 _let_15) (tptp.hAPP _let_91 _let_90 (tptp.hAPP (tptp.fun _let_15 _let_89) (tptp.fun _let_91 _let_90) (tptp.combb _let_15 _let_89 tptp.int) (tptp.combb tptp.int tptp.bool tptp.int)) _let_88)))) (let ((_let_94 (tptp.fun _let_91 _let_15))) (let ((_let_95 (tptp.hAPP _let_77 _let_94 (tptp.combb _let_15 tptp.bool tptp.int) _let_76))) (let ((_let_96 (tptp.collect tptp.int))) (let ((_let_97 (= tptp.zEven (tptp.hAPP _let_15 _let_15 _let_96 (tptp.hAPP _let_91 _let_15 _let_95 (tptp.hAPP _let_12 _let_91 _let_93 _let_87)))))) (let ((_let_98 (tptp.combc tptp.int tptp.int tptp.bool))) (let ((_let_99 (tptp.fun _let_15 _let_15))) (let ((_let_100 (tptp.fun _let_46 _let_46))) (let ((_let_101 (tptp.fun tptp.int _let_100))) (let ((_let_102 (tptp.fun tptp.int _let_46))) (let ((_let_103 (tptp.fun _let_46 _let_15))) (let ((_let_104 (tptp.fun tptp.real _let_103))) (let ((_let_105 (tptp.fun _let_102 _let_91))) (let ((_let_106 (tptp.fun tptp.real _let_105))) (let ((_let_107 (tptp.fun tptp.real _let_91))) (let ((_let_108 (tptp.fun tptp.int _let_42))) (let ((_let_109 (tptp.fun _let_15 _let_108))) (let ((_let_110 (tptp.hAPP _let_64 _let_109 (tptp.combb tptp.bool _let_42 tptp.int) tptp.fconj))) (let ((_let_111 (tptp.fun tptp.int _let_108))) (let ((_let_112 (tptp.fun _let_91 _let_111))) (let ((_let_113 (tptp.fun tptp.real _let_111))) (let ((_let_114 (tptp.combs tptp.int tptp.bool tptp.bool))) (let ((_let_115 (tptp.fun tptp.int _let_99))) (let ((_let_116 (tptp.fun _let_111 _let_115))) (let ((_let_117 (tptp.fun tptp.real _let_115))) (let ((_let_118 (tptp.fun _let_15 _let_91))) (let ((_let_119 (tptp.fun tptp.real _let_118))) (let ((_let_120 (tptp.fun tptp.int _let_12))) (let ((_let_121 (tptp.fun _let_12 _let_120))) (let ((_let_122 (tptp.hAPP _let_120 _let_121 (tptp.combb tptp.int _let_12 tptp.int) _let_11))) (let ((_let_123 (= tptp.zOdd (tptp.hAPP _let_15 _let_15 _let_96 (tptp.hAPP _let_91 _let_15 _let_95 (tptp.hAPP _let_12 _let_91 _let_93 (tptp.hAPP tptp.int _let_12 (tptp.hAPP _let_120 _let_120 (tptp.combc tptp.int tptp.int tptp.int) (tptp.hAPP _let_12 _let_120 _let_122 _let_87)) _let_2))))))) (let ((_let_124 (tptp.combc tptp.real tptp.real tptp.bool))) (let ((_let_125 (tptp.ord_less_eq tptp.real))) (let ((_let_126 (tptp.fun tptp.real _let_42))) (let ((_let_127 (tptp.hAPP _let_64 (tptp.fun _let_55 _let_126) (tptp.combb tptp.bool _let_42 tptp.real) tptp.fconj))) (let ((_let_128 (tptp.combs tptp.real tptp.bool tptp.bool))) (let ((_let_129 (tptp.fun _let_55 _let_55))) (let ((_let_130 (tptp.hAPP tptp.real _let_55 _let_125 _let_37))) (let ((_let_131 (tptp.hAPP _let_55 tptp.real (tptp.the tptp.real) (tptp.hAPP _let_55 _let_55 (tptp.hAPP _let_126 _let_129 _let_128 (tptp.hAPP _let_55 _let_126 _let_127 _let_130)) (tptp.hAPP _let_55 _let_55 (tptp.hAPP _let_126 _let_129 _let_128 (tptp.hAPP _let_55 _let_126 _let_127 (tptp.hAPP tptp.real _let_55 (tptp.hAPP _let_57 _let_57 _let_124 _let_125) _let_31))) (tptp.hAPP tptp.real _let_55 (tptp.hAPP _let_57 _let_57 _let_124 (tptp.hAPP _let_33 _let_57 (tptp.hAPP _let_57 (tptp.fun _let_33 _let_57) (tptp.combb tptp.real _let_55 tptp.real) _let_53) tptp.cos)) _let_37)))))) (let ((_let_132 (tptp.times_times tptp.real))) (let ((_let_133 (tptp.hAPP tptp.real _let_33 _let_132 _let_31))) (let ((_let_134 (= tptp.pi (tptp.hAPP tptp.real tptp.real _let_133 _let_131)))) (let ((_let_135 (= (tptp.hAPP _let_49 _let_49 (tptp.diffs tptp.real) tptp.sin_coeff) tptp.cos_coeff))) (let ((_let_136 (tptp.one_one tptp.real))) (let ((_let_137 (tptp.hAPP tptp.real _let_33 _let_32 _let_136))) (let ((_let_138 (tptp.hAPP tptp.real tptp.real _let_137 _let_31))) (let ((_let_139 (tptp.power_power tptp.real))) (let ((_let_140 (tptp.uminus_uminus tptp.int))) (let ((_let_141 (tptp.product_prod tptp.int tptp.int))) (let ((_let_142 (tptp.fun _let_141 _let_141))) (let ((_let_143 (= tptp.negateSnd (tptp.hAPP _let_12 _let_142 (tptp.product_apsnd tptp.int tptp.int tptp.int) _let_140)))) (let ((_let_144 (tptp.product_snd tptp.int tptp.int))) (let ((_let_145 (tptp.fun _let_141 _let_12))) (let ((_let_146 (tptp.fun _let_141 tptp.int))) (let ((_let_147 (tptp.hAPP _let_146 _let_145 (tptp.hAPP _let_120 (tptp.fun _let_146 _let_145) (tptp.combb tptp.int _let_12 _let_141) _let_86) (tptp.product_fst tptp.int tptp.int)))) (let ((_let_148 (tptp.fun tptp.int _let_146))) (let ((_let_149 (tptp.fun _let_141 _let_146))) (let ((_let_150 (tptp.fun _let_146 _let_149))) (let ((_let_151 (tptp.fun _let_146 _let_146))) (let ((_let_152 (tptp.fun _let_141 _let_151))) (let ((_let_153 (tptp.fun _let_141 _let_15))) (let ((_let_154 (tptp.fun _let_146 _let_153))) (let ((_let_155 (tptp.hAPP _let_91 _let_154 (tptp.combb tptp.int _let_15 _let_141) _let_88))) (let ((_let_156 (tptp.fun _let_141 _let_153))) (let ((_let_157 (tptp.fun _let_141 tptp.bool))) (let ((_let_158 (tptp.fun _let_146 _let_157))) (let ((_let_159 (tptp.fun _let_141 _let_158))) (let ((_let_160 (tptp.fun _let_141 _let_157))) (let ((_let_161 (tptp.fun tptp.int _let_157))) (let ((_let_162 (tptp.combb tptp.bool tptp.bool _let_141))) (let ((_let_163 (tptp.fun _let_157 _let_157))) (let ((_let_164 (tptp.fun _let_141 _let_42))) (let ((_let_165 (tptp.hAPP _let_157 _let_164 (tptp.hAPP _let_64 (tptp.fun _let_157 _let_164) (tptp.combb tptp.bool _let_42 _let_141) tptp.fconj) (tptp.hAPP _let_157 _let_157 (tptp.hAPP _let_42 _let_163 _let_162 tptp.fNot) (tptp.hAPP tptp.int _let_157 (tptp.hAPP _let_153 _let_161 (tptp.combc _let_141 tptp.int tptp.bool) (tptp.hAPP _let_146 _let_153 _let_155 _let_144)) _let_1))))) (let ((_let_166 (tptp.fun _let_160 _let_160))) (let ((_let_167 (tptp.fun _let_141 _let_163))) (let ((_let_168 (tptp.product_prod _let_141 _let_141))) (let ((_let_169 (tptp.fun _let_168 tptp.bool))) (let ((_let_170 (= tptp.ratrel (tptp.hAPP _let_169 _let_169 (tptp.collect _let_168) (tptp.hAPP _let_160 _let_169 (tptp.product_prod_case _let_141 _let_141 tptp.bool) (tptp.hAPP _let_160 _let_160 (tptp.hAPP _let_167 _let_166 (tptp.combs _let_141 _let_157 _let_157) (tptp.hAPP _let_164 _let_167 (tptp.hAPP (tptp.fun _let_42 _let_163) (tptp.fun _let_164 _let_167) (tptp.combb _let_42 _let_163 _let_141) _let_162) _let_165)) (tptp.hAPP _let_160 _let_160 (tptp.hAPP _let_163 _let_166 (tptp.combb _let_157 _let_157 _let_141) (tptp.hAPP _let_164 _let_163 (tptp.combs _let_141 tptp.bool tptp.bool) _let_165)) (tptp.hAPP _let_149 _let_160 (tptp.hAPP _let_159 (tptp.fun _let_149 _let_160) (tptp.combs _let_141 _let_146 _let_157) (tptp.hAPP _let_156 _let_159 (tptp.hAPP (tptp.fun _let_153 _let_158) (tptp.fun _let_156 _let_159) (tptp.combb _let_153 _let_158 _let_141) (tptp.combs _let_141 tptp.int tptp.bool)) (tptp.hAPP _let_149 _let_156 (tptp.hAPP _let_154 (tptp.fun _let_149 _let_156) (tptp.combb _let_146 _let_153 _let_141) _let_155) (tptp.hAPP _let_146 _let_149 (tptp.hAPP _let_152 _let_150 (tptp.combc _let_141 _let_146 _let_146) (tptp.hAPP _let_145 _let_152 (tptp.hAPP (tptp.fun _let_12 _let_151) (tptp.fun _let_145 _let_152) (tptp.combb _let_12 _let_151 _let_141) (tptp.combb tptp.int tptp.int _let_141)) _let_147)) _let_144)))) (tptp.hAPP _let_146 _let_149 (tptp.hAPP _let_148 _let_150 (tptp.combb tptp.int _let_146 _let_141) (tptp.hAPP _let_145 _let_148 (tptp.combc _let_141 tptp.int tptp.int) _let_147)) _let_144))))))))) (let ((_let_171 (tptp.fun tptp.int _let_91))) (let ((_let_172 (tptp.fun _let_91 _let_91))) (let ((_let_173 (tptp.hAPP tptp.int _let_15 _let_14 _let_1))) (let ((_let_174 (= tptp.frac_1 (tptp.hAPP _let_91 _let_157 (tptp.product_prod_case tptp.int tptp.int tptp.bool) (tptp.hAPP _let_91 _let_91 (tptp.hAPP _let_99 _let_172 (tptp.combb _let_15 _let_15 tptp.int) (tptp.hAPP _let_108 _let_99 _let_114 (tptp.hAPP _let_15 _let_108 _let_110 _let_173))) (tptp.hAPP tptp.int _let_91 (tptp.hAPP _let_171 _let_171 (tptp.combc tptp.int tptp.int _let_15) (tptp.hAPP _let_171 _let_171 (tptp.hAPP _let_172 (tptp.fun _let_171 _let_171) (tptp.combb _let_91 _let_91 tptp.int) _let_98) (tptp.hAPP _let_120 _let_171 (tptp.hAPP _let_92 (tptp.fun _let_120 _let_171) (tptp.combb _let_12 _let_91 tptp.int) (tptp.hAPP _let_91 _let_92 (tptp.combb tptp.int _let_15 tptp.int) _let_88)) tptp.int_gcd))) _let_2)))))) (let ((_let_175 (tptp.hAPP tptp.nat _let_12 (tptp.hAPP (tptp.fun tptp.int _let_8) (tptp.fun tptp.nat _let_12) (tptp.combc tptp.int tptp.nat tptp.int) _let_7) _let_6))) (let ((_let_176 (tptp.fun _let_12 _let_12))) (let ((_let_177 (tptp.fun tptp.int _let_176))) (let ((_let_178 (= tptp.twoSqu1094008024sum2sq (tptp.hAPP _let_120 _let_146 (tptp.product_prod_case tptp.int tptp.int tptp.int) (tptp.hAPP _let_12 _let_120 (tptp.hAPP _let_177 _let_121 (tptp.combc tptp.int _let_12 _let_12) (tptp.hAPP _let_120 _let_177 (tptp.hAPP (tptp.fun _let_12 _let_176) (tptp.fun _let_120 _let_177) (tptp.combb _let_12 _let_176 tptp.int) (tptp.combb tptp.int tptp.int tptp.int)) (tptp.hAPP _let_12 _let_120 _let_122 _let_175))) _let_175))))) (let ((_let_179 (tptp.one_one tptp.nat))) (let ((_let_180 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_181 (tptp.fun tptp.nat _let_25))) (let ((_let_182 (tptp.plus_plus tptp.nat))) (let ((_let_183 (tptp.hAPP tptp.int tptp.real _let_30 tptp.min_1))) (let ((_let_184 (tptp.combb tptp.real _let_33 tptp.nat))) (let ((_let_185 (tptp.fun tptp.nat _let_33))) (let ((_let_186 (tptp.fun _let_49 _let_185))) (let ((_let_187 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_4))) (let ((_let_188 (tptp.hAPP tptp.int tptp.real _let_30 _let_187))) (let ((_let_189 (tptp.hAPP tptp.real tptp.real _let_34 _let_188))) (let ((_let_190 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_191 (tptp.fun tptp.int tptp.rat))) (let ((_let_192 (tptp.zero_zero tptp.rat))) (let ((_let_193 (tptp.one_one tptp.rat))) (let ((_let_194 (tptp.hAPP tptp.rat tptp.real tptp.ratreal _let_193))) (let ((_let_195 (tptp.hAPP tptp.rat tptp.real tptp.ratreal _let_192))) (let ((_let_196 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_191 tptp.fract _let_2) _let_2))) (let ((_let_197 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_198 (tptp.fun tptp.int _let_141))) (let ((_let_199 (tptp.hAPP tptp.int _let_141 (tptp.hAPP tptp.int _let_198 _let_197 _let_2) _let_2))) (let ((_let_200 (= _let_44 (tptp.ring_1_of_int tptp.real)))) (let ((_let_201 (tptp.one_one tptp.quickcheck_code_int))) (let ((_let_202 (tptp.zero_zero tptp.quickcheck_code_int))) (let ((_let_203 (tptp.number_number_of tptp.quickcheck_code_int))) (let ((_let_204 (= _let_203 tptp.quickcheck_of_int))) (let ((_let_205 (tptp.fact_fact tptp.int))) (let ((_let_206 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_40))) (let ((_let_207 (tptp.one_one tptp.complex))) (let ((_let_208 (tptp.zero_zero tptp.complex))) (let ((_let_209 (tptp.zero_zero tptp.code_code_numeral))) (let ((_let_210 (tptp.size_size tptp.code_code_numeral))) (let ((_let_211 (tptp.uminus_uminus tptp.complex))) (let ((_let_212 (tptp.hAPP tptp.complex tptp.complex _let_211 tptp.ii))) (let ((_let_213 (tptp.size_size tptp.nat))) (let ((_let_214 (tptp.of_real tptp.complex))) (let ((_let_215 (tptp.number_number_of tptp.complex))) (let ((_let_216 (tptp.times_times tptp.complex))) (let ((_let_217 (tptp.fun tptp.complex tptp.complex))) (let ((_let_218 (tptp.hAPP tptp.complex tptp.complex _let_211 _let_207))) (let ((_let_219 (tptp.uminus_uminus tptp.real))) (let ((_let_220 (tptp.hAPP tptp.real tptp.real _let_219 _let_136))) (let ((_let_221 (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_217 _let_216 tptp.ii) tptp.ii))) (let ((_let_222 (tptp.hAPP tptp.int tptp.complex _let_215 tptp.min_1))) (let ((_let_223 (tptp.fun tptp.real tptp.complex))) (let ((_let_224 (tptp.hAPP tptp.real _let_223 tptp.complex_1 _let_37))) (let ((_let_225 (= tptp.ii (tptp.hAPP tptp.real tptp.complex _let_224 _let_136)))) (let ((_let_226 (= tptp.sqrt (tptp.hAPP tptp.nat _let_33 tptp.root _let_6)))) (let ((_let_227 (tptp.fact_fact tptp.nat))) (let ((_let_228 (tptp.even_odd_even tptp.nat))) (let ((_let_229 (tptp.hAPP tptp.int tptp.real _let_30 _let_20))) (let ((_let_230 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_33 _let_132 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_33 _let_32 _let_229) _let_31)) tptp.pi))) (let ((_let_231 (tptp.hAPP tptp.real tptp.real tptp.sqrt _let_31))) (let ((_let_232 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_33 _let_32 _let_231) _let_31))) (let ((_let_233 (tptp.hAPP tptp.real tptp.real tptp.sqrt _let_229))) (let ((_let_234 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_33 _let_32 _let_233) _let_31))) (let ((_let_235 (tptp.hAPP tptp.real tptp.real _let_34 _let_229))) (let ((_let_236 (tptp.hAPP tptp.real tptp.real _let_34 (tptp.hAPP tptp.int tptp.real _let_30 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_20))))) (let ((_let_237 (tptp.hAPP tptp.real tptp.real _let_133 tptp.pi))) (let ((_let_238 (= _let_43 (tptp.semiring_1_of_nat tptp.real)))) (let ((_let_239 (tptp.hAPP tptp.real tptp.real tptp.cos _let_31))) (let ((_let_240 (tptp.ord_less tptp.real))) (let ((_let_241 (= tptp.min_1 (tptp.hAPP tptp.int tptp.int _let_140 _let_2)))) (let ((_let_242 (tptp.hAPP tptp.real _let_55 _let_240 _let_37))) (let ((_let_243 (tptp.hAPP tptp.real _let_55 _let_240 tptp.pi))) (let ((_let_244 (tptp.hAPP tptp.int tptp.int _let_18 tptp.min_1))) (let ((_let_245 (tptp.hAPP tptp.int tptp.int _let_18 tptp.pls))) (let ((_let_246 (tptp.number_number_of tptp.code_code_numeral))) (let ((_let_247 (tptp.one_one tptp.code_code_numeral))) (let ((_let_248 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_206))) (let ((_let_249 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_19))) (let ((_let_250 (tptp.hAPP tptp.int tptp.nat _let_5 _let_3))) (let ((_let_251 (tptp.hAPP tptp.int tptp.nat _let_5 _let_20))) (let ((_let_252 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_2))) (let ((_let_253 (tptp.hAPP tptp.nat tptp.int _let_190 _let_179))) (let ((_let_254 (tptp.hAPP tptp.nat tptp.int _let_190 _let_40))) (let ((_let_255 (tptp.even_odd_even tptp.int))) (let ((_let_256 (tptp.fun tptp.code_code_numeral tptp.code_code_numeral))) (let ((_let_257 (tptp.ord_less_eq tptp.int))) (let ((_let_258 (tptp.hAPP tptp.int _let_15 _let_257 _let_1))) (let ((_let_259 (tptp.fun tptp.int tptp.nat))) (let ((_let_260 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1))) (let ((_let_261 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_12 _let_11 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_12 _let_86 (tptp.hAPP tptp.int tptp.int _let_18 _let_187)) tptp.m)) _let_2))) (let ((_let_262 (tptp.hAPP tptp.int _let_12 _let_86 _let_261))) (let ((_let_263 (tptp.hAPP tptp.int tptp.int _let_262 tptp.t))) (let ((_let_264 (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_12 tptp.legendre _let_244) _let_261) _let_2))) (let ((_let_265 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 tptp.quadRes _let_261) _let_244)))) (let ((_let_266 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_12 (tptp.minus_minus tptp.int) _let_10) _let_244))) (let ((_let_267 (tptp.hAPP tptp.int _let_15 (tptp.dvd_dvd tptp.int) _let_261))) (let ((_let_268 (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))))) (let ((_let_269 (tptp.hAPP tptp.int _let_15 _let_257 tptp.pls))) (let ((_let_270 (tptp.hAPP tptp.int _let_15 _let_257 tptp.min_1))) (let ((_let_271 (tptp.hAPP tptp.int _let_15 _let_14 tptp.min_1))) (let ((_let_272 (tptp.hAPP tptp.int _let_15 _let_14 tptp.pls))) (let ((_let_273 (tptp.hAPP tptp.int _let_91 tptp.zcong _let_10))) (let ((_let_274 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_8 _let_7 tptp.s1) _let_6))) (let ((_let_275 (= tptp.pls _let_1))) (let ((_let_276 (tptp.hAPP tptp.int tptp.nat _let_5 tptp.pls))) (let ((_let_277 (tptp.hAPP tptp.int _let_15 _let_14 tptp.t))) (let ((_let_278 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_173 _let_261)))) (let ((_let_279 (= _let_13 _let_263))) (let ((_let_280 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_277 _let_1)))) (let ((_let_281 (tptp.ord_gr676655987ssThan tptp.nat))) (let ((_let_282 (tptp.fun tptp.int _let_77))) (let ((_let_283 (tptp.fun tptp.real tptp.nat))) (let ((_let_284 (tptp.fun tptp.int _let_198))) (let ((_let_285 (tptp.size_size tptp.complex))) (let ((_let_286 (tptp.fun tptp.complex tptp.nat))) (let ((_let_287 (tptp.fun tptp.code_code_numeral tptp.nat))) (let ((_let_288 (tptp.fun tptp.int (tptp.fun tptp.int (tptp.product_prod tptp.int _let_141))))) (let ((_let_289 (tptp.the tptp.int))) (let ((_let_290 (tptp.gcd_gcd tptp.nat))) (let ((_let_291 (tptp.gcd_gcd tptp.int))) (let ((_let_292 (tptp.fun (tptp.product_prod _let_26 _let_26) tptp.bool))) (let ((_let_293 (tptp.product_prod tptp.real tptp.real))) (let ((_let_294 (tptp.fun tptp.real _let_223))) (let ((_let_295 (tptp.fun tptp.complex tptp.real))) (let ((_let_296 (tptp.complete_Sup_Sup tptp.real))) (let ((_let_297 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_1)))) (let ((_let_298 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_12 _let_11 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_12 _let_86 (tptp.hAPP tptp.int tptp.int _let_18 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_297))) tptp.m)) _let_2))) (let ((_let_299 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_12 _let_86 _let_298) tptp.t))) (let ((_let_300 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_12 _let_11 (tptp.hAPP tptp.nat tptp.int _let_9 (tptp.hAPP tptp.int tptp.nat _let_5 _let_297))) _let_2))) (let ((_let_301 (= _let_300 _let_299))) (let ((_let_302 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_14 _let_300) _let_1)))) (let ((_let_303 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_14 _let_299) _let_1)))) (let ((_let_304 (ASSUME :args (_let_275)))) (let ((_let_305 (ASSUME :args (_let_241)))) (let ((_let_306 (EQ_RESOLVE (ASSUME :args (_let_226)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_305 _let_304) :args (_let_226 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_307 (ASSUME :args (_let_225)))) (let ((_let_308 (SYMM (ASSUME :args (_let_204))))) (let ((_let_309 (EQ_RESOLVE (ASSUME :args (_let_178)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_308 _let_307 _let_306 _let_305 _let_304) :args (_let_178 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_310 (ASSUME :args (_let_174)))) (let ((_let_311 (ASSUME :args (_let_170)))) (let ((_let_312 (ASSUME :args (_let_143)))) (let ((_let_313 (SYMM (ASSUME :args (_let_135))))) (let ((_let_314 (EQ_RESOLVE (ASSUME :args (_let_134)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304) :args (_let_134 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_315 (EQ_RESOLVE (ASSUME :args (_let_123)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304) :args (_let_123 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_316 (AND_INTRO (ASSUME :args (_let_28)) (EQ_RESOLVE (ASSUME :args (_let_97)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304) :args (_let_97 SB_DEFAULT SBA_FIXPOINT))) _let_315 _let_314 _let_313 _let_312 _let_311 _let_310 _let_309 _let_308 _let_307 _let_306 _let_305 _let_304))) (let ((_let_317 (EQ_RESOLVE (ASSUME :args (_let_279)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_279 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_316 :args ((= _let_263 _let_13) SB_DEFAULT SBA_FIXPOINT)))))) (let ((_let_318 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO _let_316 :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_319 (not _let_280))) (let ((_let_320 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_173 _let_298)))) (let ((_let_321 (not _let_320))) (let ((_let_322 (not _let_17))) (let ((_let_323 (or _let_322 _let_321 _let_319 _let_303))) (let ((_let_324 (forall ((X_a $$unsorted) (BOUND_VARIABLE_107866 $$unsorted) (BOUND_VARIABLE_107864 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (or (not (tptp.linord20386208strict X_a)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) BOUND_VARIABLE_107866))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 BOUND_VARIABLE_107864) _let_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) BOUND_VARIABLE_107866) BOUND_VARIABLE_107864)) _let_1))))))))) (let ((_let_325 (EQ_RESOLVE (ASSUME :args (_let_268)) (MACRO_SR_EQ_INTRO :args (_let_268 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_326 (not _let_302))) (let ((_let_327 (ASSUME :args (_let_303)))) (let ((_let_328 (APPLY_UF tptp.hAPP))) (let ((_let_329 (REFL :args (tptp.int)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_327 _let_317 _let_318) :args (_let_326 _let_301 _let_303)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_318)) (CONG (CONG _let_329 (REFL :args (tptp.bool)) (CONG _let_329 (REFL :args (_let_15)) (REFL :args (_let_14)) (SYMM (SYMM _let_317)) :args _let_328) (REFL :args (_let_1)) :args _let_328) :args (APPLY_UF tptp.hBOOL)) (TRUE_INTRO _let_327))) :args (_let_303 _let_301 _let_326)) :args ((not (and _let_326 _let_301 _let_303)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_326) _let_302))) (REFL :args ((not _let_301))) (REFL :args ((not _let_303))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_323)) :args ((or _let_319 _let_321 _let_322 _let_303 (not _let_323)))) (ASSUME :args (_let_280)) (EQ_RESOLVE (ASSUME :args (_let_278)) (MACRO_SR_EQ_INTRO _let_316 :args (_let_278 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_17)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_325 :args (tptp.int _let_298 tptp.t QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_324))) _let_325 :args (_let_323 false _let_324)) :args (_let_303 false _let_280 false _let_320 false _let_17 false _let_323)) _let_318 _let_317 :args (false false _let_303 true _let_302 false _let_301)) :args ((forall ((X_a $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling X_a))) (=> (tptp.archim1727834104eiling X_a) (= (tptp.ti (tptp.fun X_a tptp.int) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor X_a))) (=> (tptp.archim1727834104eiling X_a) (= (tptp.ti (tptp.fun X_a tptp.int) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a X_b))) (=> (tptp.comm_monoid_add X_b) (= (tptp.ti (tptp.fun (tptp.fun X_a X_b) (tptp.fun (tptp.fun X_a tptp.bool) X_b)) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_a X_b))) (=> (tptp.comm_monoid_mult X_b) (= (tptp.ti (tptp.fun (tptp.fun X_a X_b) (tptp.fun (tptp.fun X_a tptp.bool) X_b)) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.bijR X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.ti (tptp.fun (tptp.fun X_a _let_2) (tptp.fun (tptp.product_prod (tptp.fun X_a tptp.bool) _let_2) tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.combb X_b X_c X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_c) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combc X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun X_b (tptp.fun X_a X_c))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.combi X_a))) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.combk X_a X_b))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_b X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.combs X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a X_c))) _let_1) _let_1))) (= (tptp.ti _let_256 tptp.code_S1047413653umeral) tptp.code_S1047413653umeral) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.code_c600343653l_case X_a))) (let ((_let_2 (tptp.fun tptp.code_code_numeral X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (= (tptp.ti _let_287 tptp.code_c271388182l_size) tptp.code_c271388182l_size) (= (tptp.ti (tptp.fun tptp.code_code_numeral (tptp.fun tptp.code_code_numeral (tptp.product_prod tptp.code_code_numeral tptp.code_code_numeral))) tptp.code_d418564891umeral) tptp.code_d418564891umeral) (= (tptp.ti (tptp.fun tptp.code_code_numeral tptp.int) tptp.code_int_of) tptp.code_int_of) (= (tptp.ti (tptp.fun tptp.code_code_numeral _let_25) tptp.code_nat_of_aux) tptp.code_nat_of_aux) (= (tptp.ti (tptp.fun _let_55 tptp.real) _let_296) _let_296) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.complete_Sup_Sup X_a))) (=> (tptp.comple44059174attice X_a) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) X_a) _let_1) _let_1)))) (= (tptp.ti _let_295 tptp.im) tptp.im) (= (tptp.ti _let_295 tptp.re) tptp.re) (= (tptp.ti _let_295 tptp.arg) tptp.arg) (= (tptp.ti _let_223 tptp.cis) tptp.cis) (= (tptp.ti _let_217 tptp.cnj) tptp.cnj) (= (tptp.ti _let_294 tptp.complex_1) tptp.complex_1) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.complex_case X_a))) (= (tptp.ti (tptp.fun (tptp.fun tptp.real (tptp.fun tptp.real X_a)) (tptp.fun tptp.complex X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.complex_rec X_a))) (= (tptp.ti (tptp.fun (tptp.fun tptp.real (tptp.fun tptp.real X_a)) (tptp.fun tptp.complex X_a)) _let_1) _let_1))) (= (tptp.ti _let_286 tptp.complex_size) tptp.complex_size) (= (tptp.ti _let_217 tptp.expi) tptp.expi) (= (tptp.ti tptp.complex tptp.ii) tptp.ii) (= (tptp.ti _let_294 tptp.rcis) tptp.rcis) (= (tptp.ti (tptp.fun (tptp.fun _let_293 tptp.bool) (tptp.fun tptp.real (tptp.fun tptp.real (tptp.fun tptp.nat _let_293)))) tptp.bolzano_bisect) tptp.bolzano_bisect) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.deriv X_a))) (=> (tptp.real_normed_field X_a) (= (tptp.ti (tptp.fun (tptp.fun X_a X_a) (tptp.fun X_a (tptp.fun X_a tptp.bool))) _let_1) _let_1)))) (= (tptp.ti (tptp.fun tptp.int _let_142) tptp.adjust) tptp.adjust) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (=> (tptp.semiring_div X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (=> (tptp.semiring_div X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (= (tptp.ti _let_284 tptp.divmod_int) tptp.divmod_int) (= (tptp.ti (tptp.fun tptp.int _let_161) tptp.divmod_int_rel) tptp.divmod_int_rel) (= (tptp.ti (tptp.fun tptp.nat (tptp.fun tptp.nat _let_26)) tptp.divmod_nat) tptp.divmod_nat) (= (tptp.ti (tptp.fun tptp.nat (tptp.fun tptp.nat _let_27)) tptp.divmod_nat_rel) tptp.divmod_nat_rel) (= (tptp.ti _let_284 tptp.negDivAlg) tptp.negDivAlg) (= (tptp.ti _let_160 tptp.negDivAlg_rel) tptp.negDivAlg_rel) (= (tptp.ti _let_142 tptp.negateSnd) tptp.negateSnd) (= (tptp.ti _let_284 tptp.pdivmod) tptp.pdivmod) (= (tptp.ti _let_284 tptp.posDivAlg) tptp.posDivAlg) (= (tptp.ti _let_160 tptp.posDivAlg_rel) tptp.posDivAlg_rel) (= (tptp.ti _let_171 tptp.bnorRset) tptp.bnorRset) (= (tptp.ti (tptp.fun _let_15 _let_120) tptp.rRset2norRR) tptp.rRset2norRR) (= (tptp.ti _let_282 tptp.rsetR) tptp.rsetR) (= (tptp.ti _let_99 tptp.is_RRset) tptp.is_RRset) (= (tptp.ti _let_171 tptp.noXRRset) tptp.noXRRset) (= (tptp.ti _let_91 tptp.norRRset) tptp.norRRset) (= (tptp.ti _let_259 tptp.phi) tptp.phi) (= (tptp.ti _let_171 tptp.zcongm) tptp.zcongm) (= (tptp.ti (tptp.fun tptp.int _let_171) tptp.multInvPair) tptp.multInvPair) (= (tptp.ti (tptp.fun tptp.int _let_282) tptp.setS) tptp.setS) (= (tptp.ti _let_15 tptp.zEven) tptp.zEven) (= (tptp.ti _let_15 tptp.zOdd) tptp.zOdd) (= (tptp.ti _let_12 _let_205) _let_205) (= (tptp.ti _let_25 _let_227) _let_227) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (=> (and (tptp.inverse X_a) (tptp.real_normed_vector X_a)) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (=> (tptp.division_ring X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (=> (tptp.division_ring X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.finite_card X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) tptp.nat) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.in_rel X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_b) tptp.bool) (tptp.fun X_a (tptp.fun X_b tptp.bool))) _let_1) _let_1))) (= (tptp.ti _let_292 tptp.pair_leq) tptp.pair_leq) (= (tptp.ti _let_292 tptp.pair_less) tptp.pair_less) (= (tptp.ti (tptp.fun tptp.nat (tptp.fun tptp.nat _let_141)) tptp.bezw) tptp.bezw) (= (tptp.ti _let_120 _let_291) _let_291) (= (tptp.ti _let_181 _let_290) _let_290) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (=> (tptp.abs_if X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (=> (tptp.ordere142940540dd_abs X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.minus_minus X_b))) (=> (tptp.minus X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b X_b)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.one X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.monoid_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.ab_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (=> (tptp.cancel_semigroup_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.sgn_sgn X_a))) (=> (tptp.sgn_div_norm X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.sgn_sgn X_a))) (=> (tptp.sgn_if X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.ab_semigroup_mult X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.power X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.dvd X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.semiring X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.mult_zero X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (=> (tptp.no_zero_divisors X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (=> (tptp.uminus X_a) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.zero X_a) (= (tptp.ti X_a _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.the X_a))) (=> (tptp.metric_space X_a) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) X_a) _let_1) _let_1)))) (= (tptp.ti (tptp.fun _let_15 tptp.int) _let_289) _let_289) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.the _let_1))) (= (tptp.ti (tptp.fun (tptp.fun _let_1 tptp.bool) _let_1) _let_2) _let_2)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.the X_a))) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.undefined X_a))) (= (tptp.ti X_a _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.hilbert_Eps X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) X_a) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.if X_a))) (= (tptp.ti (tptp.fun tptp.bool (tptp.fun X_a (tptp.fun X_a X_a))) _let_1) _let_1))) (= (tptp.ti _let_120 tptp.multInv) tptp.multInv) (= (tptp.ti _let_91 tptp.d22set) tptp.d22set) (= (tptp.ti _let_12 tptp.zfact) tptp.zfact) (= (tptp.ti _let_288 tptp.xzgcd) tptp.xzgcd) (= (tptp.ti (tptp.fun tptp.int (tptp.fun tptp.int (tptp.fun tptp.int (tptp.fun tptp.int (tptp.fun tptp.int (tptp.fun tptp.int _let_288)))))) tptp.xzgcda) tptp.xzgcda) (= (tptp.ti _let_171 tptp.zcong) tptp.zcong) (= (tptp.ti _let_15 tptp.zprime) tptp.zprime) (= (tptp.ti _let_12 tptp.bit0) tptp.bit0) (= (tptp.ti _let_12 tptp.bit1) tptp.bit1) (= (tptp.ti tptp.int tptp.min_1) tptp.min_1) (= (tptp.ti tptp.int tptp.pls) tptp.pls) (= (tptp.ti _let_161 tptp.int_ge_less_than) tptp.int_ge_less_than) (= (tptp.ti _let_161 tptp.int_ge_less_than2) tptp.int_ge_less_than2) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.iszero X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.ti (tptp.fun X_a tptp.bool) _let_1) _let_1)))) (= (tptp.ti _let_259 tptp.nat_1) tptp.nat_1) (= (tptp.ti (tptp.fun tptp.int _let_25) tptp.nat_aux) tptp.nat_aux) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (=> (tptp.number X_a) (= (tptp.ti (tptp.fun tptp.int X_a) _let_1) _let_1)))) (= (tptp.ti _let_12 tptp.pred) tptp.pred) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_a))) (=> (tptp.ring_1 X_a) (= (tptp.ti (tptp.fun X_a tptp.bool) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (=> (tptp.ring_1 X_a) (= (tptp.ti (tptp.fun tptp.int X_a) _let_1) _let_1)))) (= (tptp.ti _let_12 tptp.succ) tptp.succ) (= (tptp.ti _let_160 tptp.lazy_small_lazy_rel) tptp.lazy_small_lazy_rel) (= (tptp.ti _let_120 tptp.legacy_zgcd) tptp.legacy_zgcd) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.isCont X_a X_b))) (=> (and (tptp.topological_space X_a) (tptp.topological_space X_b)) (= (tptp.ti (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.at X_a))) (=> (tptp.topological_space X_a) (= (tptp.ti (tptp.fun X_a (tptp.filter X_a)) _let_1) _let_1)))) (= (tptp.ti _let_29 tptp.sequentially) tptp.sequentially) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.tendsto X_a X_b))) (=> (tptp.topological_space X_b) (= (tptp.ti (tptp.fun (tptp.fun X_a X_b) (tptp.fun X_b (tptp.fun (tptp.filter X_a) tptp.bool))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.trivial_limit X_a))) (= (tptp.ti (tptp.fun (tptp.filter X_a) tptp.bool) _let_1) _let_1))) (= (tptp.ti _let_160 tptp.upto_rel) tptp.upto_rel) (= (tptp.ti _let_38 tptp.log) tptp.log) (= (tptp.ti _let_38 tptp.powr) tptp.powr) (= (tptp.ti _let_25 tptp.suc) tptp.suc) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.nat_case X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.nat_rec X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun (tptp.fun tptp.nat (tptp.fun X_a X_a)) (tptp.fun tptp.nat X_a))) _let_1) _let_1))) (= (tptp.ti _let_25 tptp.nat_size) tptp.nat_size) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.ti (tptp.fun tptp.nat X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.semiri532925092at_aux X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.ti (tptp.fun _let_2 (tptp.fun tptp.nat _let_2)) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (= (tptp.ti (tptp.fun _let_1 tptp.nat) _let_2) _let_2)))) (= (tptp.ti _let_287 _let_210) _let_210) (= (tptp.ti _let_25 _let_213) _let_213) (= (tptp.ti _let_286 _let_285) _let_285) (= (tptp.ti _let_15 tptp.nat_neg) tptp.nat_neg) (= (tptp.ti _let_15 tptp.nat_is_nat) tptp.nat_is_nat) (= (tptp.ti _let_77 tptp.nat_nat_set) tptp.nat_nat_set) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.nat_tr1645093318rphism X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a X_b) (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_120 tptp.nat_tsub) tptp.nat_tsub) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.abs_Frac X_a))) (= (tptp.ti (tptp.fun (tptp.product_prod tptp.int tptp.int) X_a) _let_1) _let_1))) (= (tptp.ti _let_157 tptp.frac_1) tptp.frac_1) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.frac X_a))) (= (tptp.ti (tptp.fun tptp.int (tptp.fun tptp.int X_a)) _let_1) _let_1))) (= (tptp.ti _let_120 tptp.int_gcd) tptp.int_gcd) (= (tptp.ti _let_120 tptp.int_lcm) tptp.int_lcm) (= (tptp.ti _let_181 tptp.nat_gcd) tptp.nat_gcd) (= (tptp.ti (tptp.fun _let_26 _let_27) tptp.nat_gcd_rel) tptp.nat_gcd_rel) (= (tptp.ti _let_181 tptp.nat_lcm) tptp.nat_lcm) (= (tptp.ti _let_284 tptp.norm_frac) tptp.norm_frac) (= (tptp.ti _let_160 tptp.norm_frac_rel) tptp.norm_frac_rel) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.number_of_frac X_a))) (= (tptp.ti (tptp.fun tptp.int X_a) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_frac X_a))) (= (tptp.ti X_a _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.prod X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.product_prod X_a X_b) tptp.bool))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.refl X_a))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) tptp.bool) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_frac X_a))) (= (tptp.ti X_a _let_1) _let_1))) (= (tptp.ti _let_185 tptp.root) tptp.root) (= (tptp.ti _let_33 tptp.sqrt) tptp.sqrt) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.max X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun X_a (tptp.fun X_a X_a))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.min X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun X_a (tptp.fun X_a X_a))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_b))) (=> (tptp.ord X_b) (= (tptp.ti (tptp.fun X_b (tptp.fun X_b tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.mono tptp.nat X_a))) (=> (tptp.order X_a) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun (tptp.fun tptp.nat X_a) tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.strict_mono tptp.nat X_a))) (=> (tptp.order X_a) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun (tptp.fun tptp.nat X_a) tptp.bool)) _let_1) _let_1)))) (= (tptp.ti _let_22 _let_228) _let_228) (= (tptp.ti _let_15 _let_255) _let_255) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.power_1 X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.fun X_a (tptp.fun tptp.nat X_a)))) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (=> (tptp.power X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun tptp.nat X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.powp X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 tptp.bool)) _let_1) _let_1)))) (= (tptp.ti _let_23 tptp.coprime) tptp.coprime) (= (tptp.ti _let_25 tptp.fact) tptp.fact) (= (tptp.ti _let_22 tptp.prime) tptp.prime) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_b))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_b (tptp.product_prod X_a X_b))) _let_1) _let_1))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.product_apsnd X_c X_b X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_c X_b) (tptp.fun (tptp.product_prod X_a X_c) (tptp.product_prod X_a X_b))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.product_fst X_a X_b))) (= (tptp.ti (tptp.fun (tptp.product_prod X_a X_b) X_a) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted)) (let ((_let_1 (tptp.product_prod_case X_a X_b X_c))) (= (tptp.ti (tptp.fun (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun (tptp.product_prod X_a X_b) X_c)) _let_1) _let_1))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.product_prod_rec X_b X_c X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b (tptp.fun X_c X_a)) (tptp.fun (tptp.product_prod X_b X_c) X_a)) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.product_prod_size X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.nat) (tptp.fun (tptp.fun X_b tptp.nat) (tptp.fun (tptp.product_prod X_a X_b) tptp.nat))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.product_snd X_a X_b))) (= (tptp.ti (tptp.fun (tptp.product_prod X_a X_b) X_b) _let_1) _let_1))) (= (tptp.ti (tptp.fun tptp.int (tptp.list tptp.int)) tptp.quickc666637781d_zero) tptp.quickc666637781d_zero) (= (tptp.ti _let_91 tptp.quickc1265749348ro_rel) tptp.quickc1265749348ro_rel) (= (tptp.ti (tptp.fun tptp.quickcheck_code_int (tptp.fun tptp.quickcheck_code_int (tptp.product_prod tptp.quickcheck_code_int tptp.quickcheck_code_int))) tptp.quickc495462417de_int) tptp.quickc495462417de_int) (= (tptp.ti (tptp.fun tptp.quickcheck_code_int tptp.int) tptp.quickcheck_int_of) tptp.quickcheck_int_of) (= (tptp.ti (tptp.fun tptp.quickcheck_code_int tptp.nat) tptp.quickcheck_nat_of) tptp.quickcheck_nat_of) (= (tptp.ti (tptp.fun tptp.int tptp.quickcheck_code_int) tptp.quickcheck_of_int) tptp.quickcheck_of_int) (= (tptp.ti _let_283 tptp.natceiling) tptp.natceiling) (= (tptp.ti _let_283 tptp.natfloor) tptp.natfloor) (= (tptp.ti (tptp.fun tptp.int _let_191) tptp.fract) tptp.fract) (= (tptp.ti (tptp.fun _let_141 tptp.rat) tptp.frct) tptp.frct) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (=> (tptp.field_char_0 X_a) (= (tptp.ti (tptp.fun X_a tptp.bool) _let_1) _let_1)))) (= (tptp.ti _let_142 tptp.normalize) tptp.normalize) (= (tptp.ti (tptp.fun tptp.rat _let_141) tptp.quotient_of) tptp.quotient_of) (= (tptp.ti _let_169 tptp.ratrel) tptp.ratrel) (= (tptp.ti (tptp.fun tptp.rat tptp.real) tptp.ratreal) tptp.ratreal) (= (tptp.ti _let_46 _let_44) _let_44) (= (tptp.ti _let_49 _let_43) _let_43) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat tptp.rat) tptp.bool) tptp.vanishes) tptp.vanishes) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (=> (tptp.dist_norm X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.real)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (=> (tptp.metric_space X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.real)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (=> (tptp.sgn_div_norm X_a) (= (tptp.ti (tptp.fun X_a tptp.real) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (=> (tptp.dist_norm X_a) (= (tptp.ti (tptp.fun X_a tptp.real) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (=> (tptp.real_algebra_1 X_a) (= (tptp.ti (tptp.fun tptp.real X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (=> (tptp.sgn_div_norm X_a) (= (tptp.ti (tptp.fun tptp.real (tptp.fun X_a X_a)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (=> (tptp.real_vector X_a) (= (tptp.ti (tptp.fun tptp.real (tptp.fun X_a X_a)) _let_1) _let_1)))) (= (tptp.ti _let_120 tptp.legendre) tptp.legendre) (= (tptp.ti _let_91 tptp.quadRes) tptp.quadRes) (= (tptp.ti _let_282 tptp.resSet) tptp.resSet) (= (tptp.ti _let_91 tptp.sr) tptp.sr) (= (tptp.ti _let_91 tptp.sRStar) tptp.sRStar) (= (tptp.ti _let_120 tptp.standardRes) tptp.standardRes) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (=> (tptp.dvd X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.bseq X_a))) (=> (tptp.real_normed_vector X_a) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat X_a) tptp.bool) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.cauchy X_a))) (=> (tptp.metric_space X_a) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat X_a) tptp.bool) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.lim X_a))) (=> (tptp.metric_space X_a) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat X_a) X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.monoseq X_a))) (=> (tptp.order X_a) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat X_a) tptp.bool) _let_1) _let_1)))) (= (tptp.ti _let_120 tptp.z3div) tptp.z3div) (= (tptp.ti _let_120 tptp.z3mod) tptp.z3mod) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.suminf X_a))) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat X_a) X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.summable X_a))) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat X_a) tptp.bool) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.sums X_a))) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (= (tptp.ti (tptp.fun (tptp.fun tptp.nat X_a) (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_atLeastAtMost X_a))) (=> (tptp.order X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a (tptp.fun X_a tptp.bool))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a (tptp.fun X_a tptp.bool))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_atMost X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_gr676655987ssThan X_a))) (=> (tptp.dense_linorder X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a (tptp.fun X_a tptp.bool))) _let_1) _let_1)))) (= (tptp.ti (tptp.fun tptp.nat _let_23) _let_281) _let_281) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_gr676655987ssThan X_a))) (=> (tptp.ordered_ab_group_add X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a (tptp.fun X_a tptp.bool))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.ord_lessThan X_a))) (=> (tptp.ord X_a) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.pow X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun _let_2 (tptp.fun _let_2 tptp.bool)) _let_1) _let_1)))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (let ((_let_1 (tptp.image X_b X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_b X_a) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun X_a tptp.bool))) _let_1) _let_1))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.sum_Plus X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) (tptp.fun (tptp.fun X_b tptp.bool) (tptp.fun (tptp.sum_sum X_a X_b) tptp.bool))) _let_1) _let_1))) (= (tptp.ti _let_33 tptp.arccos) tptp.arccos) (= (tptp.ti _let_33 tptp.arcsin) tptp.arcsin) (= (tptp.ti _let_33 tptp.arctan) tptp.arctan) (= (tptp.ti _let_33 tptp.cos) tptp.cos) (= (tptp.ti _let_49 tptp.cos_coeff) tptp.cos_coeff) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.diffs X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (=> (tptp.ring_1 X_a) (= (tptp.ti (tptp.fun _let_2 _let_2) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.exp X_a))) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (= (tptp.ti (tptp.fun X_a X_a) _let_1) _let_1)))) (= (tptp.ti _let_33 tptp.ln) tptp.ln) (= (tptp.ti tptp.real tptp.pi) tptp.pi) (= (tptp.ti _let_33 tptp.sin) tptp.sin) (= (tptp.ti _let_49 tptp.sin_coeff) tptp.sin_coeff) (= (tptp.ti _let_33 tptp.tan) tptp.tan) (= (tptp.ti _let_15 tptp.twoSqu1091635170sum2sq) tptp.twoSqu1091635170sum2sq) (= (tptp.ti _let_146 tptp.twoSqu1094008024sum2sq) tptp.twoSqu1094008024sum2sq) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.accp X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun (tptp.fun X_a _let_2) _let_2) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.finite_psubset X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.ti (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool) _let_1) _let_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (let ((_let_1 (tptp.lex_prod X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (= (tptp.ti (tptp.fun (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) (tptp.fun (tptp.fun (tptp.product_prod X_b X_b) tptp.bool) (tptp.fun (tptp.product_prod _let_2 _let_2) tptp.bool))) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.measure X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.nat) (tptp.fun (tptp.product_prod X_a X_a) tptp.bool)) _let_1) _let_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.mlex_prod X_a))) (let ((_let_2 (tptp.fun (tptp.product_prod X_a X_a) tptp.bool))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.nat) (tptp.fun _let_2 _let_2)) _let_1) _let_1)))) (= (tptp.ti _let_27 tptp.pred_nat) tptp.pred_nat) (= (tptp.ti _let_120 tptp.inv) tptp.inv) (= (tptp.ti _let_171 tptp.wset) tptp.wset) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fEx X_a))) (= (tptp.ti (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool) _let_1) _let_1))) (= (tptp.ti tptp.bool tptp.fFalse) tptp.fFalse) (= (tptp.ti _let_42 tptp.fNot) tptp.fNot) (= (tptp.ti tptp.bool tptp.fTrue) tptp.fTrue) (= (tptp.ti _let_64 tptp.fconj) tptp.fconj) (= (tptp.ti _let_64 tptp.fdisj) tptp.fdisj) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fequal X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun X_a tptp.bool)) _let_1) _let_1))) (= (tptp.ti _let_64 tptp.fimplies) tptp.fimplies) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c (tptp.ti (tptp.fun X_a X_c) B_1_1) B_2_1) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_a $$unsorted) (X_c $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (= (tptp.hAPP X_a X_c B_1_1 (tptp.ti X_a B_2_1)) (tptp.hAPP X_a X_c B_1_1 B_2_1))) (forall ((X_c $$unsorted) (X_a $$unsorted) (B_1_1 $$unsorted) (B_2_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_c B_1_1 B_2_1))) (= (tptp.ti X_c _let_1) _let_1))) (forall ((B_1_1 $$unsorted)) (= (tptp.hBOOL (tptp.ti tptp.bool B_1_1)) (tptp.hBOOL B_1_1))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.member X_a))) (= (tptp.ti (tptp.fun X_a (tptp.fun (tptp.fun X_a tptp.bool) tptp.bool)) _let_1) _let_1))) (= (tptp.ti tptp.int tptp.m) tptp.m) (= (tptp.ti tptp.int tptp.s1) tptp.s1) (= (tptp.ti tptp.int tptp.s) tptp.s) (= (tptp.ti tptp.int tptp.t) tptp.t) _let_280 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_277 _let_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_14 _let_263) (tptp.hAPP tptp.int tptp.int _let_262 _let_1))) _let_279 (=> (= tptp.t _let_1) (= _let_13 _let_1)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_257 _let_2) tptp.t))) _let_278 (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 Y) _let_1))) (tptp.zero_zero X_a)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.power_power X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 X_1) _let_2)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 Y_1) _let_2)))) (or (not (= (tptp.ti X_a X_1) _let_1)) (not (= (tptp.ti X_a Y_1) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.power_power X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 X_1) _let_2)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 Y_1) _let_2)) _let_1) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_2) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (not (= (tptp.ti X_a A_2) _let_1))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_2) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) W))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_277 _let_261)) (not (forall ((T_4 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_3 (tptp.times_times tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.plus_plus tptp.int))) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_5 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) tptp.s) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_2))) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_2))) tptp.m)) _let_1)) T_4)))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime _let_261)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu1091635170sum2sq _let_263)) (forall ((W $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) W) W))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K_4) (tptp.ti tptp.int K_4))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z_1) W) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W) Z_1))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z_1) W)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W) Z_1)))))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.number_number_of tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 V)) (tptp.hAPP tptp.int tptp.int _let_3 W)) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 V) W))))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.number_number_of tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 K)) (tptp.hAPP tptp.int tptp.int _let_3 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a _let_1 X_1)) (tptp.hAPP tptp.int X_a _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) X_1) Y_1))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 Z1))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 Z2)) Z3) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) Z3))))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 J_2) K_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 K_4)))))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z_1) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W) Z_1)) (= (tptp.ti tptp.int Z_1) (tptp.ti tptp.int W))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 Z_1))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_269 tptp.pls)) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K)) (tptp.hAPP tptp.int tptp.int tptp.bit0 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Z) W_1)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Z) W_1)) (not (= (tptp.ti tptp.int Z) (tptp.ti tptp.int W_1))))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K_4))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I_1) J_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I_1)) (tptp.hAPP tptp.int tptp.int _let_1 J_2)))))))) (forall ((V_1 $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) V_1) tptp.pls)))) (forall ((V_1 $$unsorted)) (= (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) V_1) tptp.pls)))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_3 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 V)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 V_3)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 V_3)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) V) V_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 W)) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) V) W))) Z_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) V) W))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) V) W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 X_1) X_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 Y_1) Y_1))) _let_1)) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_1) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Y))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) X_1)) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) X_1) tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls) Y_1)))))) (forall ((V_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls) V_1)))) (forall ((X_a $$unsorted)) (=> (and (tptp.number X_a) (tptp.linorder X_a)) (forall ((V_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a _let_1 V_1))) (let ((_let_3 (tptp.hAPP tptp.int X_a _let_1 W_1))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) _let_2) _let_3)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less X_a) _let_3) _let_2))))))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.pls)))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted) (W_3 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 W_3) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) Z_4) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W_3) Z_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W) Z_1)))))))))) (= _let_276 _let_40) (= _let_40 _let_276) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) X_1)) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) X_1) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) Y_1)))))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_25 _let_182 _let_179) _let_179) _let_6) (forall ((W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) tptp.pls) W) tptp.pls)) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4)) L_4) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) L_4)))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.number_number_of tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 K)) (tptp.hAPP tptp.int tptp.int _let_3 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L))))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) Z_1) (tptp.one_one tptp.int)) (tptp.ti tptp.int Z_1))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.one_one tptp.int)) Z_1) (tptp.ti tptp.int Z_1))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.number_number_of tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 V)) (tptp.hAPP tptp.int tptp.int _let_3 W)) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 V) W))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.plus_plus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 Z1) Z2)) W) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z1) W)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) W))))))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) W))) (let ((_let_3 (tptp.plus_plus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 Z1) Z2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 Z1)) (tptp.hAPP tptp.int tptp.int _let_2 Z2))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K) tptp.pls))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) tptp.pls) (tptp.hAPP tptp.int tptp.int tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) tptp.pls) K))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K1) K2))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) (tptp.hAPP tptp.int tptp.int tptp.bit0 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K) L))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K1) K2))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (forall ((X_2 $$unsorted)) (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b G X_2))) (= (tptp.ti _let_1 F) (tptp.ti _let_1 G))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) A_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool A_3 X_1))))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) P_1) (tptp.ti _let_1 P_1)))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 K)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K) L))))) (forall ((V_1 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 V_1) V_2)))) (let ((_let_4 (tptp.number_number_of tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_4 V_1)) (tptp.hAPP tptp.int tptp.nat _let_4 V_2))) (and (=> _let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 tptp.pls) V_2))) _let_3))))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.one_one tptp.int)) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Z))))) (= _let_250 _let_179) (= _let_179 _let_250) (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W) (tptp.one_one tptp.int))) Z_1))))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W_1) (tptp.one_one tptp.int))) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) Z))))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z) (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) W_1) Z))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V_3 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 V)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 V_3)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 V_3)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) V_3)))))))))) (forall ((V_3 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V_3))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat _let_1 V))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) _let_3) _let_2))) (let ((_let_5 (tptp.ord_less tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 _let_5 V_3) tptp.pls)))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 _let_5 V) tptp.pls)))) (and (=> _let_8 (= _let_4 _let_2)) (=> (not _let_8) (and (=> _let_7 (= _let_4 _let_3)) (=> (not _let_7) (= _let_4 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) V_3)))))))))))))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.one_one tptp.int)) Z_1))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.ring_char_0 X_a)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (= (tptp.hAPP tptp.int X_a _let_1 X_1) (tptp.hAPP tptp.int X_a _let_1 Y_1)) (= (tptp.ti tptp.int X_1) (tptp.ti tptp.int Y_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number X_a) (forall ((W_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_2 (tptp.ti X_a X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((K $$unsorted) (L $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int tptp.bit1 K) (tptp.hAPP tptp.int tptp.int tptp.bit1 L)) (= (tptp.ti tptp.int K) (tptp.ti tptp.int L)))) (forall ((K $$unsorted) (L $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int tptp.bit0 K) (tptp.hAPP tptp.int tptp.int tptp.bit0 L)) (= (tptp.ti tptp.int K) (tptp.ti tptp.int L)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X) Y)) (= (tptp.ti tptp.int X) (tptp.ti tptp.int Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Y) X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 X_1) X_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 Y_1) Y_1)) _let_1) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_1) _let_1))))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((A_1 $$unsorted) (B $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.plus_plus X_b))) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_4 A_1) B)) _let_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 A_1) _let_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 B) _let_1)))))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.semiring X_b)) (forall ((V $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.hAPP X_b _let_1 (tptp.times_times X_b) (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V)))) (let ((_let_3 (tptp.plus_plus X_b))) (= (tptp.hAPP X_b X_b _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 B) C)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b _let_2 B)) (tptp.hAPP X_b X_b _let_2 C))))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 Z1))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 Z2)) Z3) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) Z3))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 _let_1 Y))) (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_4 Z_1)) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int _let_3 Z_1)))))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z_1) W) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 W) Z_1))))) (= _let_1 _let_245) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) K_4))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I_1) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) K_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I_1)) (tptp.hAPP tptp.int tptp.int _let_1 J_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.power_power X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (=> (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 X) _let_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 Y) _let_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_4 (tptp.power_power X_a))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_5 _let_4 X) _let_3)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_5 _let_4 Y) _let_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_4 (tptp.power_power X_a))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_5 _let_4 X) _let_3)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_5 _let_4 Y) _let_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.power_power X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 X_1) _let_2)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 Y_1) _let_2))) _let_1)) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 Y) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 X_1) X_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 Y_1) Y_1)))) (or (not (= (tptp.ti X_a X_1) _let_1)) (not (= (tptp.ti X_a Y_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Y))) (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (tptp.ti X_a A_1))))) (= _let_2 (tptp.hAPP tptp.int tptp.int _let_18 _let_3)) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4)) L_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) L_4))) L_4))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) Ma) N_1) _let_1) (and (= (tptp.ti tptp.int Ma) _let_1) (= (tptp.ti tptp.int N_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) A_2) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((K_4 $$unsorted)) (not (= (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4) tptp.pls))) (forall ((L_4 $$unsorted)) (not (= tptp.pls (tptp.hAPP tptp.int tptp.int tptp.bit1 L_4)))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (not (= (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4) (tptp.hAPP tptp.int tptp.int tptp.bit0 L_4)))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (not (= (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4) (tptp.hAPP tptp.int tptp.int tptp.bit1 L_4)))) (forall ((K $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int tptp.bit0 K) tptp.pls) (= (tptp.ti tptp.int K) tptp.pls))) (forall ((L $$unsorted)) (= (= tptp.pls (tptp.hAPP tptp.int tptp.int tptp.bit0 L)) (= tptp.pls (tptp.ti tptp.int L)))) (= (tptp.hAPP tptp.int tptp.int tptp.bit0 tptp.pls) tptp.pls) _let_275 (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit1 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_272 tptp.pls))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K)) (tptp.hAPP tptp.int tptp.int tptp.bit0 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (not (= _let_1 _let_2)) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K_4) tptp.pls) (tptp.ti tptp.int K_4))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) tptp.pls) K_4) (tptp.ti tptp.int K_4))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) L_4)))))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K_4) K_4))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z_1) (tptp.zero_zero tptp.int)) (tptp.ti tptp.int Z_1))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.zero_zero tptp.int)) Z_1) (tptp.ti tptp.int Z_1))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 I_1) J_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 I_1) K_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 J_2) K_4))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.one_one X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.plus_plus X_a) _let_2) _let_2)) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) A_1)) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) Z_1) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) Z_1) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) Z_1) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) Z_1) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.zero_zero X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.int X_a _let_1 X_1)) (tptp.hAPP tptp.int X_a _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X_1) Y_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 W)) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) W))) Z_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) W))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.pls)))))) (forall ((K1 $$unsorted) (K2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K1)) (tptp.hAPP tptp.int tptp.int tptp.bit0 K2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K1) K2)))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) (tptp.hAPP tptp.int tptp.int tptp.bit0 L))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)))))) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit1 W_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 W_1) _let_1))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K)) tptp.pls)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.pls)))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_272 _let_1))) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 W_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 W_1) _let_1))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) L_4)))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) L_4)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_173 _let_2)) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.one_one tptp.int)) K_4)) K_4))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.one_one tptp.int)) Z_1)) Z_1) (tptp.zero_zero tptp.int)))))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) W_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z) (tptp.one_one tptp.int)))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z)) (= (tptp.ti tptp.int W_1) (tptp.ti tptp.int Z)))))) (forall ((X_b $$unsorted)) (=> (and (tptp.monoid_mult X_b) (tptp.number X_b)) (forall ((W $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) W))) (= (tptp.hAPP tptp.nat X_b (tptp.hAPP X_b (tptp.fun tptp.nat X_b) (tptp.power_power X_b) _let_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) _let_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_5 (tptp.power_power X_a))) (let ((_let_6 (tptp.fun tptp.nat X_a))) (let ((_let_7 (tptp.plus_plus X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_6 _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_7 X) Y)) _let_4) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_7 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_7 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_6 _let_5 X) _let_4)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_6 _let_5 Y) _let_4))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) _let_1)) X)) Y))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a _let_1 W))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)) _let_2)) _let_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a _let_1 W))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.one_one X_a)) _let_2)) _let_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.one_one X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.plus_plus tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 (tptp.one_one tptp.int)) Z)) Z)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Z) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) X_1)) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X_1) tptp.pls)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls) Y_1)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.number_semiring X_a) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) _let_1) _let_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.number_ring X_a) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) _let_1) _let_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) X_1)) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X_1) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) Y_1)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_267 _let_13)) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.int tptp.nat _let_3 _let_2))) (let ((_let_5 (tptp.power_power tptp.int))) (let ((_let_6 (tptp.fun tptp.nat tptp.int))) (let ((_let_7 (tptp.hAPP tptp.int _let_6 _let_5 B))) (let ((_let_8 (tptp.hAPP tptp.int tptp.nat _let_3 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1)))) (let ((_let_9 (tptp.times_times tptp.int))) (let ((_let_10 (tptp.fun tptp.int tptp.int))) (let ((_let_11 (tptp.hAPP tptp.int _let_10 _let_9 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) _let_2)))) (let ((_let_12 (tptp.hAPP tptp.int _let_6 _let_5 A_1))) (let ((_let_13 (tptp.plus_plus tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_6 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_13 A_1) B)) _let_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_13 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_13 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_13 (tptp.hAPP tptp.nat tptp.int _let_12 _let_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_9 (tptp.hAPP tptp.int tptp.int _let_11 (tptp.hAPP tptp.nat tptp.int _let_12 _let_8))) B))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_9 (tptp.hAPP tptp.int tptp.int _let_11 A_1)) (tptp.hAPP tptp.nat tptp.int _let_7 _let_8)))) (tptp.hAPP tptp.nat tptp.int _let_7 _let_4))))))))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_3 (tptp.power_power tptp.int))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (let ((_let_5 (tptp.times_times tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.plus_plus tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 A_1) B)) _let_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 A_1) _let_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) _let_1)) A_1)) B))) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 B) _let_2))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ti tptp.int X))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) _let_2) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) X) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (or (= _let_1 _let_2) (= _let_1 (tptp.one_one tptp.int))))))))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_258 tptp.s)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_14 tptp.s) _let_261)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 (tptp.hAPP tptp.int _let_91 tptp.zcong tptp.s1) tptp.s) _let_261))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.number_number_of tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) (tptp.hAPP tptp.nat tptp.int _let_3 (tptp.hAPP tptp.int tptp.nat _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1)))) (tptp.hAPP tptp.nat tptp.int _let_3 (tptp.hAPP tptp.int tptp.nat _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_1)))))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) X) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (forall ((R_4 $$unsorted) (Q_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 (tptp.zero_zero tptp.int)) A_1)) (=> (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.plus_plus tptp.int) R_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) A_1) Q_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 R_4) A_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.one_one tptp.int)) Q_3))))))))) (forall ((R_4 $$unsorted) (Q_3 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_3) A_1)) (=> (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.plus_plus tptp.int) R_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.times_times tptp.int) A_1) Q_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_3) R_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_3) (tptp.one_one tptp.int))))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_258 _let_19)) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X))) (let ((_let_2 (tptp.hAPP tptp.nat X_a _let_1 N))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) _let_2) _let_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) X) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_273 _let_274) _let_261)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) tptp.m)) (tptp.one_one tptp.int)))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) X_2) _let_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.zcong tptp.s1) X_2) _let_2)) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) tptp.m)) (tptp.one_one tptp.int)))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) Y_2) _let_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.zcong tptp.s1) Y_2) _let_2))) (= (tptp.ti tptp.int Y_2) (tptp.ti tptp.int X_2)))))))))))) (not (forall ((S_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) tptp.m)) (tptp.one_one tptp.int)))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (not (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) S_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) S_1) _let_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.zcong tptp.s1) S_1) _let_2))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 (tptp.hAPP tptp.int _let_91 tptp.zcong _let_274) _let_244) _let_261)) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X_1) N_1))) (or (= N_1 _let_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 X_1))))))) (forall ((A_1 $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1) N))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a _let_3 P_5)) Q_3) (tptp.hAPP tptp.nat X_a _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) P_5) Q_3))))))))) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) P_5) N)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 P_5) B))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 A_1))))))))) (forall ((N $$unsorted) (B $$unsorted) (A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) P_5) N)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 P_5) A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 B))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int))) (let ((_let_2 (tptp.fun tptp.nat tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 X))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int _let_3 Y)) Z_1) (tptp.hAPP tptp.nat tptp.int _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Y) Z_1))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 (tptp.zero_zero tptp.int)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 M) N)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) N) M)))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 M) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 N) M)) (= (tptp.ti tptp.int M) (tptp.ti tptp.int N)))))))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 M)) (tptp.hAPP tptp.int tptp.int _let_3 N))) (=> (not (= (tptp.ti tptp.int K_4) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 M) N)))))))) (forall ((K $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) N_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) K) Ma)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N_1)))))) (forall ((C_1 $$unsorted) (X_1 $$unsorted) (Ta $$unsorted) (A_2 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 _let_2 X_1))) (let ((_let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) A_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 D_1)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 (tptp.hAPP tptp.int tptp.int _let_3 Ta))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) C_1) D_1))) Ta)))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime _let_19)) (forall ((Z_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) Z_1) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) Z_1) N)))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu1091635170sum2sq X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu1091635170sum2sq Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu1091635170sum2sq (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y)))))) (forall ((V_1 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) V_1))) (let ((_let_2 (tptp.number_number_of tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_2 V_1)) (tptp.hAPP tptp.int tptp.nat _let_2 V_2))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 V_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Ly)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Rx) Ry)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Rx)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ly) Ry))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Lx) Ly)))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Rx))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Ry)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Ry)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Rx) Ry))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_4 Ly)) _let_3) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ly) _let_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Ly)) Rx) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Rx)) Ly)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Ly $$unsorted) (Rx $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Ly)) Rx) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Ly) Rx))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Rx) Ry)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Rx)) Ry)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((Lx $$unsorted) (Rx $$unsorted) (Ry $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Lx))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Rx))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Ry)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Ry)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 C))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 D)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 D)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) D)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X) (tptp.one_one tptp.nat)) (tptp.ti X_a X))))) (forall ((X_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) W_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X_1) _let_3))) (or (= _let_3 _let_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 X_1)))))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) Z_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) Z_1) Z_1)))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) Z_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) Z_1) Z_1)))) (forall ((V_3 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_1 V)) (tptp.hAPP tptp.int tptp.nat _let_1 V_3)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V) tptp.pls)))) (and (=> _let_3 (= _let_2 (tptp.zero_zero tptp.nat))) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) V) V_3))))))))) (forall ((V_3 $$unsorted) (K_4 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V_3)) K_4)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V) tptp.pls)))) (and (=> _let_5 (= _let_4 (tptp.zero_zero tptp.nat))) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) V) V_3))) K_4)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 A_1))) (= (tptp.hAPP tptp.nat X_a _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) _let_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_4 N)) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) K_4))) _let_1)) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) _let_1) A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (= (= (tptp.ti X_a B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B_1) A_2)) (= (tptp.ti X_a A_2) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_2))) (let ((_let_5 (tptp.plus_plus X_a))) (= (and (not (= (tptp.ti X_a A_2) (tptp.ti X_a B_1))) (not (= (tptp.ti X_a C_1) (tptp.ti X_a D_1)))) (not (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_5 (tptp.hAPP X_a X_a _let_4 C_1)) (tptp.hAPP X_a X_a _let_3 D_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_5 (tptp.hAPP X_a X_a _let_4 D_1)) (tptp.hAPP X_a X_a _let_3 C_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) M)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) M)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) M)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((W_1 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X_1))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 W_1))) (let ((_let_5 (tptp.plus_plus X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_5 (tptp.hAPP X_a X_a _let_4 Y_1)) (tptp.hAPP X_a X_a _let_3 Z)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_5 (tptp.hAPP X_a X_a _let_4 Z)) (tptp.hAPP X_a X_a _let_3 Y_1))) (or (= (tptp.ti X_a W_1) (tptp.ti X_a X_1)) (= (tptp.ti X_a Y_1) (tptp.ti X_a Z)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 X) Y)) Q_3) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) Q_3)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 Y) Q_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 P_5)) (tptp.hAPP tptp.nat X_a _let_1 Q_3)) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) P_5) Q_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X) (tptp.zero_zero tptp.nat)) (tptp.one_one X_a))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_258 _let_1)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiri456707255roduct X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) R_4))) (let ((_let_3 (tptp.plus_plus X_a))) (=> (not (= (tptp.ti X_a R_4) (tptp.zero_zero X_a))) (=> (and (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (not (= (tptp.ti X_a C) (tptp.ti X_a D)))) (not (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 A_1) (tptp.hAPP X_a X_a _let_2 C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 B) (tptp.hAPP X_a X_a _let_2 D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 M) M) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 _let_1) _let_1)) M)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 M) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) M)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) (tptp.one_one X_a))) M)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) M)) M) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) (tptp.one_one X_a))) M)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (forall ((A_2 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) W_1))) (let ((_let_2 (tptp.zero_zero X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_2) _let_1) _let_2) (and (= (tptp.ti X_a A_2) _let_2) (not (= _let_1 (tptp.zero_zero tptp.nat)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 B)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_258 _let_2)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) N)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((W $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) W))) (let ((_let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) _let_2))) (let ((_let_4 (= _let_2 (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 (tptp.one_one X_a))) (=> (not _let_4) (= _let_3 _let_1)))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_258 _let_21)) (forall ((B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.times_times tptp.int) B_5) Q_5)) R_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_5) B_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_1) B_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 Q_5))))))))))) (forall ((B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.times_times tptp.int) B_5) Q_5)) R_5)) _let_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) R_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_4 _let_1) B_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Q_5) _let_1))))))))))) (forall ((B $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 (tptp.times_times tptp.int) B))) (let ((_let_6 (tptp.plus_plus tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int _let_5 Q_5)) R_5)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int _let_5 Q_3)) R_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) R_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 R_5) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 R_4) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_5) Q_3))))))))))))) (forall ((B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted) (B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_2 _let_1 _let_3))) (let ((_let_6 (tptp.times_times tptp.int))) (let ((_let_7 (tptp.fun tptp.int tptp.int))) (let ((_let_8 (tptp.plus_plus tptp.int))) (let ((_let_9 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_8 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_6 B_5) Q_5)) R_5))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_8 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_6 B) Q_3)) R_4) _let_9) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 _let_9)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_5) B_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_3) B_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_5) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_3) Q_5)))))))))))))))))) (forall ((B $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) B))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 (tptp.times_times tptp.int) B))) (let ((_let_6 (tptp.plus_plus tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int _let_5 Q_5)) R_5)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int _let_5 Q_3)) R_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 R_4) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 R_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_3) Q_5))))))))))))) (forall ((B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted) (B_5 $$unsorted) (Q_5 $$unsorted) (R_5 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.times_times tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.plus_plus tptp.int))) (let ((_let_8 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 B_5) Q_5)) R_5))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 B) Q_3)) R_4) _let_8) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_8) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 R_4) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_3) R_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_3) B_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_5) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Q_5) Q_3))))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat))) (let ((_let_3 (tptp.power_power tptp.int))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 _let_3 X))) (let ((_let_6 (tptp.hAPP tptp.int tptp.nat _let_2 _let_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.nat tptp.int _let_5 _let_6)) _let_6) (tptp.hAPP tptp.nat tptp.int _let_5 (tptp.hAPP tptp.int tptp.nat _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_273 _let_244) _let_261)) (forall ((Y $$unsorted) (X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong X) (tptp.zero_zero tptp.int)) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) Y) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) X) P_5)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) P_5) Y)))))))) (forall ((P_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) P_4)) (forall ((M_2 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int M_2))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) M_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.dvd_dvd tptp.int) M_2) P_4))) (or (= _let_1 (tptp.one_one tptp.int)) (= _let_1 (tptp.ti tptp.int P_4)))))))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) (let ((_let_3 (tptp.number_number_of tptp.int))) (let ((_let_4 (tptp.ti tptp.int P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (= _let_4 (tptp.hAPP tptp.int tptp.int _let_3 _let_2))) (=> (not (= _let_4 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_2))) P_5)))))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_22 (tptp.ord_less tptp.nat) _let_40) _let_6)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 B) N))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord626643107strict X_a) (forall ((V $$unsorted) (U $$unsorted) (Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.ord_less X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.hAPP X_a _let_5 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 X) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 Y) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_6 U)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_6 V)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 U) V) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 U) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 V) Y))) A_1)))))))))))))))) (forall ((Y $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) Y) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y))))))) (forall ((N $$unsorted) (P_5 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) M) N))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 N))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) A_1)) (=> (and (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong A_1) _let_1) P_5))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong B) _let_1) P_5)))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) B)) _let_1) P_5)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) B)) _let_1) P_5)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong A_1) _let_1) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong B) _let_1) P_5)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) (tptp.zero_zero X_a)))))) (not (forall ((S1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) S1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (tptp.hAPP tptp.int tptp.int _let_2 tptp.min_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) tptp.m)) (tptp.one_one tptp.int))))))))))) _let_264 (forall ((K $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int tptp.bit1 K) tptp.min_1) (= (tptp.ti tptp.int K) tptp.min_1))) (forall ((L $$unsorted)) (= (= tptp.min_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 L)) (= tptp.min_1 (tptp.ti tptp.int L)))) (= (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.min_1) tptp.min_1) (not (= tptp.pls tptp.min_1)) (not (= tptp.min_1 tptp.pls)) (forall ((K_4 $$unsorted)) (not (= (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4) tptp.min_1))) (forall ((L_4 $$unsorted)) (not (= tptp.min_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 L_4)))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_271 tptp.min_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_270 tptp.min_1)) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) tptp.min_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.min_1)))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.min_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_272 tptp.min_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_271 tptp.pls)) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.min_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_271 _let_1)) (forall ((K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.min_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K)) tptp.min_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.min_1)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_270 tptp.pls)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_269 tptp.min_1))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K)) tptp.min_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) tptp.min_1)))))) (not (= _let_245 _let_244)) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 K)) tptp.min_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K) tptp.min_1))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) tptp.min_1) (tptp.hAPP tptp.int tptp.int tptp.bit0 K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) tptp.min_1) K))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1))) (let ((_let_2 (tptp.ti tptp.int N_1))) (let ((_let_3 (tptp.ti tptp.int Ma))) (let ((_let_4 (tptp.one_one tptp.int))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) Ma) N_1) _let_4) (or (and (= _let_3 _let_4) (= _let_2 _let_4)) (and (= _let_3 _let_1) (= _let_2 _let_1))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ti tptp.int M))) (let ((_let_2 (tptp.one_one tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) M) N) _let_2) (or (= _let_1 _let_2) (= _let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong A_2) B_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong B_1) A_2) Ma)))))) (forall ((K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong K_4) K_4) M)))) (forall ((D $$unsorted) (C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 tptp.zcong A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 B) M)) (=> (= (tptp.ti tptp.int B) (tptp.ti tptp.int C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong C) D) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 D) M))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 tptp.zcong A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong B) C) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 C) M)))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong X))) (let ((_let_3 (tptp.number_number_of tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int _let_3 tptp.min_1)) P_5)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 (tptp.one_one tptp.int)) P_5))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B) _let_1) (or (= (tptp.ti X_a A_1) _let_1) (= (tptp.ti X_a B) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.no_zero_divisors X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (=> (not (= (tptp.ti X_a B) _let_1)) (not (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_n68954251visors X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_2) B_1) _let_1) (or (= (tptp.ti X_a A_2) _let_1) (= (tptp.ti X_a B_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.mult_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) _let_1) A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.zero_zero X_a) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.zero_neq_one X_a) (not (= (tptp.one_one X_a) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring X_a) (forall ((A_1 $$unsorted) (E_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) E_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) E_1)) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) E_1)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (not (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) _let_1) A_1)) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) B)) N) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 B) N)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.dvd_dvd X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dvd X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (K_4 $$unsorted)) (=> (= (tptp.ti X_a A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) K_4)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) B) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) N) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) (tptp.one_one X_a)) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.dvd_dvd X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 Y) N))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((M $$unsorted) (A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.dvd_dvd X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N)) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 M)) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((N $$unsorted) (M $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.dvd_dvd X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 X) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 Y) M)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))) (forall ((M $$unsorted) (N $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) I_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X_1) N_1))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 X_1)) (= N_1 _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP tptp.nat X_a _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a _let_3 M)) N)))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 B) C)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.one_one tptp.nat)) (tptp.ti X_a A_1))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong M) (tptp.zero_zero tptp.int)) M)))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) B_1) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int A_2) (tptp.ti tptp.int B_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_1) B) (tptp.one_one tptp.int))))) (forall ((A_1 $$unsorted) (M $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) M)) M)))))) (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 tptp.zcong C_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong A_2) B_1) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_2) D_1)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B_1) D_1)) Ma)))))))))) (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) D_1))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.hAPP tptp.int _let_3 tptp.zcong C_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong A_2) B_1) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 (tptp.hAPP tptp.int tptp.int _let_1 A_2)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 (tptp.hAPP tptp.int tptp.int _let_1 B_1)) Ma))))))))) (forall ((K_4 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong A_1) B) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) K_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) K_4)) M)))))))) (forall ((K_4 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) K_4))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong A_1) B) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP tptp.int tptp.int _let_1 A_1)) (tptp.hAPP tptp.int tptp.int _let_1 B)) M))))))) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong A_1) B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong C) D) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) D)) M))))))))) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong A_1) B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong C) D) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) D)) M))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong A_1) B) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) C)) M)))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int))) (let ((_let_2 (tptp.fun tptp.nat tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong X) Y) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 X) Z_1)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Y) Z_1)) M)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (=> (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (=> (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere1490568538miring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) A_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere453448008miring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero 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B_1))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a 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$$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times 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(tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_2)) (tptp.hAPP X_a X_a _let_3 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_4 A_2)) (tptp.hAPP X_a X_a _let_4 B_1))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) _let_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.times_times X_a))) (let ((_let_5 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 A_2) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 B_1) C_1))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) _let_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_ring X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) A_1)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 B) N)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) M) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.idom X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_2)) (tptp.hAPP X_a X_a _let_3 B_1))) (or (= (tptp.ti X_a C_1) (tptp.zero_zero X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.idom X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_2) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B_1) C_1))) (or (= (tptp.ti X_a C_1) (tptp.zero_zero X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_5 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) N_5)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N)) (tptp.hAPP tptp.nat X_a _let_1 N_5))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Ma $$unsorted) (N_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) A_2)) (= (= (tptp.hAPP tptp.nat X_a _let_1 Ma) (tptp.hAPP tptp.nat X_a _let_1 N_1)) (= Ma N_1))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.mult_zero X_a) (tptp.no_zero_divisors X_a) (tptp.zero_neq_one X_a)) (forall ((A_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_2) N_1) _let_1) (and (= (tptp.ti X_a A_2) _let_1) (not (= N_1 (tptp.zero_zero tptp.nat))))))))) (forall ((X_a $$unsorted)) (=> (tptp.power X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.zero_zero tptp.nat)) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 _let_2 (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 A_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 B) A_1)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_1) B) M))))))))))) (forall ((M $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 X) M)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong X) _let_1) M))))))))) (forall ((M $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong X) Y) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Y) M)) (= (tptp.ti tptp.int X) (tptp.ti tptp.int Y)))))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.dvd_dvd tptp.int) N) M)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 M) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 N) M))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) B_1) Ma)) (exists ((K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.ti tptp.int B_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) A_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) Ma) K_1)))))))) (forall ((X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong X_1) (tptp.zero_zero tptp.int)) P_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) P_4) X_1))))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) (tptp.zero_zero tptp.int)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) Ma) A_2))))) (forall ((M $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) M) N))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semiring X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semiring X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (let ((_let_6 (tptp.ord_less_eq X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_5) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 _let_5) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (let ((_let_6 (tptp.ord_less_eq X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 _let_5) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_5) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord20386208strict X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_5) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) _let_5) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) C_1) (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_2)) (tptp.hAPP X_a X_a _let_3 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord581940658strict X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_2)) (tptp.hAPP X_a X_a _let_3 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) Y) X)) X))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) Y)) X))))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.linordered_semidom X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) _let_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.power_power X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 B) N))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_5 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) N_5)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N_5)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.one_one X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) B_1))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.one_one X_a)) B_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_1 X_1)) (tptp.hAPP tptp.nat X_a _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X_1) Y_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) N))) (let ((_let_3 (= N (tptp.zero_zero tptp.nat)))) (and (=> _let_3 (= _let_2 (tptp.one_one X_a))) (=> (not _let_3) (= _let_2 _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_5 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N_5)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N)) (tptp.hAPP tptp.nat X_a _let_1 N_5))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) B_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.one_one X_a)) B_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 X_1)) (tptp.hAPP tptp.nat X_a _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X_1) Y_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_3 (tptp.number_number_of tptp.real))) (let ((_let_4 (tptp.times_times tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.power_power tptp.real))) (let ((_let_7 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.int tptp.real _let_3 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_7 _let_6 X) _let_2)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.int tptp.real _let_3 _let_1)) X)) _let_2)))))))))) (forall ((M $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) X) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong X) _let_1) M)) (= (tptp.ti tptp.int X) _let_1))))))) (forall ((M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) A_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong A_1) _let_1) M)) (= (tptp.ti tptp.int A_1) _let_1))))))) (forall ((B $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 A_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_1) B) M)) (= (tptp.ti tptp.int A_1) (tptp.ti tptp.int B))))))))))) (forall ((P_5 $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) Y) N))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.nat tptp.int _let_2 Y)) _let_1) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Y) Z_1))) _let_1) P_5)))))))) (forall ((Y $$unsorted) (X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong X) _let_1) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong Y) _let_1) P_5))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y)) _let_1) P_5)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1278240602ring_1 X_a) (forall ((V $$unsorted) (U $$unsorted) (Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.ord_less_eq X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.hAPP X_a _let_5 _let_4 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 X) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 Y) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_6 U)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_6 V)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 U) V) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 U) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 V) Y))) A_1)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) _let_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (N_5 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N_5)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N_5)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (=> (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 A_1) N) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 B) N)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.ti X_a A_1) (tptp.ti X_a B)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.ti X_a X) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) X) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X) N))))))) _let_265 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_267 _let_266)) (forall ((J_2 $$unsorted) (K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 tptp.min_1)))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.int _let_2 K_4))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.int _let_2 J_2))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_5) tptp.zcong _let_4) _let_3) M)) (= _let_4 _let_3))))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong (tptp.one_one tptp.int)) (tptp.hAPP tptp.int tptp.int _let_1 tptp.min_1)) M))))))) (= _let_266 _let_13) (=> (not _let_265) (not _let_264)) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.number_number_of tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) M)) _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime _let_4)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.legendre (tptp.hAPP tptp.int tptp.int _let_2 tptp.min_1)) _let_4) _let_1))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int _let_1 N))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 N)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 N))))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) A_1)) (exists ((P_6 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_6)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_6) A_1)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) X_1) X_1)))) (= X_1 _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) V) W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W))))))) (forall ((K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N_1) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1))))) (forall ((Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) Ma) _let_1)) (= Ma _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) Y) Z_1))))))))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K_4) tptp.pls) (tptp.ti tptp.int K_4))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) L_4)))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.minus_minus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 Z1) Z2)) W) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z1) W)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z2) W))))))) (forall ((W $$unsorted) (Z1 $$unsorted) (Z2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) W))) (let ((_let_3 (tptp.minus_minus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 Z1) Z2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 Z1)) (tptp.hAPP tptp.int tptp.int _let_2 Z2))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) A_1) B) (tptp.ti tptp.int C)) (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) C) B))))) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong A_1) B) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong C) D) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) D)) M))))))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) M) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.zero_zero tptp.nat)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 M) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) N) M)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_ring X_a) (tptp.dvd X_a)) (forall ((Ta $$unsorted) (D_1 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) D_1) D_2)) (forall ((X_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) D_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 X_2) Ta))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) X_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) K_1) D_2))) Ta)))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_ring X_a) (tptp.dvd X_a)) (forall ((Ta $$unsorted) (D_1 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) D_1) D_2)) (forall ((X_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) D_1))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 X_2) Ta)))) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) X_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) K_1) D_2))) Ta))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_2 $$unsorted) (E_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 A_2) E_2)) C_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 B_1) E_2)) D_1)) (= (tptp.ti X_a C_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) B_1) A_2)) E_2)) D_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_2 $$unsorted) (E_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 A_2) E_2)) C_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 B_1) E_2)) D_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_2) B_1)) E_2)) C_1) (tptp.ti X_a D_1))))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((V $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.hAPP X_b _let_1 (tptp.times_times X_b) (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V)))) (let ((_let_3 (tptp.minus_minus X_b))) (= (tptp.hAPP X_b X_b _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 B) C)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_1 _let_3 (tptp.hAPP X_b X_b _let_2 B)) (tptp.hAPP X_b X_b _let_2 C))))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ring X_b)) (forall ((A_1 $$unsorted) (B $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V))) (let ((_let_2 (tptp.times_times X_b))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.minus_minus X_b))) (= (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_4 A_1) B)) _let_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 A_1) _let_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_3 _let_2 B) _let_1)))))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) L_4)))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) L_4)))))) (forall ((L_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) tptp.pls))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int _let_1 L_4))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) L)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K) L)) (tptp.zero_zero tptp.int))))))) (forall ((K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) K_4) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) K_4) N)))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))))) (forall ((A_1 $$unsorted) (R_4 $$unsorted) (B $$unsorted) (M $$unsorted) (C $$unsorted) (D $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.plus_plus tptp.int))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 _let_1 R_4))) (let ((_let_5 (tptp.minus_minus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_5 A_1) (tptp.hAPP tptp.int tptp.int _let_4 B))) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_5 C) (tptp.hAPP tptp.int tptp.int _let_4 D))) N)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 C) N))) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 D) N))))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) B_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) Ma) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) A_2) B_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_2 $$unsorted) (E_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.ord_less_eq X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 A_2) E_2)) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 B_1) E_2)) D_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_2) B_1)) E_2)) C_1)) D_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_2 $$unsorted) (E_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.ord_less_eq X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 A_2) E_2)) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 B_1) E_2)) D_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 C_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) B_1) A_2)) E_2)) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_2 $$unsorted) (E_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.ord_less X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 A_2) E_2)) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 B_1) E_2)) D_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 C_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) B_1) A_2)) E_2)) D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring X_a) (forall ((A_2 $$unsorted) (E_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.ord_less X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 A_2) E_2)) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 B_1) E_2)) D_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_2) B_1)) E_2)) C_1)) D_1))))))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Ma) N_1)) Ma)) (= N_1 (tptp.one_one tptp.nat)))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) N_1) Ma)) Ma)) (= N_1 (tptp.one_one tptp.nat)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.minus_minus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 W)) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) W))) C)))))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) A_1) (tptp.one_one tptp.int)))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.int _let_3 _let_2 X))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 A_1)) (=> (not (= (tptp.ti tptp.int X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 _let_1)))))))))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) W_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Z) (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) Z))))) (forall ((L_4 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 tptp.pls) (tptp.hAPP tptp.int tptp.int tptp.bit1 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 tptp.min_1) L_4)))))) (forall ((L_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) tptp.min_1))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int _let_1 L_4))))) (forall ((L_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) tptp.min_1))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int _let_1 L_4))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_4) _let_1))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) A_2) _let_3)) _let_1) P_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong A_2) _let_3) P_4))))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (= Ma N_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) Ma))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= X Y)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) N)))) (forall ((N $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) M)) (not (= M N)))) (forall ((S_3 $$unsorted) (T_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) S_3) T_5)) (not (= S_3 T_5)))) (forall ((P_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 P_1 N_1) Ma)))) (let ((_let_3 (tptp.ord_less tptp.nat))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 Ma) N_1)) _let_2) (=> (=> (= Ma N_1) _let_2) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_3 N_1) Ma)) _let_2) _let_2))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) M))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat _let_4 Z_1)) (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 Z_1)))))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 N)) K_4) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_4))))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (= Ma N_1)))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Ma) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K)) (= Ma N_1))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)) (= M N)))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K_4)))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M N) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) N))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) M))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 N)) K_4) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_4))))))) (forall ((I_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_2 M)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.one_one tptp.nat)) I_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ti tptp.int A_1))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 A_1) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) A_1) A_1)) _let_1) P_5)) (or (= _let_3 _let_1) (= _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_5) _let_1))))))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 tptp.zcong A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) A_1) A_1)) _let_1) P_5)) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 _let_1) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_5) _let_1)) P_5)))))))))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (not (= N_1 _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.zero_zero tptp.nat))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (not (= N (tptp.zero_zero tptp.nat))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (not (= N _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.zero_zero tptp.nat)) N) N)) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) (tptp.zero_zero tptp.nat)) M)) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) N_1) _let_1) (and (= Ma _let_1) (= N_1 _let_1))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N) M) (= N (tptp.zero_zero tptp.nat)))) (forall ((P_2 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hBOOL P_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (and _let_2 _let_3) (and _let_2 _let_1))))))) (forall ((P_2 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hBOOL P_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)))) (let ((_let_3 (tptp.hBOOL P_1))) (=> (=> _let_2 (= _let_3 _let_1)) (= (=> _let_2 _let_3) (=> _let_2 _let_1))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) N))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) _let_1)) (= N_1 _let_1)))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) _let_1) N) _let_1))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) _let_1) _let_1))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Ma) N_1) _let_1) (or (= Ma _let_1) (= N_1 _let_1))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (or (= Ma N_1) (= K (tptp.zero_zero tptp.nat)))))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Ma) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K)) (or (= Ma N_1) (= K (tptp.zero_zero tptp.nat))))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_1) J_2)) I_1)))) (forall ((J_2 $$unsorted) (I_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) I_1)) I_1)))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))))))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) M)))))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) J_2)))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_1) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_4))))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_1) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K_4) L_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) L_4)))))))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_4) L_4)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 M) L_4) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 K_4) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_1) J_2)) K_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_4)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Ma) N_1)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) N_1)) (not (= Ma N_1)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) N_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Ma) N_1)) (= Ma N_1))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (=> (not (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (= M N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.int))) (let ((_let_3 (tptp.fun tptp.nat tptp.int))) (let ((_let_4 (tptp.minus_minus tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.plus_plus tptp.int) A_1) B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 A_1) B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 A_1) _let_1)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 B) _let_1))))))))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)))) (forall ((N $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) M)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) N_1)) (exists ((K_1 $$unsorted)) (= N_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) K_1))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))))))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) J_2) M)))))) (forall ((M $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) J_2)))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_1) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_4))))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_1) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K_4) L_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) L_4)))))))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K_4)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_4) N)))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K_4)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K_4)) N)) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_4) N))))))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K_4))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 M) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) N)) K_4) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_4))))))) (forall ((M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) M)))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_1) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_4))))))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K_4))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) J_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 I_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 J_2)))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_1) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 K_4) L_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) L_4)))))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.one_one tptp.nat)) N) N)) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Ma) N_1)) (and (= Ma _let_1) (= N_1 _let_1))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) N) (tptp.one_one tptp.nat)) N)) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Ma) N_1) _let_1) (and (= Ma _let_1) (= N_1 _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_5 (tptp.power_power X_a))) (let ((_let_6 (tptp.fun tptp.nat X_a))) (let ((_let_7 (tptp.minus_minus X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_6 _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_7 X) Y)) _let_4) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_7 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_6 _let_5 X) _let_4)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_6 _let_5 Y) _let_4))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) _let_1)) X)) Y))))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_3 (tptp.power_power tptp.int))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (let ((_let_5 (tptp.times_times tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.minus_minus tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 A_1) B)) _let_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 A_1) _let_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) _let_1)) A_1)) B))) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 B) _let_2))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_1))) (let ((_let_3 (tptp.number_number_of tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.int tptp.nat _let_3 _let_2))) (let ((_let_5 (tptp.power_power tptp.int))) (let ((_let_6 (tptp.fun tptp.nat tptp.int))) (let ((_let_7 (tptp.hAPP tptp.int _let_6 _let_5 B))) (let ((_let_8 (tptp.hAPP tptp.int tptp.nat _let_3 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1)))) (let ((_let_9 (tptp.times_times tptp.int))) (let ((_let_10 (tptp.fun tptp.int tptp.int))) (let ((_let_11 (tptp.hAPP tptp.int _let_10 _let_9 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) _let_2)))) (let ((_let_12 (tptp.hAPP tptp.int _let_6 _let_5 A_1))) (let ((_let_13 (tptp.minus_minus tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_6 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_13 A_1) B)) _let_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_13 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_13 (tptp.hAPP tptp.nat tptp.int _let_12 _let_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_9 (tptp.hAPP tptp.int tptp.int _let_11 (tptp.hAPP tptp.nat tptp.int _let_12 _let_8))) B))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_10 _let_9 (tptp.hAPP tptp.int tptp.int _let_11 A_1)) (tptp.hAPP tptp.nat tptp.int _let_7 _let_8)))) (tptp.hAPP tptp.nat tptp.int _let_7 _let_4))))))))))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) N_1))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1)))))))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N_1) K))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))))))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 I_1) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.zero_zero tptp.nat)) K_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_4)))))))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K_4))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I_1) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.zero_zero tptp.nat)) K_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 I_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 J_2))))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (= M (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N)) (or (= N (tptp.one_one tptp.nat)) (= M (tptp.zero_zero tptp.nat))))) (forall ((Ma $$unsorted) (Ta $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) K))) (let ((_let_2 (tptp.dvd_dvd tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (not (= (tptp.ti tptp.int K) (tptp.zero_zero tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Ma) Ta)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 Ma)) (tptp.hAPP tptp.int tptp.int _let_1 Ta))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.dvd X_a) (tptp.semiring_0 X_a)) (forall ((P_1 $$unsorted) (L $$unsorted)) (= (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) L) X_2)))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) L) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X_2) (tptp.zero_zero X_a)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_258 _let_245)) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1)))))))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N_1) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) _let_1) N))) (or (= _let_2 (tptp.one_one tptp.int)) (= _let_2 _let_1))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legendre A_1) P_5))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 tptp.quadRes P_5) A_1)))) (let ((_let_4 (tptp.zero_zero tptp.int))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong A_1) _let_4) P_5)))) (and (=> _let_5 (= _let_1 _let_4)) (=> (not _let_5) (and (=> _let_3 (= _let_1 (tptp.one_one tptp.int))) (=> (not _let_3) (= _let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)))))))))))) (forall ((Ma $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) tptp.quadRes Ma) X_1)) (exists ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) Y_2) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) X_1) Ma)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_5 (tptp.power_power tptp.real))) (let ((_let_6 (tptp.fun tptp.nat tptp.real))) (let ((_let_7 (tptp.plus_plus tptp.real))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_7 X) Y)) _let_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_7 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_6 _let_5 X) _let_4)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_6 _let_5 Y) _let_4))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1)) X)) Y))))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) N) M)) (or (= M (tptp.zero_zero tptp.nat)) (= M N) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)) M)))))) (forall ((K $$unsorted) (P_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) D_1)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_2) D_1))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) K)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K) D_1))))))))))))) (forall ((N_1 $$unsorted) (P_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_1)) (exists ((K_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) K_1) N_1)) (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) K_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_1) (tptp.one_one tptp.nat))))))))) (forall ((K $$unsorted) (P_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) D_1)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) D_1))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) K)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K) D_1))))))))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 X_1) _let_2)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 Y_1) _let_2)) _let_1) (and (= X_1 _let_1) (= Y_1 _let_1)))))))) (forall ((A_1 $$unsorted) (M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) M)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) X_2) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_1) X_2) M)) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Y_2) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_1) Y_2) M))) (= (tptp.ti tptp.int Y_2) (tptp.ti tptp.int X_2)))))))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X) X))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X_1) Y_1)) (tptp.zero_zero tptp.real))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X) X)))) (not (and _let_1 (not _let_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (= X_1 Y_1) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X_1))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1)))) (= _let_3 (or (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X_1)))) (= X_1 Y_1))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1)))) (= (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X_1)))) (and _let_3 (not (= X_1 Y_1)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X_1)))))) (= _let_3 _let_3))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X_1))) (= X_1 Y_1))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B)))) (=> (not (= A_1 B)) (=> _let_3 (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) A_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X) Y)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1)) (= X_1 Y_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (=> _let_3 (or (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (= X Y))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B)))) (=> _let_3 (=> (not (= A_1 B)) (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) A_1)))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (= A_1 B) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B)) (=> (= B C) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 C)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) M)) (= M N)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)) (= X Y)))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Z_1)))))))) (forall ((N $$unsorted) (K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 C))) (=> (= A_1 B) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) C)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 B)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 A_1)))))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 Z_1))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Y)) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) Z_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Z_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 X))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (not (= X Y)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (=> (and _let_3 (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) _let_3))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (not (= X Y)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (not (= Y X)))))) (forall ((P_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X_1)))) (=> (and _let_3 (not _let_4)) (=> (and _let_4 (not _let_3)) (tptp.hBOOL P_1)))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 A_1))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 B)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) A_1)))) (=> (= B C) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 C)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 C) A_1)))))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 X)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Z_1)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Z_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Z_1) X))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) A_1)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 Z_1))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Y)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 X)))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 Z_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Y)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 Z_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 X)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y) X)))) (=> (and _let_3 (not _let_4)) (not (and _let_4 (not _let_3))))))))) (not (= _let_37 _let_136)) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Z_1) W)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 W) Z_1)) (= Z_1 W)))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 J_2) K_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 K_4)))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) Z_1))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 Y)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) X_1) Y_1)) (or (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) X_1) Y_1)) (= X_1 Y_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) X_1) Y_1)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) X_1) Y_1)) (not (= X_1 Y_1)))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (or (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Z_1) W)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 W) Z_1)))))) (forall ((W $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) W) W))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 M) N) _let_1) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 N) M) _let_1) (= M N))))))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) M) (tptp.zero_zero tptp.nat))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) (tptp.zero_zero tptp.nat)) M)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_1) N) _let_1))) (forall ((L_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L_4))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 L_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))))))) (forall ((N $$unsorted) (J_2 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) J_2) N)) K_4)))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 N) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) K_4))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 _let_2 I_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_3 J_2)) K_4) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) J_2) K_4))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M)) N) M))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M) N)) N) M))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) M))) (forall ((L_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) L_4))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (tptp.hAPP tptp.nat tptp.nat _let_1 M)))))))) (forall ((L_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) L_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) L_4))))))))) (forall ((I_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) N)) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat _let_1 I_1)) I_1)))) (forall ((N_1 $$unsorted) (K $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N_1)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Ma) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K)) (= Ma N_1)))))))) (forall ((N $$unsorted) (K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_4)) (tptp.hAPP tptp.nat tptp.nat _let_3 N))))))))) (forall ((N_1 $$unsorted) (K $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 _let_1 K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N_1) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))))))))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) N) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M)))))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) N) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N)))))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) N)) K_4) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_4))))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K_4))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 M) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) M)))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) Ma))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M)) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N) (tptp.zero_zero tptp.nat)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) Ma) N_1) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) N_1)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) M)))) (forall ((I $$unsorted) (J $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I) K)) J))))))) (forall ((N_1 $$unsorted) (K $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_5 N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N_1) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 (tptp.ord_less_eq tptp.nat) C) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) C)))))))))) (forall ((I_1 $$unsorted) (K_4 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_4) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J_2) I_1)) K_4) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_4)) I_1))))))) (forall ((I_1 $$unsorted) (K_4 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_4) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J_2) K_4)) I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) I_1)) K_4))))))) (forall ((I_1 $$unsorted) (K_4 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_4) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J_2)) K_4) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_4)))))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J) I) K) (= J (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) K) I)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) N) M)))) (forall ((I $$unsorted) (K $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K) J)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 I) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J) K))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I) K)) J)))))))) (forall ((I_1 $$unsorted) (K_4 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_4) J_2)) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 J_2) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 J_2)) K_4))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) M)))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 K_4) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) M)) K_4)))))))) (forall ((J $$unsorted) (K $$unsorted) (I $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J) K)) I)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 J) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I) K)))))))) (forall ((I_1 $$unsorted) (K_4 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_4) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_2) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) I_1) K_4)) J_2)))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) A_2) B_1))) (and (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) A_2) B_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat)))) (forall ((D_3 $$unsorted)) (=> (= A_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) B_1) D_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 D_3))))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) A_2) B_1))) (not (or (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) A_2) B_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat))))) (exists ((D_3 $$unsorted)) (and (= A_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) B_1) D_3)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 D_3))))))))) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) D))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B)))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.one_one tptp.real)) Z_1) Z_1)) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 Z_1) W) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 W) Z_1))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (Z3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 Z1))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 Z2)) Z3) (tptp.hAPP tptp.real tptp.real _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 Z2) Z3))))))) (forall ((Z1 $$unsorted) (Z2 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.plus_plus tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_3 Z1) Z2)) W) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 Z1) W)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 Z2) W))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X_1) X_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y_1) Y_1)) _let_1) (and (= X_1 _let_1) (= Y_1 _let_1))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (not (= C_1 (tptp.zero_zero tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 A_2) C_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 B_1) C_1)) (= A_2 B_1)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) C_1))) (=> (not (= C_1 (tptp.zero_zero tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real _let_1 A_2) (tptp.hAPP tptp.real tptp.real _let_1 B_1)) (= A_2 B_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.times_times tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) Z)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 X_1) Z)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 Y_1) Z))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) X) Y))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) Z_1))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) Z_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 Y))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) Z))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Z)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 X_1)) (tptp.hAPP tptp.real tptp.real _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.times_times tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Z)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 X_1) Z)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 Y_1) Z))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) C))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 A_1)) (tptp.hAPP tptp.nat tptp.nat _let_1 B)))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.dvd_dvd tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat)))) X) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.power_power tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.dvd_dvd tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 X) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Y) N))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N))) (let ((_let_4 (tptp.zero_zero tptp.nat))) (let ((_let_5 (= M _let_4))) (and (=> _let_5 (= _let_3 _let_4)) (=> (not _let_5) (= _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) (tptp.one_one tptp.nat))) N))))))))))) (forall ((P_5 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.power_power tptp.nat) P_5))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 M))) (let ((_let_5 (= M (tptp.zero_zero tptp.nat)))) (and (=> _let_5 (= _let_4 _let_1)) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) P_5) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) M) _let_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_4 (tptp.power_power tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 X) _let_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 Y) _let_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) X) Y)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 X) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) D)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) A_1) B)) (or (= B (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) A_1) B)))))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N_1) K))) (or (= K (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) N_1) Ma) _let_1) (and (= N_1 _let_1) (= Ma _let_1))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) Ma) N_1) _let_1) (and (not (= N_1 _let_1)) (= Ma _let_1))))) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.power_power tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 A_1) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 B) N))) (=> (not (= N (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (not (= N (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X) N)) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((X $$unsorted) (Y $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_3 X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_4 Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) B))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) A_1)) B)))))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X_1) N_1) _let_1) (or (= X_1 _let_1) (= N_1 (tptp.zero_zero tptp.nat)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.minus_minus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_4 X) X)) _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.plus_plus X_a) X) _let_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 X) _let_1)))))))))) (forall ((X $$unsorted) (Q_3 $$unsorted) (N $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (= X (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.times_times tptp.nat) Q_3) N)) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.zero_zero tptp.nat)) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 R_4) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) N) X)))))))))) (forall ((A_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) A_1)) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_2)) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X_2) N) A_1) (forall ((Y_2 $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Y_2)) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) Y_2) N) A_1)) (= Y_2 X_2)))))))) (forall ((A_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) A_1)) (exists ((R_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) R_2) N) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.power X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) M))) (let ((_let_2 (tptp.hAPP tptp.nat X_a _let_1 N))) (let ((_let_3 (= N (tptp.zero_zero tptp.nat)))) (and (=> _let_3 (= _let_2 (tptp.one_one X_a))) (=> (not _let_3) (= _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) M) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))))))))))))) (= (tptp.hAPP _let_141 tptp.int tptp.twoSqu1094008024sum2sq (tptp.hAPP tptp.int _let_141 (tptp.hAPP tptp.int _let_198 _let_197 tptp.s) _let_2)) _let_263) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) B) (tptp.one_one tptp.int)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_1) B))))) (forall ((U_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (J $$unsorted) (I $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less_eq tptp.nat) J) I)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I) U_1)) Ma)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) U_1)) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) I) J)) U_1)) Ma)) N_1)))))))))) (forall ((U_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less_eq tptp.nat) I) J)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I) U_1)) Ma)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) U_1)) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J) I)) U_1)) N_1))))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1)))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1)))))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 I_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 J_2)) K_4) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 K_4)) J_2)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 B))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 _let_1 A_1))) (let ((_let_5 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_6 (tptp.product_prod tptp.int tptp.int))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP _let_6 tptp.int tptp.twoSqu1094008024sum2sq (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 _let_5 A_1) B))) (tptp.hAPP _let_6 tptp.int tptp.twoSqu1094008024sum2sq (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 _let_5 P_5) Q_3))) (tptp.hAPP _let_6 tptp.int tptp.twoSqu1094008024sum2sq (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int _let_4 P_5)) (tptp.hAPP tptp.int tptp.int _let_3 Q_3))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) (tptp.hAPP tptp.int tptp.int _let_4 Q_3)) (tptp.hAPP tptp.int tptp.int _let_3 P_5))))))))))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (or (= K (tptp.zero_zero tptp.nat)) (= Ma N_1))))) (forall ((I_1 $$unsorted) (U $$unsorted) (J_2 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.times_times tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 I_1) U)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J_2) U)) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_2)) U)) K_4)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (= Ma N_1))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1)))))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (or (= K (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1)))))))) (forall ((U_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I) U_1)) Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) U_1)) N_1)) (= Ma (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J) I)) U_1)) N_1)))))))) (forall ((U $$unsorted) (M $$unsorted) (N $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_1) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 I_1) U)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J_2) U)) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J_2) I_1)) U)) N))))))))) (forall ((U_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less_eq tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 I) J)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I) U_1)) Ma)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) U_1)) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) J) I)) U_1)) N_1))))))))))) (forall ((U_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (J $$unsorted) (I $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J) I)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I) U_1)) Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) U_1)) N_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) I) J)) U_1)) Ma) N_1))))))) (forall ((U $$unsorted) (M $$unsorted) (N $$unsorted) (J_2 $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.times_times tptp.nat))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) J_2) I_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 I_1) U)) M)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 J_2) U)) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_2)) U)) M)) N)))))))) (forall ((U_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted) (J $$unsorted) (I $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.ord_less_eq tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 J) I)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 I) U_1)) Ma)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J) U_1)) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) I) J)) U_1)) Ma)) N_1)))))))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.twoSqu1091635170sum2sq X_1)) (exists ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP _let_1 tptp.int tptp.twoSqu1094008024sum2sq (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) A_4) B_4)) (tptp.ti tptp.int X_1)))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong (tptp.hAPP tptp.int tptp.int tptp.zfact (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_5) (tptp.one_one tptp.int)))) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)) P_5))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.inv P_5))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_1) P_5)) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int _let_1 A_1)) (tptp.ti tptp.int A_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.zero X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ti X_a X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) A_1)) (= (tptp.ti X_a B) (tptp.ti X_a C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel146912293up_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1))) (=> (= (tptp.hAPP X_a X_a _let_1 B) (tptp.hAPP X_a X_a _let_1 C)) (= (tptp.ti X_a B) (tptp.ti X_a C))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C_1) A_2)) (= (tptp.ti X_a B_1) (tptp.ti X_a C_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.cancel_semigroup_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2))) (= (= (tptp.hAPP X_a X_a _let_1 B_1) (tptp.hAPP X_a X_a _let_1 C_1)) (= (tptp.ti X_a B_1) (tptp.ti X_a C_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_semigroup_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.one X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ti X_a X_1))) (= (= _let_1 _let_2) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C_1) D_1)) (= (= (tptp.ti X_a A_2) (tptp.ti X_a B_1)) (= (tptp.ti X_a C_1) (tptp.ti X_a D_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) A_2)) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.zero_zero X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere779506340up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_2)) (tptp.hAPP X_a X_a _let_3 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_2) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B_1) C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) C))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) C_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_2)) (tptp.hAPP X_a X_a _let_3 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_2) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B_1) C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_2) B_1) (tptp.zero_zero X_a)) (= (tptp.ti X_a A_2) (tptp.ti X_a B_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (= (tptp.ti X_a A_2) (tptp.ti X_a B_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_2) B_1) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) A_1) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_2) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 C_1) D_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) D_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_2) B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 C_1) D_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) D_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.one_one X_a)) A_1) (tptp.ti X_a A_1))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_5) _let_1))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 A_1) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.inv P_5) A_1)) _let_3))))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 _let_3 _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) P_5) _let_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.inv P_5) A_1)))))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_5) _let_1))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 A_1) _let_3)) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.inv P_5) A_1) _let_3))))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_5) _let_1))) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.inv P_5) A_1) _let_1)))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) P_5) _let_2))) (not (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.inv P_5) A_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) B)) B) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) B)) B) (tptp.ti X_a A_1)))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) P_5) _let_2))) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.inv P_5) A_1) (tptp.zero_zero tptp.int))))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 A_1) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.inv P_5) A_1))) (tptp.one_one tptp.int)) P_5))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (C $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) C))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y_1)) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X_1) Y_1) _let_1) (and (= (tptp.ti X_a X_1) _let_1) (= (tptp.ti X_a Y_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere216010020id_add X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere223160158up_add X_a) (forall ((C $$unsorted) (D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) C) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_2) B_1)) (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_2) B_1)) (tptp.zero_zero X_a))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int tptp.zfact N))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) N) (tptp.zero_zero tptp.int))))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) N) (tptp.hAPP tptp.int tptp.int tptp.zfact (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) N) _let_1))))))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.wset A_2) P_4))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.member tptp.int))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.minus_minus tptp.int) P_4) (tptp.one_one tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 B_1) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.inv P_4) B_1)) _let_2)))))))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.wset A_2) P_4))) (let ((_let_3 (tptp.member tptp.int))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (let ((_let_6 (tptp.one_one tptp.int))) (let ((_let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.minus_minus tptp.int) P_4) _let_6))) (let ((_let_8 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_8 A_2) _let_7)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_8 _let_6) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_8 B_1) _let_7)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 tptp.inv P_4) B_1)) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 B_1) _let_2))))))))))))))))) (forall ((J_2 $$unsorted) (A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.hAPP tptp.int _let_3 tptp.zcong J_2))) (let ((_let_5 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong A_1) _let_5) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_5) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 tptp.quadRes P_5) A_1))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.multInv P_5) J_2))) P_5)))))))))))))) (forall ((P_1 $$unsorted) (I $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 K)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I_2) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I)))))) (forall ((X_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_4 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) A_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) A_4) _let_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 A_4))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_1)))) (forall ((P_1 $$unsorted) (I $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K) (tptp.one_one tptp.int)))) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I_2) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I)))))) (forall ((P_1 $$unsorted) (K $$unsorted) (I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K) I)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 K)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K) I_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I)))))) (forall ((J_2 $$unsorted) (A_1 $$unsorted) (P_5 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.times_times tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.multInv P_5) K_4)))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong J_2) _let_3) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 J_2) K_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 _let_3) K_4)) P_5))))))))) (forall ((J_2 $$unsorted) (K_4 $$unsorted) (A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.times_times tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.multInv P_5) J_2)))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 J_2) K_4)) A_1) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int _let_3 J_2)) K_4)) (tptp.hAPP tptp.int tptp.int _let_3 A_1)) P_5))))))))) (forall ((P_4 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) A_2) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.wset A_2) P_4)))))) (forall ((B_1 $$unsorted) (P_4 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1))) (let ((_let_4 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) _let_4) A_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.wset (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) A_2) _let_4)) P_4))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.wset A_2) P_4)))))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_4) _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_3 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.wset A_2) P_4))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) B_1))))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_4) (tptp.one_one tptp.int)))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_3 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.wset A_2) P_4))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 B_1) _let_1))))))))) (forall ((B_1 $$unsorted) (P_4 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.ti tptp.int B_1))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.hAPP tptp.int (tptp.fun _let_3 tptp.bool) (tptp.member tptp.int) B_1))) (let ((_let_6 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_6) A_2)) (=> (not (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.wset (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) A_2) _let_6)) P_4)))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.wset A_2) P_4))) (or (= _let_2 (tptp.ti tptp.int A_2)) (= _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.inv P_4) A_2))))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.multInv P_5))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong X) Y) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP tptp.int tptp.int _let_1 X)) (tptp.hAPP tptp.int tptp.int _let_1 Y)) P_5)))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 A_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_4) _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 _let_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_1) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.wset A_2) P_4))))))))))) (forall ((A_1 $$unsorted) (J_2 $$unsorted) (K_4 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.multInv P_5))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) A_1))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong J_2) K_4) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_2 J_2))) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_2 K_4))) P_5)))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong X) _let_1) P_5))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.multInv P_5) X)) _let_1) P_5)))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.multInv P_5))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong X) (tptp.zero_zero tptp.int)) P_5))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int _let_1 X))) X) P_5))))))))) (forall ((Y $$unsorted) (X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 tptp.zcong X))) (let ((_let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.multInv P_5))) (let ((_let_5 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 _let_5) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong Y) _let_5) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong (tptp.hAPP tptp.int tptp.int _let_4 X)) (tptp.hAPP tptp.int tptp.int _let_4 Y)) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 Y) P_5))))))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.multInv P_5))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_2 X))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int _let_2 _let_3))) (let ((_let_5 (tptp.times_times tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 tptp.zcong X) (tptp.zero_zero tptp.int)) P_5))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 tptp.zcong _let_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_5 X) _let_3)) _let_4)) P_5))))))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.multInv P_5))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_2 X))) (let ((_let_4 (tptp.times_times tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 tptp.zcong X) (tptp.zero_zero tptp.int)) P_5))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_4 X) _let_3)) (tptp.hAPP tptp.int tptp.int _let_2 _let_3))) X) P_5)))))))))))) (forall ((J_2 $$unsorted) (K_4 $$unsorted) (A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 tptp.zcong J_2))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 tptp.multInv P_5))) (let ((_let_6 (tptp.hAPP tptp.int _let_4 (tptp.times_times tptp.int) A_1))) (let ((_let_7 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong A_1) _let_7) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong K_4) _let_7) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 _let_7) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong (tptp.hAPP tptp.int tptp.int _let_6 (tptp.hAPP tptp.int tptp.int _let_5 J_2))) (tptp.hAPP tptp.int tptp.int _let_6 (tptp.hAPP tptp.int tptp.int _let_5 K_4))) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_3 K_4) P_5)))))))))))))))) (forall ((A_1 $$unsorted) (J_2 $$unsorted) (K_4 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.multInv P_5))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) A_1))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.hAPP tptp.int _let_5 tptp.zcong K_4))) (let ((_let_7 (tptp.hAPP tptp.int _let_5 tptp.zcong J_2))) (let ((_let_8 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_6 _let_8) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_7 _let_8) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_7 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_2 K_4))) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_2 J_2))) P_5)))))))))))))))) (forall ((J_2 $$unsorted) (A_1 $$unsorted) (K_4 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 J_2) K_4)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong K_4) (tptp.zero_zero tptp.int)) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.multInv P_5) K_4))) K_4)) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 A_1) P_5)))))))))))) (forall ((K_4 $$unsorted) (A_1 $$unsorted) (J_2 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.multInv P_5) J_2))) (let ((_let_3 (tptp.times_times tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.hAPP tptp.int _let_1 _let_3 _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong J_2) (tptp.zero_zero tptp.int)) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_6 J_2)) K_4)) (tptp.hAPP tptp.int tptp.int _let_6 A_1)) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong K_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 A_1) _let_2)) P_5))))))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong X) (tptp.zero_zero tptp.int)) P_5))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.multInv P_5) X))) (tptp.one_one tptp.int)) P_5))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong X) (tptp.zero_zero tptp.int)) P_5))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.multInv P_5) X)) X)) (tptp.one_one tptp.int)) P_5))))))))) (forall ((P_1 $$unsorted) (K $$unsorted) (I $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K) I)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K) (tptp.one_one tptp.int)))) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K) I_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I)))))) (forall ((Ma $$unsorted) (K $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F M_2)) (tptp.hAPP tptp.nat tptp.nat F N_2))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F Ma)) K)) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Ma) K)))))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_4) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (= (tptp.hAPP tptp.int _let_2 tptp.d22set _let_1) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.wset _let_1) P_4)))))) (forall ((N_1 $$unsorted) (P_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_1)) (exists ((K_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) N_1)) (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) K_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 K_1))))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) J_2)) (exists ((K_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_1) K_1) J_2))))) (forall ((X_a $$unsorted)) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (forall ((D_1 $$unsorted) (Sa $$unsorted)) (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.dvd_dvd X_a) D_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z_2)) (= _let_2 _let_2))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (forall ((D_1 $$unsorted) (Sa $$unsorted)) (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.dvd_dvd X_a) D_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X_2) Sa)))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_2) X_2)) (= _let_2 _let_2))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (forall ((D_1 $$unsorted) (Sa $$unsorted)) (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.dvd_dvd X_a) D_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z_2)) (= _let_2 _let_2))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_2) B_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_1 tptp.d22set A_2))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_1 tptp.d22set A_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_1) A_2))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_1 tptp.d22set A_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) B_1))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_1) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_1 tptp.d22set A_2))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.plus X_a) (tptp.linorder X_a) (tptp.dvd X_a)) (forall ((D_1 $$unsorted) (Sa $$unsorted)) (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.dvd_dvd X_a) D_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X_2) Sa))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_2) X_2)) (= _let_2 _let_2))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.power_power tptp.int))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (=> (not (= N_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 A_2) N_1)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 B_1) N_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_2) B_1))))))))) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.power_power tptp.int))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 A_1) N)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 B) N))) (=> (not (= N (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_1) B))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.power_power tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (not (= N_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 A_2) N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 B_1) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_2) B_1))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) M) N)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (= N (tptp.zero_zero tptp.nat)))))) (forall ((N $$unsorted) (M $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_4)) (=> (= (tptp.hAPP tptp.nat tptp.nat _let_1 N) (tptp.hAPP tptp.nat tptp.nat _let_1 M)) (= N M))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X $$unsorted) (Y $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) B))) (let ((_let_4 (tptp.times_times X_a))) (let ((_let_5 (tptp.hAPP X_a _let_2 _let_4 A_1))) (let ((_let_6 (tptp.hAPP X_a _let_2 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) A_1)))) (let ((_let_7 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 X) Y)) (tptp.hAPP X_a X_a _let_5 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_7 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_7 (tptp.hAPP X_a X_a _let_6 _let_3)) (tptp.hAPP X_a X_a _let_6 B))) (tptp.hAPP X_a X_a _let_5 _let_3))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((B $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) _let_1) B) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) _let_1) Y) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (B_5 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 B) B_5)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 B_5))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Xa_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Xa_1))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 X)) (tptp.hAPP X_a X_a _let_2 Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (A_6 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) A_6)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_6) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X $$unsorted) (Y $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Ya) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Ya)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Ya))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X $$unsorted) (Y $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Ya) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Ya)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Ya))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (A_6 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) A_6)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_6) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Xa_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Xa_1))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 X)) (tptp.hAPP X_a X_a _let_2 Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (B_5 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 B) B_5)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 B_5))))))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (not (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) A_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_1) _let_1))))))))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) A_1) (tptp.zero_zero tptp.nat)))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (not (= A_2 _let_1)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_2) _let_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) A_2))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) _let_1) A_2)) (= A_2 _let_1)))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) _let_1) A_1)) (= A_1 _let_1)))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (not (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_1) _let_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) A_1))))))))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.one_one tptp.nat)) A_1))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (not (= A_2 _let_1)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) A_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_2) _let_1))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) A_2) _let_1)) (= A_2 _let_1)))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) A_1) _let_1)) (= A_1 _let_1)))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.hAPP tptp.int _let_1 tptp.sr P_4) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_1) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.int tptp.int tptp.bool) (tptp.ord_less tptp.int)) P_4))))))))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.number_number_of tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_2 W))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int _let_2 V))) (let ((_let_5 (tptp.plus_plus tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.div_mod tptp.int))) (let ((_let_8 (tptp.hAPP tptp.int _let_6 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_9 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit1 V))) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 W))))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) _let_3)))) (and (=> _let_10 (= _let_9 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 (tptp.hAPP tptp.int tptp.int _let_8 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 _let_4) _let_3))) _let_1))) (=> (not _let_10) (= _let_9 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 (tptp.minus_minus tptp.int) (tptp.hAPP tptp.int tptp.int _let_8 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 _let_4) _let_1)) _let_3))) _let_1))))))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.div_mod tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) A_1) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 _let_1) (tptp.hAPP tptp.int tptp.int _let_5 B))) (tptp.hAPP tptp.int tptp.int _let_5 A_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.minus_minus tptp.int) (tptp.hAPP tptp.int tptp.int _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 B) _let_1)) A_1))) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 tptp.standardRes M))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 X)) (tptp.hAPP tptp.int tptp.int _let_3 Y))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 X) Y)) M)))))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 W))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.one_one tptp.int))) (let ((_let_5 (tptp.product_prod tptp.int tptp.int))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.hAPP tptp.int _let_6 tptp.negDivAlg _let_4))) (let ((_let_8 (tptp.hAPP tptp.int _let_5 _let_7 _let_2))) (let ((_let_9 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.plus_plus tptp.int) _let_4) _let_2))) (let ((_let_10 (tptp.zero_zero tptp.int))) (let ((_let_11 (tptp.fun tptp.int tptp.bool))) (let ((_let_12 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_11 (tptp.ord_less_eq tptp.int) _let_10) _let_9)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_11 (tptp.ord_less tptp.int) _let_10) _let_2)) (and (=> _let_12 (= _let_8 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 tptp.min_1)) _let_9))) (=> (not _let_12) (= _let_8 (tptp.hAPP _let_5 _let_5 (tptp.hAPP tptp.int (tptp.fun _let_5 _let_5) tptp.adjust _let_2) (tptp.hAPP tptp.int _let_5 _let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) _let_2)))))))))))))))))))) (forall ((X_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.ti tptp.int X_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) K)) (tptp.one_one tptp.int))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) tptp.zOdd)))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.one_one tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) A_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int _let_3 B))) (tptp.hAPP tptp.int tptp.int _let_3 A_1)) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) A_1)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.div_div tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) A_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.one_one tptp.int)) (tptp.hAPP tptp.int tptp.int _let_3 B))) (tptp.hAPP tptp.int tptp.int _let_3 A_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 _let_3) B) _let_3))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) A_1) B)) B) (tptp.zero_zero tptp.int)))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (and (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) A_1) _let_1) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_mod tptp.int) A_1) _let_1) (tptp.ti tptp.int A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_mod X_a) A_1) B)) B) (tptp.zero_zero X_a)))))) (forall ((X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) (tptp.hAPP tptp.int _let_1 tptp.sr P_4))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes P_4) X_1) (tptp.ti tptp.int X_1))))) (forall ((M $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.standardRes M) X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) X) M)))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.plus_plus tptp.int))) (let ((_let_4 (tptp.div_div tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 A_1) B)) C) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 A_1) C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 B) C))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) C))) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_mod X_a) A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) A_1) B)) B)) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) A_1) B))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_mod X_a) A_1) B)) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) A_1) B)) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_mod X_a) A_1) B)) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.times_times X_a) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.div_div X_a) A_1) B))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.div_mod X_a) A_1) B))) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.div_div X_a) A_1) B)) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.div_mod X_a) A_1) B))) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) B) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) A_1) B))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) A_1) B))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) A_1))) (let ((_let_3 (tptp.div_div tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 B)) C) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 B) C))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) B) C))) C))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) B) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) A_1) B))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_mod tptp.int) A_1) B))) K_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) K_4))))) (forall ((A_1 $$unsorted) (B $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) A_1) B)) B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_mod tptp.int) A_1) B))) K_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) K_4))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) M) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) M) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) M) N)) N))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) M) N)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) M) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) M) N))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) A_1) A_1) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) A_1) (tptp.zero_zero X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) _let_1) A_1) _let_1))))) (forall ((L_4 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.zero_zero tptp.int))) (let ((_let_5 (tptp.ord_less tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 _let_5 K_4) _let_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 _let_5 _let_4) L_4)) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.negDivAlg K_4) L_4) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) K_4) L_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) K_4) L_4)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.times_times X_a) A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) B)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.times_times X_a) C))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.div_mod X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) C)) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (B_5 $$unsorted) (A_1 $$unsorted) (C $$unsorted) (A_6 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.div_mod X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_6) C)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B_5) C)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_6) B_5)) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (B_5 $$unsorted) (A_1 $$unsorted) (C $$unsorted) (A_6 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.div_mod X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_6) C)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B_5) C)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_6) B_5)) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.div_mod X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) C)) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1))) (let ((_let_3 (tptp.div_mod X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 B) C))) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 B)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) B)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) B) A_1)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) A_1) B)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((B $$unsorted) (B_5 $$unsorted) (A_1 $$unsorted) (C $$unsorted) (A_6 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.div_mod X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_6) C)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B_5) C)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_6) B_5)) C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) B)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.minus_minus X_a) A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) K))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) Ma) N_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Ma)))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) C) B)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((N $$unsorted) (K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) K_4))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) M) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) K_4))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) M) N))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 M)))))))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) _let_1) B) _let_1))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) A_1) (tptp.zero_zero tptp.int))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) _let_1) B) _let_1))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) A_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 B)) C) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) C))) C)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) A_1))) (let ((_let_3 (tptp.div_mod tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 B) C))) C) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 B)) C)))))) (forall ((X $$unsorted) (M $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.div_mod tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 X) M)) Y)) M) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 X) Y)) M)))))) (forall ((X $$unsorted) (Y $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X))) (let ((_let_3 (tptp.div_mod tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 Y) M))) M) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 Y)) M)))))) (forall ((X $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) X) M)) M)))) (forall ((X $$unsorted) (M $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.div_mod tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 X) M) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 Y) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong X) Y) M))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong A_2) B_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_2) Ma)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B_1) Ma)) Ma)))))))) (forall ((N $$unsorted) (F_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) F_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) M) N))))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) M) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)))))) (forall ((X $$unsorted) (M $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int))) (let ((_let_2 (tptp.fun tptp.nat tptp.int))) (let ((_let_3 (tptp.div_mod tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_3 X) M)) Y)) M) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 X) Y)) M))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_div X_a) A_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_div X_a) _let_1) A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_div X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.div_div X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.hAPP X_a _let_2 _let_1 A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B_1) A_2)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 C_1) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) C_1))))))))))))) (forall ((R_4 $$unsorted) (S_3 $$unsorted) (T_5 $$unsorted) (R_5 $$unsorted) (S_4 $$unsorted) (M $$unsorted) (T_6 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.times_times tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) R_5) R_4)))) (let ((_let_4 (tptp.minus_minus tptp.int))) (let ((_let_5 (tptp.plus_plus tptp.int))) (=> (= (tptp.ti tptp.int R_5) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 S_4) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 T_6) N))) (=> (= (tptp.ti tptp.int R_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 S_3) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 T_5) N))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) R_5) R_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_4 S_4) (tptp.hAPP tptp.int tptp.int _let_3 S_3))) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_4 T_6) (tptp.hAPP tptp.int tptp.int _let_3 T_5))) N))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.minus_minus tptp.int))) (let ((_let_4 (tptp.div_div tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 A_1) B) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) M) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 A_1) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 B) M)))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) M))))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 Y_1) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X_1) Y_1)) tptp.zOdd)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X_1) Y_1)) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zOdd))))))) (forall ((X $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes M) X)) M)))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_mod X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) B) A_1)) B) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_mod X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) B)) B) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) A_1) (tptp.one_one X_a)) (tptp.zero_zero X_a))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 A_1))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) B))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) C)) (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_4 C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) A_1) B)) C))) (tptp.hAPP tptp.int tptp.int _let_3 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.times_times X_a) C) B))) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.times_times X_a) B) C))) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) B)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) B) A_1) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_2) B_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) B_1) A_2) (tptp.zero_zero X_a)))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B)) _let_1)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 B_1) _let_1)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_2) B_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) A_2)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_2) B_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_2) _let_1)))))))) (forall ((A_1 $$unsorted)) (=> (not (= (tptp.ti tptp.int A_1) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) A_1) (tptp.one_one tptp.int)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) X) Y))))))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.div_div tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 V))) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 V)) (tptp.hAPP tptp.int tptp.int _let_1 W))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) B))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B)) B)))))) (forall ((K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) M) K_4)) M)))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) X) Y))))))) (forall ((Ma $$unsorted) (D_1 $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) Ma) D_1) (tptp.zero_zero tptp.int)) (exists ((Q_4 $$unsorted)) (= (tptp.ti tptp.int Ma) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) D_1) Q_4))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) N) M)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) M) N)) (tptp.ti tptp.int M))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.div_mod tptp.int))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 X_1) N_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 Y_1) N_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) N_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_1) Y_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.times_times X_a) C))) (=> (not (= (tptp.ti X_a C) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (=> (not (= (tptp.ti X_a C) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) B) A_1)) B) (tptp.ti X_a A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) B)) B) (tptp.ti X_a A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.times_times X_a) C))) (let ((_let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)))) (let ((_let_5 (tptp.zero_zero X_a))) (let ((_let_6 (= (tptp.ti X_a C) _let_5))) (and (=> _let_6 (= _let_4 _let_5)) (=> (not _let_6) (= _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted)) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_div X_a) A_1) A_1) (tptp.one_one X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((Z_1 $$unsorted) (W $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.div_div X_a))) (let ((_let_4 (tptp.dvd_dvd X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 Z_1) W)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 W) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.div_div X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) B)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) A_1)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) B)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) B) A_1)) A_1) (tptp.ti X_a B))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1))) (let ((_let_3 (tptp.div_div X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) C) B)) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 B) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 B)) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_1) B)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) B) A_1)) (tptp.ti X_a B))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((Y $$unsorted) (Z_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 Y)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((N $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.div_div X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) Y) X)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 X) Y)) N) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 Y) N))))))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) K) (tptp.zero_zero tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) N_1) K)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) N_1) K))) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) K) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) J_1) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int N_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) K) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 P_1 I_2) J_1))))))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) K)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) N_1) K)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) N_1) K))) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) J_1) K)) (= (tptp.ti tptp.int N_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) K) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 P_1 I_2) J_1))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.semiring_div X_a) (tptp.number X_a)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a _let_1 X_1))) (let ((_let_3 (tptp.hAPP tptp.int X_a _let_1 Y_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) _let_2) _let_3)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_mod X_a) _let_3) _let_2) (tptp.zero_zero X_a))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes P_5) X)) P_5)))))) (forall ((Ma $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes Ma) X_1) _let_1) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong X_1) _let_1) Ma)))))) (forall ((X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong X_1) _let_1) P_4))) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes P_4) X_1) _let_1)))))) (forall ((K_4 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.one_one tptp.int)) K_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) X) K_4)) X))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A_6 $$unsorted)) (let ((_let_1 (tptp.div_div tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less_eq tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) A_6)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) B) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_6) B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (A_6 $$unsorted)) (let ((_let_1 (tptp.div_div tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less_eq tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) A_6)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_6) B)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) B) A_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B) _let_1)))))) (forall ((B $$unsorted) (B_5 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.zero_zero tptp.int))) (let ((_let_5 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 A_1) _let_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 _let_4) B_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 B_5) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 B_5)) (tptp.hAPP tptp.int tptp.int _let_1 B)))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_1) _let_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B)) _let_1)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) B_1) _let_1)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_2) _let_1)))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) A_1) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B) _let_1)))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) B) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B)) _let_1)))))))) (forall ((B $$unsorted) (B_5 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_4) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_4) B_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 B_5) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 B)) (tptp.hAPP tptp.int tptp.int _let_1 B_5))))))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1))) (let ((_let_4 (tptp.ord_less_eq tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_1) A_2)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_2) B_1))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 B_1) A_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 B_1)))))))))) (forall ((I $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 K)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) I) K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K) I))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 A_2)))))))) (forall ((I $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less_eq tptp.int))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) I) K) _let_3) (or (= (tptp.ti tptp.int K) _let_3) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 _let_3) I)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 I) K))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_4 I) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) I)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) Z_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) Y) Z_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) X) Z_1)) Y)))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_div tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) C)) (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) B) C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 B)) C))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) A_1) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) B) A_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B) (tptp.ti tptp.int A_1)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) B))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 _let_4)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) _let_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 _let_1))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) B) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B)) _let_1)))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_1) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B) (tptp.ti tptp.int A_1)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_4) B)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) _let_4) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) B))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.zcong A_2) B_1) Ma)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_2) Ma) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B_1) Ma)))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 A_1))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.dvd_dvd tptp.int) M) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 B)) M) (tptp.hAPP tptp.int tptp.int _let_3 M))))))))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)) (tptp.zero_zero tptp.int))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 X_1))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_1 Y_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) _let_2) _let_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) _let_3) _let_2) (tptp.zero_zero tptp.int))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.times_times X_a) C) B))) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.times_times X_a) B) C))) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) A_1)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.one_one X_a)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.one_one X_a)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((D_1 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.div_div X_a))) (let ((_let_4 (tptp.dvd_dvd X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_2) _let_6)) (=> (not (= (tptp.ti X_a C_1) _let_6)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 C_1) D_1)) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B_1) A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 D_1) C_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B_1) C_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) D_1)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((C_1 $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a A_2) (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) A_2) B_1)) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) B_1) A_2) (tptp.ti X_a C_1)) (= (tptp.ti X_a B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) C_1) A_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) X) Y))) X)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X_1) N_1)) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zOdd)))))))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) _let_1) B) _let_1)))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) A_1) B))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) _let_3) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) _let_2) _let_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) A_1) B) _let_2)))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes P_5) X))))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_1) P_4)) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_4 tptp.bool) (tptp.member tptp.int) P_4) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_4) (tptp.one_one tptp.int))) _let_1)))))))))) (forall ((X1_2 $$unsorted) (X2_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes Ma))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (= (= (tptp.hAPP tptp.int tptp.int _let_2 X1_2) (tptp.hAPP tptp.int tptp.int _let_2 X2_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong X1_2) X2_2) Ma))))))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.div_mod tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 V))) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 V)) (tptp.hAPP tptp.int tptp.int _let_1 W)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 (tptp.zero_zero tptp.int)) Z_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_3 X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) Y) Z_1)) Z_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) X) Z_1)) Y)))))))) (forall ((A_9 $$unsorted) (B_8 $$unsorted) (Y $$unsorted) (R_6 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.ord_less_eq tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.ord_less tptp.int))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 _let_2) B_8)))) (=> (= (tptp.ti tptp.int A_9) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) B_8) Y)) R_6)) (=> (and (=> _let_6 (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_2) R_6)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 R_6) B_8)))) (=> (not _let_6) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 B_8) R_6)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 R_6) _let_2))))) (=> (not (= (tptp.ti tptp.int B_8) _let_2)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) A_9) B_8) (tptp.ti tptp.int Y)))))))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) N_1) K))) (and (=> (= (tptp.ti tptp.int K) _let_1) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) K)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) J_1) K)) (= (tptp.ti tptp.int N_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 K) _let_1)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) K) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) J_1) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int N_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2))))))))))))) (forall ((A_9 $$unsorted) (B_8 $$unsorted) (Q_6 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.ord_less_eq tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.ord_less tptp.int))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 _let_2) B_8)))) (=> (= (tptp.ti tptp.int A_9) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) B_8) Q_6)) Y)) (=> (and (=> _let_6 (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_2) Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 Y) B_8)))) (=> (not _let_6) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 B_8) Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 Y) _let_2))))) (=> (not (= (tptp.ti tptp.int B_8) _let_2)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) A_9) B_8) (tptp.ti tptp.int Y)))))))))))) (forall ((Q_3 $$unsorted) (B $$unsorted) (R_4 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.ord_less_eq tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 _let_1) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_5 B) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 R_4) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) B) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_mod tptp.int) Q_3) C))) R_4)) _let_1))))))))))) (forall ((Q_3 $$unsorted) (B $$unsorted) (R_4 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) B))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_5) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 B) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) R_4) _let_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) Q_3) C))) R_4)))))))))))) (forall ((Q_3 $$unsorted) (B $$unsorted) (R_4 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) B))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_5) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) _let_5) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 R_4) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) Q_3) C))) R_4)) (tptp.hAPP tptp.int tptp.int _let_2 C)))))))))))) (forall ((Q_3 $$unsorted) (B $$unsorted) (R_4 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) _let_2))) (let ((_let_5 (tptp.ord_less tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 _let_2) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_5 R_4) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) B) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) Q_3) C))) R_4)))))))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) N_1) K))) (and (=> (= (tptp.ti tptp.int K) _let_1) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) K)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) J_1) K)) (= (tptp.ti tptp.int N_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 J_1))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 K) _let_1)) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) K) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) J_1) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int N_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K) I_2)) J_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 J_1))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) X_1) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (= (not (= _let_1 (tptp.zero_zero tptp.int))) (= _let_1 (tptp.one_one tptp.int))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) A_1) B)) _let_2)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) A_1) B) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)))))))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)) B) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) B) (tptp.one_one tptp.int)))))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 W))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_1 V))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.div_div tptp.int))) (let ((_let_6 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_5 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 V))) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W))))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) _let_2)))) (and (=> _let_7 (= _let_6 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_5 _let_3) _let_2))) (=> (not _let_7) (= _let_6 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.plus_plus tptp.int) _let_3) (tptp.one_one tptp.int))) _let_2)))))))))))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.negDivAlg _let_1) B) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 (tptp.product_Pair tptp.int tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) B) (tptp.one_one tptp.int)))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 tptp.negDivAlg A_1))) (let ((_let_6 (tptp.hAPP tptp.int _let_3 _let_5 B))) (let ((_let_7 (tptp.zero_zero tptp.int))) (let ((_let_8 (tptp.ord_less_eq tptp.int))) (let ((_let_9 (tptp.fun tptp.int tptp.bool))) (let ((_let_10 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) A_1) B))) (let ((_let_11 (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 _let_7) _let_10)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 B) _let_7))))) (and (=> _let_11 (= _let_6 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 tptp.min_1)) _let_10))) (=> (not _let_11) (= _let_6 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.int (tptp.fun _let_3 _let_3) tptp.adjust B) (tptp.hAPP tptp.int _let_3 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) B)))))))))))))))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) P_4) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)))))) (forall ((W $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 V))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int _let_1 W))) (let ((_let_5 (tptp.product_prod tptp.int tptp.int))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.hAPP tptp.int _let_6 tptp.negDivAlg _let_4))) (let ((_let_8 (tptp.hAPP tptp.int _let_5 _let_7 _let_2))) (let ((_let_9 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.plus_plus tptp.int) _let_4) _let_2))) (let ((_let_10 (tptp.zero_zero tptp.int))) (let ((_let_11 (tptp.fun tptp.int tptp.bool))) (let ((_let_12 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_11 (tptp.ord_less_eq tptp.int) _let_10) _let_9)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_11 (tptp.ord_less tptp.int) _let_10) _let_2)) (and (=> _let_12 (= _let_8 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 tptp.min_1)) _let_9))) (=> (not _let_12) (= _let_8 (tptp.hAPP _let_5 _let_5 (tptp.hAPP tptp.int (tptp.fun _let_5 _let_5) tptp.adjust _let_2) (tptp.hAPP tptp.int _let_5 _let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) _let_2)))))))))))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 tptp.negDivAlg A_1))) (let ((_let_6 (tptp.hAPP tptp.int _let_3 _let_5 B))) (let ((_let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) A_1) B))) (let ((_let_8 (tptp.zero_zero tptp.int))) (let ((_let_9 (tptp.fun tptp.int tptp.bool))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 (tptp.ord_less_eq tptp.int) _let_8) _let_7)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 (tptp.ord_less tptp.int) _let_8) B)) (and (=> _let_10 (= _let_6 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 tptp.min_1)) _let_7))) (=> (not _let_10) (= _let_6 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.int (tptp.fun _let_3 _let_3) tptp.adjust B) (tptp.hAPP tptp.int _let_3 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) B)))))))))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.div_div tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) A_1) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 _let_1) (tptp.hAPP tptp.int tptp.int _let_5 B))) (tptp.hAPP tptp.int tptp.int _let_5 A_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 B) _let_1)) A_1))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) tptp.zOdd)) (not (forall ((K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (not (= (tptp.ti tptp.int X_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) K_1)) (tptp.one_one tptp.int)))))))))) (forall ((X_1 $$unsorted) (A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.member tptp.int))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) (tptp.zero_zero tptp.int)) P_4))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 X_1) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.standardRes P_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) A_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.multInv P_4) X_1)))) _let_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.ti X_a A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_div X_a) A_1) B)) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.div_mod X_a) A_1) B))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_5) (tptp.one_one tptp.int)))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) _let_1) P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong A_1) (tptp.zero_zero tptp.int)) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 tptp.quadRes P_5) A_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP tptp.int tptp.int tptp.zfact _let_3)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) _let_3) _let_1)))) P_5)))))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) _let_2) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong X) (tptp.zero_zero tptp.int)) P_5))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 tptp.quadRes P_5) X))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.div_div tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.minus_minus tptp.int) P_5) (tptp.one_one tptp.int))) _let_2)))) (tptp.hAPP tptp.int tptp.int _let_1 tptp.min_1)) P_5)))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 tptp.posDivAlg A_1))) (let ((_let_4 (tptp.hAPP tptp.int _let_1 _let_3 B))) (let ((_let_5 (tptp.zero_zero tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 (tptp.ord_less tptp.int) A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 (tptp.ord_less_eq tptp.int) B) _let_5))))) (and (=> _let_7 (= _let_4 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 (tptp.product_Pair tptp.int tptp.int) _let_5) A_1))) (=> (not _let_7) (= _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.int (tptp.fun _let_1 _let_1) tptp.adjust B) (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) B)))))))))))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 W))) (let ((_let_3 (tptp.one_one tptp.int))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.hAPP tptp.int _let_5 tptp.posDivAlg _let_3))) (let ((_let_7 (tptp.hAPP tptp.int _let_4 _let_6 _let_2))) (let ((_let_8 (tptp.ord_less tptp.int))) (let ((_let_9 (tptp.fun tptp.int tptp.bool))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 _let_3) _let_2)))) (let ((_let_11 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 _let_11) _let_2)) (and (=> _let_10 (= _let_7 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 (tptp.product_Pair tptp.int tptp.int) _let_11) _let_3))) (=> (not _let_10) (= _let_7 (tptp.hAPP _let_4 _let_4 (tptp.hAPP tptp.int (tptp.fun _let_4 _let_4) tptp.adjust _let_2) (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) _let_2))))))))))))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) _let_2) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong X) (tptp.zero_zero tptp.int)) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 tptp.quadRes P_5) X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.div_div tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.minus_minus tptp.int) P_5) _let_1)) _let_2)))) _let_1) P_5)))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.div_div tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 A_1) B)) C) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 B) C))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) C))) C)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.bool (tptp.fun tptp.int _let_1) (tptp.if tptp.int) P_1) X_1) Y_1)))) (let ((_let_3 (tptp.hBOOL P_1))) (and (=> _let_3 (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1) _let_2)) (=> (not _let_3) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y_1) _let_2))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 A_1))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) B))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat _let_4 C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.div_div tptp.nat) A_1) B)) C))) (tptp.hAPP tptp.nat tptp.nat _let_3 B)))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) A_1))) (let ((_let_3 (tptp.div_div tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 B)) C) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 B) C))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) B) C))) C))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) M) N)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) M) N))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) M) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) M) N)) N))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.div_div tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_less_eq tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_4))))))))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) M) N)) M))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M) N) M))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.div_div tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 A_1))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) B) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 B)) C)))))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M) N)) M))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K_4))) (let ((_let_3 (tptp.div_mod tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 M) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.div_mod tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) N)) K_4) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) K_4))))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) X) Y)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) X) Y))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) X) Y)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) X) Y))))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) M) N) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.div_div tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) K_4))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 N)))) (let ((_let_5 (tptp.zero_zero tptp.nat))) (let ((_let_6 (= K_4 _let_5))) (and (=> _let_6 (= _let_4 _let_5)) (=> (not _let_6) (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))))))) (forall ((X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes P_4) X_1) (tptp.ti tptp.int X_1))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M) N)) N)))))) (= _let_40 _let_260) (= _let_260 _let_40) (forall ((Ma $$unsorted) (D_1 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) Ma) D_1) (tptp.zero_zero tptp.nat)) (exists ((Q_4 $$unsorted)) (= Ma (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) D_1) Q_4))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y_1)) (= (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y_1)) (= (tptp.ti tptp.int X_1) (tptp.ti tptp.int Y_1))))))) (forall ((P_1 $$unsorted)) (= (forall ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 X1))) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_2))))))) (forall ((P_1 $$unsorted)) (= (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 X1))) (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_2))))))) (forall ((Z_3 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_3)) (= (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_3)) (= (tptp.ti tptp.int Z) (tptp.ti tptp.int Z_3))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.div_mod tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.div_mod tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)))) (and (=> _let_4 (= _let_3 M)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) N))))))))) (forall ((K_4 $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) K_4) N)) M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))) (forall ((V $$unsorted)) (= (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V)))) (forall ((W $$unsorted)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) W))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.div_mod tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) N)))))) (= _let_179 _let_252) (forall ((X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP tptp.int _let_1 tptp.sr P_4))))))) (forall ((K_4 $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) K_4))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (tptp.hAPP tptp.nat tptp.nat _let_1 M))))))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.div_div tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_4)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 M)) (tptp.hAPP tptp.nat tptp.nat _let_3 N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) M) N)) N) M)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) N) M)) N) M)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.one_one tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) M) N)) M))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M) N)) N))))) (forall ((Z_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Z_1) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1) (tptp.zero_zero tptp.nat)))) (forall ((I $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 I) (tptp.zero_zero tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I) (tptp.zero_zero tptp.int))))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 W_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W_1) Z))))))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) Z)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 W_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W_1) Z))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 Y_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X_1) Y_1))))))))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.posDivAlg _let_1) B) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 (tptp.product_Pair tptp.int tptp.int) _let_1) _let_1)))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (= (tptp.hAPP tptp.int _let_2 tptp.sRStar P_4) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.bool) _let_1) P_4)))))))))) (forall ((X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong X_1) (tptp.zero_zero tptp.int)) P_4)))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (= K _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) N_1) K))) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 _let_1))) (=> (not _let_2) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_1) K)) (=> (= N_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K) I_2)) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I_2)))))))))))) (forall ((Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Z)))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (= K (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) N_1) K))) (and (=> _let_1 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_1))) (=> (not _let_1) (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_1) K)) (=> (= N_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K) I_2)) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 J_1))))))))))) (forall ((Q_3 $$unsorted) (R_4 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) B))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.zero_zero tptp.nat)) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 R_4) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) Q_3) C))) R_4)) (tptp.hAPP tptp.nat tptp.nat _let_2 C)))))))))) (= _let_251 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_21)) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 Y_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) X_1) Y_1)))))))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) W_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 W_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) Z)))))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (=> (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_3) W_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_3) Z))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 W_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 W_1) Z)))))))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z_1)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) Z_1) Z_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_4))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y))))))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Z_4)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z_1) Z_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_4))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 Y_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) X_1) Y_1)))))))) (forall ((Z_1 $$unsorted) (Z_4 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) Z_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 Z_4) Z_1)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Z_1) Z_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_4)))))))) (forall ((N $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) N) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) N))))) (forall ((N $$unsorted) (Z_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z_1)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) Z_1) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1)) N)))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M) M)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M))) (= _let_6 _let_249) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 P_5))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) P_5)) (= (tptp.hAPP tptp.nat tptp.int _let_2 _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_1) (tptp.one_one tptp.nat))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_2 tptp.bool) (tptp.member tptp.int) X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) _let_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1)) _let_1)))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.dvd_dvd tptp.int) P_5) X))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_5) _let_1)))) _let_1) P_5))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.one_one tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) N) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))) (forall ((Ma $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) Ma) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) _let_1)) (= _let_1 (tptp.one_one tptp.nat))))) (forall ((P_5 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.multInv P_5) X) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) P_5) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))) (forall ((L_4 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 K_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 L_4)) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.posDivAlg K_4) L_4) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) K_4) L_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) K_4) L_4)))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat))) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) P_5)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_5) _let_1))))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_2) P_5)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 P_5)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_5) _let_2))))))) (forall ((P_5 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.inv P_5) A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) P_5) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) P_5)))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) _let_1))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.div_div tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.minus_minus tptp.int) P_5) (tptp.one_one tptp.int))) _let_2))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_4)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) _let_2) _let_4)))))))) (forall ((X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))) (let ((_let_3 (tptp.member tptp.int))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 X_1) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes P_4) X_1)) _let_2)))))))))) (forall ((X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.standardRes P_4) X_1)) (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong X_1) (tptp.zero_zero tptp.int)) P_4))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.member tptp.int))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 X_1) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 Y_1) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.standardRes P_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) X_1) Y_1))) _let_2)))))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) _let_1) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong A_1) _let_3) P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.zcong _let_3) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_5) (tptp.one_one tptp.int))) _let_1)))) P_5))))))))))) (forall ((X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.member tptp.int))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 X_1) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.standardRes P_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.multInv P_4) X_1))) _let_2))))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_1) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legendre A_1) P_5)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_5) (tptp.one_one tptp.int))) _let_1)))) P_5)))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 tptp.posDivAlg A_1))) (let ((_let_4 (tptp.hAPP tptp.int _let_1 _let_3 B))) (let ((_let_5 (tptp.ord_less tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 _let_5 A_1) B)))) (let ((_let_8 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 _let_5 _let_8) B)) (and (=> _let_7 (= _let_4 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 (tptp.product_Pair tptp.int tptp.int) _let_8) A_1))) (=> (not _let_7) (= _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.int (tptp.fun _let_1 _let_1) tptp.adjust B) (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) B)))))))))))))))) (forall ((W $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 V))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_1 W))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.hAPP tptp.int _let_5 tptp.posDivAlg _let_3))) (let ((_let_7 (tptp.hAPP tptp.int _let_4 _let_6 _let_2))) (let ((_let_8 (tptp.ord_less tptp.int))) (let ((_let_9 (tptp.fun tptp.int tptp.bool))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 _let_3) _let_2)))) (let ((_let_11 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 _let_11) _let_2)) (and (=> _let_10 (= _let_7 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 (tptp.product_Pair tptp.int tptp.int) _let_11) _let_3))) (=> (not _let_10) (= _let_7 (tptp.hAPP _let_4 _let_4 (tptp.hAPP tptp.int (tptp.fun _let_4 _let_4) tptp.adjust _let_2) (tptp.hAPP tptp.int _let_4 _let_6 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) _let_2))))))))))))))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.number_number_of tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M) (tptp.hAPP tptp.int tptp.nat _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_3))))) (or (= _let_4 (tptp.zero_zero tptp.nat)) (= _let_4 (tptp.one_one tptp.nat)) (= _let_4 (tptp.hAPP tptp.int tptp.nat _let_2 _let_3)) (= _let_4 (tptp.hAPP tptp.int tptp.nat _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_1))))))))) (forall ((I_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.int _let_1 tptp.nat_aux I_1) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 I_1)) N)))) (forall ((M_5 $$unsorted) (D_4 $$unsorted)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) M_5) D_4) (tptp.zero_zero tptp.int)) (exists ((Q_4 $$unsorted)) (= (tptp.ti tptp.int M_5) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) D_4) Q_4))))) (forall ((X $$unsorted) (N $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 X) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Y) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Y) X)) (exists ((Q_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= X (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) N) Q_4)))))))))) (forall ((P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (= (tptp.hAPP tptp.int tptp.nat tptp.phi P_5) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_5) (tptp.one_one tptp.int)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 tptp.negDivAlg A_2))) (let ((_let_6 (tptp.hAPP tptp.int _let_3 _let_5 B_1))) (let ((_let_7 (tptp.zero_zero tptp.int))) (let ((_let_8 (tptp.ord_less_eq tptp.int))) (let ((_let_9 (tptp.fun tptp.int tptp.bool))) (let ((_let_10 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) A_2) B_1))) (let ((_let_11 (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 _let_7) _let_10)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_9 _let_8 B_1) _let_7))))) (let ((_let_12 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_13 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun _let_3 _let_13) _let_13 (tptp.accp _let_3) tptp.negDivAlg_rel) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 _let_12 A_2) B_1))) (and (=> _let_11 (= _let_6 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 _let_12 (tptp.hAPP tptp.int tptp.int _let_1 tptp.min_1)) _let_10))) (=> (not _let_11) (= _let_6 (tptp.hAPP _let_3 _let_3 (tptp.hAPP tptp.int (tptp.fun _let_3 _let_3) tptp.adjust B_1) (tptp.hAPP tptp.int _let_3 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) B_1))))))))))))))))))))) (tptp.hBOOL (tptp.hAPP _let_15 tptp.bool (tptp.hAPP _let_259 _let_77 (tptp.nat_tr1645093318rphism tptp.int tptp.nat) tptp.nat_1) _let_258)) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.nat_tr1645093318rphism X_a X_b) F) A_3)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 tptp.bool) (tptp.nat_tr1645093318rphism X_a X_b) F) A_3)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (= X_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) Y_1) Z)) (= Y_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X_1) Z))))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun _let_1 _let_2) _let_2 (tptp.accp _let_1) tptp.negDivAlg_rel) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) A0) A1))) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 P_1 A_4))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.zero_zero tptp.int))) (let ((_let_5 (tptp.ord_less_eq tptp.int))) (let ((_let_6 (tptp.product_prod tptp.int tptp.int))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP (tptp.fun _let_6 _let_7) _let_7 (tptp.accp _let_6) tptp.negDivAlg_rel) (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_6) (tptp.product_Pair tptp.int tptp.int) A_4) B_4))) (=> (=> (not (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_5 _let_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.plus_plus tptp.int) A_4) B_4))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_5 B_4) _let_4)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) B_4)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 B_4)))))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) P_1 A0) A1))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 tptp.posDivAlg A_2))) (let ((_let_4 (tptp.hAPP tptp.int _let_1 _let_3 B_1))) (let ((_let_5 (tptp.zero_zero tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 (tptp.ord_less tptp.int) A_2) B_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_6 (tptp.ord_less_eq tptp.int) B_1) _let_5))))) (let ((_let_8 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun _let_1 _let_9) _let_9 (tptp.accp _let_1) tptp.posDivAlg_rel) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 _let_8 A_2) B_1))) (and (=> _let_7 (= _let_4 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 _let_8 _let_5) A_2))) (=> (not _let_7) (= _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.int (tptp.fun _let_1 _let_1) tptp.adjust B_1) (tptp.hAPP tptp.int _let_1 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) B_1))))))))))))))))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun _let_1 _let_2) _let_2 (tptp.accp _let_1) tptp.posDivAlg_rel) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) A0) A1))) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 P_1 A_4))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun _let_3 _let_4) _let_4 (tptp.accp _let_3) tptp.posDivAlg_rel) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) (tptp.product_Pair tptp.int tptp.int) A_4) B_4))) (=> (=> (not (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_4) B_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_4) (tptp.zero_zero tptp.int))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) B_4)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 B_4))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) P_1 A0) A1))))))) (forall ((M $$unsorted) (D $$unsorted) (R_4 $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M) D) R_4) (exists ((Q_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= M (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) R_4) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) Q_4) D))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 X_1) N_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) N_1)) (exists ((Q1 $$unsorted) (Q2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) N_1))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 X_1) (tptp.hAPP tptp.nat tptp.nat _let_2 Q1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 Y_1) (tptp.hAPP tptp.nat tptp.nat _let_2 Q2))))))))))) (forall ((M_5 $$unsorted) (D_4 $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M_5) D_4) (tptp.zero_zero tptp.nat)) (exists ((Q_4 $$unsorted)) (= M_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) D_4) Q_4))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) B))) (let ((_let_3 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_6) tptp.divmod_int_rel A_1))) (let ((_let_8 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.int _let_6 _let_7 B) (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 _let_3 Q_3) R_4))) (=> (not (= (tptp.ti tptp.int B) _let_8)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_8) C)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.int _let_6 _let_7 (tptp.hAPP tptp.int tptp.int _let_2 C)) (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) Q_3) C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) Q_3) C))) R_4)))))))))))))))) (forall ((Q_5 $$unsorted) (R_5 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.divmod_int_rel A_1) B))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 _let_1 Q_3) R_4))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 _let_1 Q_5) R_5))) (=> (not (= (tptp.ti tptp.int B) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int R_4) (tptp.ti tptp.int R_5))))))))))) (forall ((Q_5 $$unsorted) (R_5 $$unsorted) (A_1 $$unsorted) (B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.divmod_int_rel A_1) B))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 _let_1 Q_3) R_4))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_5 (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 _let_1 Q_5) R_5))) (=> (not (= (tptp.ti tptp.int B) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int Q_3) (tptp.ti tptp.int Q_5))))))))))) (forall ((A_1 $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.divmod_int_rel A_1) A_1) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.product_Pair tptp.int tptp.int) Q_3) R_4))) (=> (not (= (tptp.ti tptp.int A_1) _let_1)) (= (tptp.ti tptp.int R_4) _let_1))))))) (forall ((B $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (not (= (tptp.ti tptp.int B) _let_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.divmod_int_rel _let_1) B) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.product_Pair tptp.int tptp.int) _let_1) _let_1)))))))) (forall ((A_1 $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.divmod_int_rel A_1) A_1) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) Q_3) R_4))) (=> (not (= (tptp.ti tptp.int A_1) (tptp.zero_zero tptp.int))) (= (tptp.ti tptp.int Q_3) (tptp.one_one tptp.int))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.divmod_int_rel A_1) B) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) Q_3) R_4))) (=> (not (= (tptp.ti tptp.int B) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B) (tptp.ti tptp.int Q_3))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.divmod_int_rel A_1) B) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) Q_3) R_4))) (=> (not (= (tptp.ti tptp.int B) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B) (tptp.ti tptp.int R_4))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 A_1) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 _let_3) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.divmod_int_rel A_1) B) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.negDivAlg A_1) B))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (not (= (tptp.ti tptp.int B) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.divmod_int_rel A_1) B) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) A_1) B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) A_1) B))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) _let_3) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) _let_3) B)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.divmod_int_rel A_1) B) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.posDivAlg A_1) B)))))))))) (forall ((B $$unsorted) (Bq $$unsorted) (Br $$unsorted) (A_1 $$unsorted) (C $$unsorted) (Aq $$unsorted) (Ar $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Ar) Br))) (let ((_let_4 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_5 (tptp.product_prod tptp.int tptp.int))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 tptp.divmod_int_rel A_1) C) (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 Aq) Ar))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 tptp.divmod_int_rel B) C) (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 Bq) Br))) (=> (not (= (tptp.ti tptp.int C) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 tptp.divmod_int_rel (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B)) C) (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Aq) Bq)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) _let_3) C))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_mod tptp.int) _let_3) C)))))))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less_eq tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.ord_less tptp.int))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_6 _let_3) B)))) (let ((_let_8 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_8 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_8 (tptp.times_times tptp.int) B) Q_3)) R_4)) (=> (and (=> _let_7 (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 _let_3) R_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_6 R_4) B)))) (=> (not _let_7) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_6 B) R_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 R_4) _let_3))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.divmod_int_rel A_1) B) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) Q_3) R_4)))))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) A_1))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_2 R_4))) (let ((_let_4 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_5 (tptp.product_prod tptp.int tptp.int))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 tptp.divmod_int_rel B) C) (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 Q_3) R_4))) (=> (not (= (tptp.ti tptp.int C) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 tptp.divmod_int_rel (tptp.hAPP tptp.int tptp.int _let_2 B)) C) (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 Q_3)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) _let_3) C))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) _let_3) C))))))))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.nat_tsub X) Y))))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.number_number_of tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_5))) (let ((_let_4 (tptp.times_times tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) (let ((_let_7 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_2 _let_6))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_6))) P_5)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 _let_7) _let_7) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.one_one tptp.int)))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_1)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) X))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) X) _let_1))) (tptp.one_one tptp.int)) (tptp.ti tptp.int X)))))) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.code_code_numeral (tptp.number_number_of tptp.code_code_numeral) _let_1))) (let ((_let_3 (tptp.fun tptp.code_code_numeral tptp.code_code_numeral))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) _let_1)) (tptp.hAPP tptp.code_code_numeral tptp.int tptp.code_int_of (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral (tptp.hAPP tptp.code_code_numeral _let_3 (tptp.div_div tptp.code_code_numeral) K_4) _let_2))))) (let ((_let_6 (tptp.hAPP tptp.code_code_numeral tptp.int tptp.code_int_of K_4))) (let ((_let_7 (tptp.zero_zero tptp.code_code_numeral))) (let ((_let_8 (= (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral (tptp.hAPP tptp.code_code_numeral _let_3 (tptp.div_mod tptp.code_code_numeral) K_4) _let_2) _let_7))) (let ((_let_9 (= K_4 _let_7))) (and (=> _let_9 (= _let_6 (tptp.zero_zero tptp.int))) (=> (not _let_9) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (= _let_6 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.plus_plus tptp.int) _let_5) (tptp.one_one tptp.int))))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1)) (tptp.one_one tptp.int)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (let ((_let_2 (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X)) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) X))) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) _let_2) _let_2)))))))) (forall ((I $$unsorted) (J $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I_2)) (tptp.hAPP tptp.nat tptp.nat F J_1))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) J)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat F I)) (tptp.hAPP tptp.nat tptp.nat F J)))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((K_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) K_4))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.nat_tsub (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) X) Y))))) (= (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral (tptp.hAPP tptp.code_code_numeral _let_256 (tptp.minus_minus tptp.code_code_numeral) _let_209) _let_247) _let_209) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.nat tptp.suc X) (tptp.hAPP tptp.nat tptp.nat tptp.suc Y)) (= X Y))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_char_0 X_a) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (= (tptp.hAPP tptp.nat X_a _let_1 Ma) (tptp.hAPP tptp.nat X_a _let_1 N_1)) (= Ma N_1)))))) (forall ((Nat $$unsorted) (Nat_5 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_5)) (= Nat Nat_5))) (forall ((N $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) N))) (forall ((N $$unsorted)) (not (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.nat X_a _let_1 M))))))) (= (tptp.hAPP tptp.nat tptp.int _let_190 _let_206) _let_2) (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) W_1) Z)) (exists ((N_2 $$unsorted)) (= (tptp.ti tptp.int Z) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.one_one tptp.int)) (tptp.hAPP tptp.nat tptp.int _let_1 M))))) (forall ((M $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) (forall ((Nat_4 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_4) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat tptp.suc M) (tptp.zero_zero tptp.nat)))) (forall ((Nat_3 $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_3)))) (forall ((M $$unsorted)) (not (= (tptp.zero_zero tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)) N)) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N))) (= M N))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_1) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J_2) K_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1)) K_4))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) N)) (=> (not (= _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) N)))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (= M N))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma))) (= N_1 Ma))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)) (= Ma N_1))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat _let_1 N))))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) N)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) Ma)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N_1)) (= Ma _let_1)))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N_1) Ma)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 _let_1)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N))) (= M _let_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)) (= Ma N_1)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc K_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) K_4))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))) N))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_2 (tptp.power_power tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 X_1) _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 Y_1) _let_1)) (= X_1 Y_1)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_255 _let_1)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_255 _let_2))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X_1) Y_1))) (or (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y_1)))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y)))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_1)))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_1) Y_1))) (or (and _let_3 _let_2) (and (not _let_3) (not _let_2)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_1)))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_1) Y_1))) (or (and _let_3 _let_2) (and (not _let_3) (not _let_2)))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) N))))))) (not (tptp.hBOOL (tptp.hAPP _let_15 tptp.bool (tptp.hAPP tptp.int _let_77 (tptp.member tptp.int) _let_2) tptp.zEven))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X_1) Y_1)) tptp.zEven))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X_1) Y_1)) tptp.zEven)) (or (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 Y_1) tptp.zEven)))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 Y_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_1) Y_1)) tptp.zEven)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_1) Y_1)) tptp.zEven)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 Y_1) tptp.zEven)))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 Y_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_1) Y_1)) tptp.zEven)))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 tptp.zOdd))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 tptp.zEven)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1))) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 tptp.zEven)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 tptp.zOdd)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 tptp.zEven))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1))) (not (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 tptp.zEven))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) M)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) M)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.zero_zero tptp.nat)) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a _let_1 Ma)) (tptp.hAPP tptp.nat X_a _let_1 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) N_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a _let_1 Ma)) (tptp.hAPP tptp.nat X_a _let_1 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) N_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.one_one tptp.nat)) (tptp.one_one X_a)))) (= _let_254 _let_1) (forall ((N_1 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1) (tptp.zero_zero tptp.int)) (= N_1 (tptp.zero_zero tptp.nat)))) (= _let_1 _let_254) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) N)))))) (forall ((K_4 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) K_4)) (tptp.zero_zero tptp.int))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)))) (forall ((Z_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Z_1)))) (forall ((P_1 $$unsorted)) (= (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)))) (exists ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_2)))))) (forall ((P_1 $$unsorted)) (= (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)))) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_2)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Ma)) (tptp.hAPP tptp.nat tptp.int _let_1 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) N_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP tptp.nat tptp.int _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X_1) Y_1))))) (forall ((X_a $$unsorted)) (=> (and (tptp.power X_a) (tptp.semiring_0 X_a)) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) _let_1))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Ma)) (tptp.hAPP tptp.nat tptp.int _let_1 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) Ma) N_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP tptp.nat tptp.int _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X_1) Y_1))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) X) Y))))) (forall ((W_1 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) W_1) Z)) (exists ((N_2 $$unsorted)) (= (tptp.ti tptp.int Z) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 N)) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.power X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.hAPP tptp.nat X_a _let_1 N))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_1 Q_3)) X) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Q_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) (tptp.hAPP tptp.nat X_a _let_1 Q_3)) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Q_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Q_3)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) (tptp.hAPP tptp.nat X_a _let_1 Q_3))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N))))) (forall ((M $$unsorted) (N $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 N)) Z_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N))) Z_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) X) Y))))) (= _let_253 _let_2) (= _let_2 _let_253) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP tptp.nat tptp.int _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X_1) Y_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X_1) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP tptp.nat tptp.int _let_1 Y_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_2))) (or (= X _let_1) (= X _let_2)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (or (= Ma (tptp.zero_zero tptp.nat)) (exists ((J_1 $$unsorted)) (and (= Ma (tptp.hAPP tptp.nat tptp.nat tptp.suc J_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) J_1) N_1))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= N_1 _let_1)))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (exists ((M_2 $$unsorted)) (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))) (forall ((Ma $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) Ma) _let_1)) (= Ma _let_1)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) N_1) _let_2) (or (and (= Ma _let_2) (= N_1 _let_1)) (and (= Ma _let_1) (= N_1 _let_2))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) N_1)) (or (and (= Ma _let_2) (= N_1 _let_1)) (and (= Ma _let_1) (= N_1 _let_2))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Ma) N_1) _let_1) (and (= Ma _let_1) (= N_1 _let_1))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) N_1)) (exists ((K_1 $$unsorted)) (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) K_1)))))) (forall ((I_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) I_1))))) (forall ((I_1 $$unsorted) (M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_1) M))))) (= _let_179 _let_206) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma))) (= N_1 Ma))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Ma) N_1))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) Ma) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) N_1))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) N_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) Ma))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))))))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) M))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat _let_2 N)))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) N_1))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.one_one tptp.nat)) N))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.one_one tptp.nat)) N)) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 M))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.one_one tptp.nat))) N)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) A_1) B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 A_1)) (tptp.hAPP tptp.nat tptp.int _let_1 B))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) X) Y))))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) M)) (forall ((M $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1)) _let_1))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N))) (let ((_let_5 (= _let_3 N))) (and (=> _let_5 (= _let_4 (tptp.zero_zero tptp.nat))) (=> (not _let_5) (= _let_4 _let_3))))))))) (forall ((X_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X_1) Ma) _let_2) (or (= Ma _let_1) (= X_1 _let_2)))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) _let_1) N) _let_1))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) N)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) N) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) N))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) N) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X) N))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) A_1) B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 A_1)) (tptp.hAPP tptp.nat tptp.int _let_1 B))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) X) Y))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_4 (tptp.power_power tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 X_1) _let_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 Y_1) _let_3))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1))))))))) (forall ((N $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) Y) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_4 (tptp.power_power tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 X_1) _let_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 Y_1) _let_3))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1))))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X_1) N_1))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_1)) (not (= N_1 (tptp.zero_zero tptp.nat))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 A_2) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 B_1) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) A_2) B_1)) tptp.zEven)))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 A_2) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 B_1) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) A_2) B_1)) tptp.zOdd)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) A_2) B_1)) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 A_2) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 B_1) tptp.zEven)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) A_2) B_1)) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 A_2) tptp.zEven)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 B_1) tptp.zOdd)))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 Y_1) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_1) Y_1)) tptp.zOdd)))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 Y_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_1) Y_1)) tptp.zOdd)))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 Y_1) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_1) Y_1)) tptp.zEven)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N)))))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1)) (tptp.zero_zero tptp.int))) (= N_1 (tptp.zero_zero tptp.nat)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (let ((_let_3 (tptp.power_power X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (=> (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 A_1) _let_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 B) _let_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (= (tptp.ti X_a A_1) (tptp.ti X_a B)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (let ((_let_4 (tptp.power_power X_a))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_5 _let_4 A_1) _let_3)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_5 _let_4 B) _let_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) _let_1) Z_1)))) (and (=> _let_3 (= _let_2 (tptp.ti tptp.int Z_1))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((Ma $$unsorted) (Z $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma) (tptp.ti tptp.int Z)) (and (= Ma (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z))))) (forall ((Z_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z_1)) (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1)) (tptp.ti tptp.int Z_1)))) (forall ((Ma $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma)) Z)))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M)) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) N) M))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) M)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N) M) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1)))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 K_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_3)) M)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N) K_4) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) K_4))))))))))) (forall ((M $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) K_4))) (=> (not (= M _let_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 _let_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 K_4))))))) (forall ((M $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (=> (not (= M (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) K_4))) (=> (not (= M _let_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) M)))))) (forall ((I_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.zero_zero tptp.nat)) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1))) N)))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) N)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)))))) (= _let_252 _let_206) (forall ((M $$unsorted) (K_4 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_4) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_2) K_4))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M) K_4)) (tptp.hAPP tptp.nat tptp.nat tptp.suc J_2))))))) (forall ((M $$unsorted) (K_4 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_4) J_2)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 J_2) K_4))) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc J_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) K_4) M))))))) (forall ((N $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 I_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) I_1) N)))))) (forall ((K_4 $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) K_4) N)) M))) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N))))) (= _let_209 (tptp.hAPP tptp.int tptp.code_code_numeral _let_246 tptp.pls)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X_1) N_1)) tptp.zEven)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zEven)))))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 X_1) tptp.zOdd)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_1) (tptp.one_one tptp.int))) tptp.zEven))))))) (= _let_21 (tptp.hAPP tptp.nat tptp.int _let_190 _let_251)) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) K_4)))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 I_1) J_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 I_1)) (tptp.hAPP tptp.int tptp.int _let_1 J_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) R_4)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 R_4) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) R_4) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) R_4))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) _let_1)))))))))) (forall ((P_1 $$unsorted) (I $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 I))) (and (forall ((N_2 $$unsorted)) (=> (= (tptp.ti tptp.int I) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_2)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat))))))) (forall ((Ma $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) W_1)))) (= (= Ma (tptp.hAPP tptp.int tptp.nat tptp.nat_1 W_1)) (and (=> _let_1 (= (tptp.ti tptp.int W_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma))) (=> (not _let_1) (= Ma (tptp.zero_zero tptp.nat))))))) (forall ((W_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) W_1)))) (= (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 W_1) Ma) (and (=> _let_1 (= (tptp.ti tptp.int W_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma))) (=> (not _let_1) (= Ma (tptp.zero_zero tptp.nat))))))) (forall ((Ma $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_1))) (= (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma) _let_1) (and (= Ma (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) _let_1)))))) (= _let_251 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_248)) (= _let_250 _let_206) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((Y $$unsorted) (P_5 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) Y))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) P_5) N)) (= (tptp.hAPP tptp.nat X_a _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) P_5)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N) P_5))) Y))))))))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat)))))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))) N))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N))) (let ((_let_4 (= M (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 N)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) (tptp.one_one tptp.nat))) N)))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.div_div tptp.nat))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.zero_zero tptp.nat)) N)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 M) N))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) N)))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.div_div tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 M) N)))) (let ((_let_7 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 _let_7) N)) (and (=> _let_6 (= _let_3 _let_7)) (=> (not _let_6) (= _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) N)))))))))))))) (forall ((M $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) K_4)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.div_mod tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) K_4) M))) K_4) _let_1))))) (forall ((A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (let ((_let_2 (tptp.div_mod tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (let ((_let_5 (tptp.div_div tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_5 (tptp.hAPP tptp.nat tptp.nat tptp.suc A_1)) C) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_5 A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_5 _let_1) C))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 A_1) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) C))) C))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.nat_tsub X) Y))))))) (= _let_19 (tptp.hAPP tptp.nat tptp.int _let_190 _let_6)) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Y) X)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.nat_tsub X) Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X) Y))))) (forall ((Ma $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) W_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 W_1)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) W_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.minus_minus X_a))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (let ((_let_4 (tptp.power_power X_a))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_5 _let_4 X) _let_3)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_5 _let_4 Y) _let_3)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) X) Y))))))))))) (forall ((P_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) X_1) Y_1)))) (and (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Y_1) X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_2 X_1)) (tptp.hAPP tptp.nat tptp.int _let_2 Y_1))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_1) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.zero_zero tptp.int))))))))) (= _let_6 _let_248) (= _let_248 _let_6) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_1 tptp.pls)) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 N) (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))) (forall ((Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) Z)))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) _let_1)) (= _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_1) (tptp.one_one tptp.nat))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.div_div tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) _let_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 M) _let_1))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.div_mod tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 M) _let_1)))))) (forall ((Z_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z_1)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.one_one tptp.int)) Z_1))))) (forall ((M $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.div_div tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) _let_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M)) _let_2))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.div_div tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M)) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) M))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)))))) (forall ((M $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.div_mod tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) _let_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M)) _let_2))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.div_mod tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc M)))) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M)) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) M))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)))))) (forall ((Q_2 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) N_1))) (let ((_let_3 (tptp.ord_less tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.zero_zero tptp.nat)) N_1)) (= (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_2 Q_2)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 Ma) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc Q_2))))) (= Q_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) Ma) N_1))))))))) (forall ((P_1 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) Ma) N_1))) (or (and (= N_1 _let_1) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 _let_1))) (exists ((Q_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) N_1))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_1 Q_4)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) Ma) (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Q_4)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 Q_4)))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.div_div tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N)) N))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (and (=> _let_2 (= _let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V))) (=> (not _let_2) (= _let_1 (tptp.zero_zero X_a))))))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) X_1)) (exists ((Y_2 $$unsorted)) (= (tptp.ti tptp.int X_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) Y_2))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) X_1)))) (forall ((Z $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z)) Ma)) (and (=> _let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) Z) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma)))) (=> (not _let_2) (= Ma (tptp.zero_zero tptp.nat)))))))) (forall ((X_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (= (tptp.ti tptp.int X_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) K)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) tptp.zEven))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (or (= N _let_1) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1)))))) (= _let_249 _let_248) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) X_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) X_1) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.zero_zero tptp.int)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) X)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) X) _let_1)) (tptp.ti tptp.int X)))))) (= _let_247 (tptp.hAPP tptp.int tptp.code_code_numeral _let_246 _let_3)) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 A_1))) (= (tptp.hAPP tptp.nat X_a _let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) _let_1) N))) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_4 N)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X))) (let ((_let_2 (tptp.hAPP tptp.nat X_a _let_1 N))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 _let_2) _let_2)))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.nat_tsub X) Y))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Y) X)))) (and (=> _let_3 (= _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X) Y))) (=> (not _let_3) (= _let_2 (tptp.zero_zero tptp.int)))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) N))) (=> (not (= N (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.minus_minus tptp.nat) _let_4) (tptp.hAPP tptp.int tptp.nat _let_2 _let_1)))) _let_4))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) _let_1) N))) (=> (not (= N (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) _let_3) _let_1))) _let_3)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) tptp.zEven)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) X_1) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.zero_zero tptp.int))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.div_div tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_5 tptp.bool) (tptp.member tptp.int) Y_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 X_1) _let_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 Y_1) _let_1))))))))))) (forall ((K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) K_4)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) (tptp.hAPP tptp.nat tptp.int _let_2 M)) K_4) (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.div_div tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.times_times tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_5 tptp.bool) (tptp.member tptp.int) X_1) tptp.zEven)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_4 X_1) Y_1)) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 X_1) _let_1)) Y_1))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_3 tptp.bool) (tptp.member tptp.int) X_1) tptp.zEven)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) X_1) _let_1)) (tptp.ti tptp.int X_1))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.div_div tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.plus_plus tptp.int))) (let ((_let_5 (tptp.member tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP tptp.int _let_7 _let_5 X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP tptp.int _let_7 _let_5 Y_1) tptp.zEven)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_4 X_1) Y_1)) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 X_1) _let_1)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 Y_1) _let_1))))))))))))) (forall ((V_3 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_3)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) (tptp.one_one tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_3))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)))) (let ((_let_2 (tptp.member tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_5 Y_1)) (=> (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.int _let_4 _let_2 X_1) tptp.zEven)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.int _let_4 _let_2 Y_1) tptp.zEven))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y_1)))))))))))) (forall ((X_1 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) X_1))) (exists ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.ti tptp.int X_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) Y_2)) (tptp.one_one tptp.int))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)))) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.div_div tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.plus_plus tptp.int))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) X))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_5 X) _let_1)) _let_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_3 X) _let_2)) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.div_div tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) X)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.plus_plus tptp.int) X) (tptp.one_one tptp.int))) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 X) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N))) _let_1))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N))) (=> (not (= N (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) _let_2) (tptp.one_one tptp.nat))) _let_2))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) M))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) M)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_2 _let_1))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) tptp.zEven)) (not (forall ((K_1 $$unsorted)) (not (= (tptp.ti tptp.int X_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) K_1)))))))) (forall ((I $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) P_4)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I) P_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat))))))) (forall ((N $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) A_1)) (exists ((R_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) R_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) A_1))))) (forall ((K_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) K_4)) (exists ((N_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_2)) (= (tptp.ti tptp.int K_4) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_2)))))) (forall ((J $$unsorted) (I $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2)) P_4)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I) P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 J) P_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 J))))))))) (forall ((N_1 $$unsorted) (N_7 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat F N_2)) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) N_1) N_7)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat F N_1)) (tptp.hAPP tptp.nat tptp.nat F N_7))))))) (forall ((P_1 $$unsorted) (I $$unsorted) (J $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 J)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) J)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 I)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.bool (tptp.fun tptp.nat _let_1) (tptp.if tptp.nat) P_1) X_1) Y_1)))) (let ((_let_4 (tptp.hBOOL P_1))) (and (=> _let_4 (= (tptp.hAPP tptp.nat tptp.int _let_2 X_1) _let_3)) (=> (not _let_4) (= (tptp.hAPP tptp.nat tptp.int _let_2 Y_1) _let_3)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (= (tptp.hAPP tptp.nat tptp.int _let_1 X_1) (tptp.hAPP tptp.nat tptp.int _let_1 Y_1)) (= X_1 Y_1)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (= (tptp.hAPP tptp.nat tptp.int _let_1 Ma) (tptp.hAPP tptp.nat tptp.int _let_1 N_1)) (= Ma N_1)))) (forall ((N $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.code_code_numeral _let_1 tptp.code_nat_of_aux I_1) N))) (let ((_let_3 (= I_1 (tptp.zero_zero tptp.code_code_numeral)))) (and (=> _let_3 (= _let_2 N)) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.code_code_numeral _let_1 tptp.code_nat_of_aux (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral (tptp.hAPP tptp.code_code_numeral (tptp.fun tptp.code_code_numeral tptp.code_code_numeral) (tptp.minus_minus tptp.code_code_numeral) I_1) (tptp.one_one tptp.code_code_numeral))) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))))) (forall ((Z_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z_1)) (not (forall ((M_2 $$unsorted)) (not (= (tptp.ti tptp.int Z_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) M_2))))))) (forall ((K_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) K_4)) (not (forall ((N_2 $$unsorted)) (not (= (tptp.ti tptp.int K_4) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_2))))))) (forall ((K_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) K_4)) (exists ((N_2 $$unsorted)) (= (tptp.ti tptp.int K_4) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_2))))) (forall ((M $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (exists ((K_1 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) K_1)))))) (forall ((N_1 $$unsorted) (N_7 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat F N_1))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat F N_7))) (let ((_let_3 (tptp.dvd_dvd tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat F N_2))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))) (let ((_let_3 (tptp.dvd_dvd tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 _let_2) _let_1))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 (tptp.ord_less tptp.nat) N_1) N_7)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 _let_2) _let_1))))))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat F N_1))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat F Ma))) (let ((_let_4 (tptp.dvd_dvd tptp.nat))) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat F N_2))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))) (let ((_let_3 (tptp.dvd_dvd tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 _let_1) _let_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 _let_2) _let_1))))))))) (= (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_4 _let_2) _let_3)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_4 _let_3) _let_2)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) N_1) Ma))))))))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (exists ((M_2 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((N_1 $$unsorted) (N_7 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a F N_2)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) N_7)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a F N_1)) (tptp.hAPP tptp.nat X_a F N_7)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((N_1 $$unsorted) (N_7 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N_2)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) N_7)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N_1)) (tptp.hAPP tptp.nat X_a F N_7)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((N_1 $$unsorted) (Ma $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N_2)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F N_1)) (tptp.hAPP tptp.nat X_a F Ma))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) Ma))))))) (forall ((V_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_3))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) _let_2) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_3)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) (tptp.one_one tptp.int)) _let_1)))))))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_2))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))))) (forall ((Z_5 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg Z_5)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Z_5) (tptp.zero_zero tptp.int))))) (forall ((X_1 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg X_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)))) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 W_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_1 W_1)))))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_245))) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W_1)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_1 W_1)))))) (forall ((Z_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg Z_1)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1) (tptp.zero_zero tptp.nat)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_244)) (forall ((Z_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg Z_1))) (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1)) (tptp.ti tptp.int Z_1)))) (forall ((V $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))) (= (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V) (tptp.zero_zero tptp.nat)))) (forall ((V_1 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 V_2))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_2)))) (let ((_let_4 (tptp.zero_zero tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int _let_1 V_1))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_5)))) (let ((_let_7 (tptp.number_number_of tptp.nat))) (= (= (tptp.hAPP tptp.int tptp.nat _let_7 V_1) (tptp.hAPP tptp.int tptp.nat _let_7 V_2)) (and (=> _let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) _let_2) _let_4))) (=> (not _let_6) (and (=> _let_3 (= _let_5 _let_4)) (=> (not _let_3) (= (tptp.ti tptp.int V_1) (tptp.ti tptp.int V_2))))))))))))))) (forall ((V_3 $$unsorted) (K_4 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V_3)) K_4))) (let ((_let_5 (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V)))) (let ((_let_6 (tptp.hAPP tptp.nat tptp.nat _let_5 _let_4))) (let ((_let_7 (tptp.number_number_of tptp.int))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_7 V_3))))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int _let_7 V))))) (and (=> _let_9 (= _let_6 _let_4)) (=> (not _let_9) (and (=> _let_8 (= _let_6 (tptp.hAPP tptp.nat tptp.nat _let_5 K_4))) (=> (not _let_8) (= _let_6 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) V_3))) K_4)))))))))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)))) (and (=> _let_3 (= _let_2 (tptp.zero_zero tptp.int))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (and (=> _let_2 (= _let_1 (tptp.zero_zero X_a))) (=> (not _let_2) (= _let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V))))))))) (forall ((V_3 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 V))) (let ((_let_3 (tptp.number_number_of tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_3 V)) (tptp.hAPP tptp.int tptp.nat _let_3 V_3)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_2)))) (and (=> _let_5 (= _let_4 (tptp.zero_zero tptp.nat))) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) _let_2) (tptp.hAPP tptp.int tptp.int _let_1 V_3)))))))))))) (forall ((W $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat _let_1 W))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))) (let ((_let_4 (tptp.power_power tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.int tptp.nat _let_1 V)) _let_2))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_3)))) (and (=> _let_7 (= _let_6 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.zero_zero tptp.nat)) _let_2))) (=> (not _let_7) (= _let_6 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) _let_3) _let_2))))))))))))) (forall ((N $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))) (let ((_let_2 (tptp.power_power tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V)) N))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)))) (and (=> _let_5 (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.zero_zero tptp.nat)) N))) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) _let_1) N))))))))))) (forall ((V_3 $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 V_3))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_1 V))) (let ((_let_4 (tptp.number_number_of tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.int tptp.nat _let_4 V))) (let ((_let_6 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) _let_5) (tptp.hAPP tptp.int tptp.nat _let_4 V_3)))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_2)))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_3)))) (and (=> _let_8 (= _let_6 (tptp.zero_zero tptp.nat))) (=> (not _let_8) (and (=> _let_7 (= _let_6 _let_5)) (=> (not _let_7) (= _let_6 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) _let_3) _let_2)))))))))))))))) (forall ((N $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 V)) N)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (and (=> _let_5 (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.one_one tptp.nat)) N))) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ V))) N)))))))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) P_4) (tptp.one_one tptp.int)))))) (forall ((Z_1 $$unsorted)) (not (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (not (= (tptp.ti tptp.int Z_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M_2)) (tptp.hAPP tptp.nat tptp.int _let_1 N_2)))))))) (forall ((I $$unsorted) (P_1 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 K)) (=> (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_2)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) K) I)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 (tptp.zero_zero X_a)) Z_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 Z_2) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) Z_2) X)) Y))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((N $$unsorted) (M_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) M_4)) (exists ((M_2 $$unsorted)) (= M_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))) (= (tptp.hAPP tptp.int tptp.int tptp.succ tptp.pls) _let_3) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int tptp.succ (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.succ K_4)))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int tptp.succ (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int tptp.succ K_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K_4) (tptp.one_one tptp.int)))) (= (tptp.hAPP tptp.int tptp.int tptp.succ tptp.min_1) tptp.pls) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K_4) tptp.min_1) (tptp.hAPP tptp.int tptp.int tptp.succ K_4))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ K_4)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 K_4))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) (tptp.hAPP tptp.int tptp.int tptp.succ L_4))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls) V)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ V)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_semiring X_a) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) tptp.pls) V)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ V)))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.one_one tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_1 V)) _let_2))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V) tptp.pls)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ V)))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.one_one tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) _let_2) (tptp.hAPP tptp.int tptp.nat _let_1 V)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V) tptp.pls)))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ V)))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.int tptp.nat _let_1 V)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (and (=> _let_3 (= _let_2 (tptp.one_one tptp.nat))) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.succ V))))))))) (forall ((J $$unsorted) (A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) _let_1)) P_4)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong A_2) _let_4) P_4))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 tptp.quadRes P_4) A_2))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong J) _let_4) P_4))) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.multInvPair A_2) P_4) J)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1)))))))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) (tptp.zero_zero tptp.int)) P_4))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 tptp.quadRes P_4) A_2))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.setS A_2) P_4))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) X_2) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (forall ((E $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) (tptp.zero_zero X_a)) E)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) Y) E)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) X))))) (forall ((I_1 $$unsorted) (K_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) K_4)) (=> (not (= K_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1))) (not (forall ((J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) J_1)) (not (= K_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc J_1))))))))) (forall ((I_1 $$unsorted) (K_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc I_1)) K_4)) (not (forall ((J_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_1) J_1)) (not (= K_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc J_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b G X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (= (tptp.ti X_a X) (tptp.ti X_a Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((X_1 $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a X_b G X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= X Y) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b G X_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1))) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a X) (tptp.ti X_a Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a X) (tptp.ti X_a Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y)) (not (= (tptp.ti X_a Y) (tptp.ti X_a X))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((P_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1)) (tptp.hBOOL P_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) C))) (=> (= (tptp.ti X_a A_1) (tptp.ti X_a B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)) (=> (= (tptp.ti X_a B) (tptp.ti X_a C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Y))) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y_1) X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Y_1) X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_1)) (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) X_1) Y_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_1)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_1)) (= (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_1) Y_1))) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X) Y)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_1) B)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) B) A_1)) (=> (not (= (tptp.ti X_a A_1) (tptp.ti X_a B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) Z_1) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z_1) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.preorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X))))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_1) P_4)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.zcong A_2) (tptp.zero_zero tptp.int)) P_4))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 tptp.quadRes P_4) A_2))) (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP _let_4 tptp.nat (tptp.finite_card _let_3) (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.setS A_2) P_4))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_4) (tptp.one_one tptp.int))) _let_1))))))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) (tptp.zero_zero tptp.int)) P_4))) (= (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.setS A_2) P_4)) (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4)))))))) (forall ((D2 $$unsorted) (D1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 D1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 D2)) (exists ((E $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 E))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) E)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 D1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 D2))))))))))) (forall ((X $$unsorted) (Y $$unsorted) (Xa_1 $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.plus_plus tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Xa_1) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Ya) _let_1)))))))))))) (forall ((Y $$unsorted)) (=> (not (= Y (tptp.zero_zero tptp.nat))) (not (forall ((Nat_2 $$unsorted)) (not (= Y (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_2))))))) (forall ((P_1 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 K)) (=> (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_2)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat)))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less _let_1) F) G)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 F) G)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 G) F))))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1) (tptp.hAPP tptp.real tptp.real tptp.sqrt Y_1)) (= X_1 Y_1))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X)) (tptp.hAPP tptp.real tptp.real tptp.sqrt Y))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1)) (tptp.hAPP tptp.real tptp.real tptp.sqrt Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1) _let_1) (= X_1 _let_1)))) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt _let_37) _let_37) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X)) (tptp.hAPP tptp.real tptp.real tptp.sqrt Y))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1)) (tptp.hAPP tptp.real tptp.real tptp.sqrt Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X)) (tptp.hAPP tptp.real tptp.real tptp.sqrt Y)))))) (forall ((X $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_2 _let_1 X) K_4)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X)) K_4))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1) _let_1) (= X_1 _let_1)))) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt _let_136) _let_136) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) _let_1) X)) (=> (= (tptp.hAPP tptp.real tptp.real tptp.sqrt X) _let_1) (= X _let_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1))))))) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_1) X)) (not (= (tptp.hAPP tptp.real tptp.real tptp.sqrt X) _let_1))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1))))))) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y_1))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.one_one tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1))))))) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.one_one tptp.real)))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y_1))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1))))))) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.one_one tptp.real)))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 X) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 Y) Y)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 X) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 Y) Y)))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_130 _let_231)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_242 _let_231)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_55 _let_240 _let_136) _let_231)) (forall ((Y $$unsorted) (X $$unsorted)) (=> (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) Y) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) X) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) Y)) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt X) Y)))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sqrt X)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) X))) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) X_1) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sqrt X)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))) (forall ((A_1 $$unsorted) (C $$unsorted) (B $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.plus_plus tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 A_1) C)) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 B) D)) _let_1)))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 A_1) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 B) _let_1)))) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 C) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 D) _let_1)))))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) Y) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (=> (= (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1))) Y) (= X (tptp.zero_zero tptp.real))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (=> (= (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1))) X) (= Y (tptp.zero_zero tptp.real))))))) (forall ((X $$unsorted) (Y $$unsorted) (Xa_1 $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.plus_plus tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Xa_1) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Ya) _let_1))))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sqrt _let_6)) _let_1) _let_6)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1))))))))) (forall ((Y $$unsorted) (X $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.ord_less tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.zero_zero tptp.real))) (let ((_let_9 (tptp.hAPP tptp.real _let_7 (tptp.ord_less_eq tptp.real) _let_8))) (let ((_let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.inverse_divide tptp.real) U) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 _let_8) U)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 X) _let_10)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 Y) _let_10)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_9 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_9 Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 X) _let_2)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 Y) _let_2)))) U)))))))))))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (X_3 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_3) C_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) C_2))))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.setS A_2) P_4)))))))) (forall ((N $$unsorted)) (=> (not (= N (tptp.zero_zero tptp.nat))) (exists ((M_2 $$unsorted)) (= N (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))))) (forall ((N_1 $$unsorted) (P_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat))) (=> (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_1))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ord X_b) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b G X_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) F) G))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) _let_1) Y) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.divisi14063676e_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) _let_1) A_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1))) (let ((_let_3 (tptp.inverse_divide X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 B) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 B)) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 Z_1) W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) W))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X $$unsorted) (Y $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Ya) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Ya)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Ya))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_1) (tptp.one_one X_a)) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X $$unsorted) (Y $$unsorted) (Ya $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Ya) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Ya)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Ya))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) B)) C) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) B)) N) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 B) N)))))))))) (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_divide tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) R_4))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 A_1)) (tptp.hAPP tptp.real tptp.real _let_3 R_4)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 A_1) R_4)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.inverse_divide tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X)) (tptp.hAPP tptp.real tptp.real tptp.sqrt Y)))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.wset A_2) P_4))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.setS A_2) P_4))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) X_2)))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP tptp.int _let_1 tptp.d22set A_2))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_2) B_1)) _let_1)) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_2) B_1))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_2) B_1))) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_2) B_1)) _let_1)) (or (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.inverse_divide X_a))) (let ((_let_5 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 A_2) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 B_1) C_1))) (and (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) A_2))) (not (= (tptp.ti X_a C_1) _let_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Y) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) Y)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) Y)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Y) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) Y))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)) C)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ti X_a A_2))) (let ((_let_3 (= (tptp.ti X_a C_1) _let_1))) (let ((_let_4 (tptp.fun X_a X_a))) (= (= _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.inverse_divide X_a) B_1) C_1)) (and (=> (not _let_3) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.times_times X_a) A_2) C_1) (tptp.ti X_a B_1))) (=> _let_3 (= _let_2 _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ti X_a A_2))) (let ((_let_3 (= (tptp.ti X_a C_1) _let_1))) (let ((_let_4 (tptp.fun X_a X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.inverse_divide X_a) B_1) C_1) _let_2) (and (=> (not _let_3) (= (tptp.ti X_a B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.times_times X_a) A_2) C_1))) (=> _let_3 (= _let_2 _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a C_1) (tptp.zero_zero X_a))) (= (= (tptp.ti X_a A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1) (tptp.ti X_a B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a C_1) (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1) (tptp.ti X_a A_2)) (= (tptp.ti X_a B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.times_times X_a))) (=> (not (= (tptp.ti X_a C) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 A_1) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 B) C)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.times_times X_a) C))) (=> (not (= (tptp.ti X_a C) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((X_1 $$unsorted) (W_1 $$unsorted) (Z $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (let ((_let_4 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a Y_1) _let_4)) (=> (not (= (tptp.ti X_a Z) _let_4)) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X_1) Y_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 W_1) Z)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X_1) Z) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 W_1) Y_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a C) (tptp.zero_zero X_a))) (=> (= (tptp.ti X_a B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) C)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B) C) (tptp.ti X_a A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a C) (tptp.zero_zero X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) C) (tptp.ti X_a B)) (= (tptp.ti X_a A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B) C)))))))) (forall ((X_a $$unsorted)) (=> (tptp.divisi14063676e_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_1) A_1))) (let ((_let_2 (tptp.zero_zero X_a))) (let ((_let_3 (= (tptp.ti X_a A_1) _let_2))) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 (tptp.one_one X_a)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_1) A_1) (tptp.one_one X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ti X_a B_1))) (=> (not (= _let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_2) B_1) (tptp.one_one X_a)) (= (tptp.ti X_a A_2) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) B)) N) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 B) N))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) (tptp.one_one X_a)))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) N)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 _let_2 _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) X_1) Y_1))) (and (or (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_4 Y_1))) (or (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_4 X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.ord_less X_a))) (let ((_let_5 (tptp.inverse_divide X_a))) (let ((_let_6 (tptp.fun X_a X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 _let_5 A_2) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 _let_5 B_1) C_1))) (and (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 _let_3) C_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 C_1) _let_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_1) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) Y))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) Y) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) Y)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Z_1 $$unsorted) (W $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less_eq X_a) X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 W)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 W) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) W))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Z_1 $$unsorted) (W $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.ord_less_eq X_a))) (let ((_let_6 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_5 _let_6) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_6) W)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_5 W) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) W)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Z_1 $$unsorted) (W $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_5) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 X) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less X_a) _let_5) W)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 W) Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) W))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) _let_1) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) Y)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) _let_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) Y) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) Y))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 A_2))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C_1) _let_1)))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 (tptp.times_times X_a) A_2) C_1))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) C_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 (tptp.inverse_divide X_a) B_1) C_1))) (and (=> _let_8 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_7) B_1))) (=> (not _let_8) (and (=> _let_5 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_7))) (=> (not _let_5) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 _let_1)))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C_1) _let_1)))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 (tptp.times_times X_a) A_2) C_1))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 C_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 (tptp.inverse_divide X_a) B_1) C_1)) A_2)) (and (=> _let_8 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_7))) (=> (not _let_8) (and (=> _let_5 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_7) B_1))) (=> (not _let_5) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_2)))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1)) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1)) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((X $$unsorted) (Z_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) X) Y)) Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) Y)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) X) Y))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C_1) (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 C_1) (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1)) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1)) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) C))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a _let_2 A_1)) (tptp.hAPP X_a X_a _let_2 B)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) C))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) _let_5)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_5) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a _let_2 A_1)) (tptp.hAPP X_a X_a _let_2 B)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (=> (not (= (tptp.ti X_a Y) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) Y))) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (=> (not (= (tptp.ti X_a Z_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) X)) Y)) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((X $$unsorted) (Z_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (=> (not (= (tptp.ti X_a Y) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 X) Y)) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) Y))) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (=> (not (= (tptp.ti X_a Z_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 X) Z_1)) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) Y))) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((X $$unsorted) (W $$unsorted) (Z_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.inverse_divide X_a))) (let ((_let_5 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a Y) _let_5)) (=> (not (= (tptp.ti X_a Z_1) _let_5)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 W) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 W) Y))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.number X_a)) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ti X_a A_2))) (let ((_let_3 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_4 (= _let_3 _let_1))) (let ((_let_5 (tptp.fun X_a X_a))) (= (= _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 (tptp.inverse_divide X_a) B_1) _let_3)) (and (=> (not _let_4) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 (tptp.times_times X_a) A_2) _let_3) (tptp.ti X_a B_1))) (=> _let_4 (= _let_2 _let_1)))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.number X_a)) (forall ((W_1 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_3 (= (tptp.ti X_a C_1) _let_1))) (let ((_let_4 (tptp.fun X_a X_a))) (= (= _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.inverse_divide X_a) B_1) C_1)) (and (=> (not _let_3) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.times_times X_a) _let_2) C_1) (tptp.ti X_a B_1))) (=> _let_3 (= _let_2 _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.number X_a)) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_3 (= (tptp.ti X_a C_1) _let_1))) (let ((_let_4 (tptp.fun X_a X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.inverse_divide X_a) B_1) C_1) _let_2) (and (=> (not _let_3) (= (tptp.ti X_a B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.times_times X_a) _let_2) C_1))) (=> _let_3 (= _let_2 _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.number X_a)) (forall ((B_1 $$unsorted) (W_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ti X_a A_2))) (let ((_let_3 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_4 (= _let_3 _let_1))) (let ((_let_5 (tptp.fun X_a X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 (tptp.inverse_divide X_a) B_1) _let_3) _let_2) (and (=> (not _let_4) (= (tptp.ti X_a B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 (tptp.times_times X_a) A_2) _let_3))) (=> _let_4 (= _let_2 _let_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((X $$unsorted) (W $$unsorted) (Z_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.inverse_divide X_a))) (let ((_let_5 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a Y) _let_5)) (=> (not (= (tptp.ti X_a Z_1) _let_5)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 W) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 W) Y))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.minus_minus X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (=> (not (= (tptp.ti X_a Z_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 X) Z_1)) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) Y))) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.minus_minus X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (=> (not (= (tptp.ti X_a Z_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) X)) Y)) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.inverse_divide X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 _let_1) _let_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.ord_less X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.inverse_divide X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 _let_1) _let_1))) B))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.number_ring X_a)) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls)) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field X_a) (tptp.number_ring X_a)) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field X_a) (tptp.number_ring X_a)) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 A_2))) (let ((_let_5 (tptp.ord_less X_a))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_5 C_1) _let_1)))) (let ((_let_7 (tptp.fun X_a X_a))) (let ((_let_8 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.times_times X_a) A_2) C_1))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_5 _let_1) C_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.inverse_divide X_a) B_1) C_1))) (and (=> _let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_8) B_1))) (=> (not _let_9) (and (=> _let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_8))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 _let_1))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.ord_less X_a))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_4 C_1) _let_1)))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 (tptp.times_times X_a) A_2) C_1))) (let ((_let_8 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_4 _let_1) C_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 (tptp.inverse_divide X_a) B_1) C_1)) A_2)) (and (=> _let_8 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_7))) (=> (not _let_8) (and (=> _let_5 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_7) B_1))) (=> (not _let_5) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_2)))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1)) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) (tptp.zero_zero X_a)) C_1)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1)) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((X $$unsorted) (Z_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) (tptp.zero_zero X_a)) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) X) Y)) Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) (tptp.zero_zero X_a)) Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Z_1) Y)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) X) Y))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) C_1) (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) C_1) (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) B_1) C_1)) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_2) C_1)) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((C $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) C))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_5) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less X_a) _let_5) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a _let_2 A_1)) (tptp.hAPP X_a X_a _let_2 B)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) C))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C) _let_5)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.ord_less X_a) _let_5) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) B))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a _let_2 A_1)) (tptp.hAPP X_a X_a _let_2 B)))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number X_a)) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 A_2))) (let ((_let_5 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_5) _let_1)))) (let ((_let_7 (tptp.fun X_a X_a))) (let ((_let_8 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.times_times X_a) A_2) _let_5))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) _let_5)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.inverse_divide X_a) B_1) _let_5))) (and (=> _let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_8) B_1))) (=> (not _let_9) (and (=> _let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_8))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 _let_1))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number X_a)) (forall ((W_1 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 _let_2))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C_1) _let_1)))) (let ((_let_7 (tptp.fun X_a X_a))) (let ((_let_8 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.times_times X_a) _let_2) C_1))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_1) C_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.inverse_divide X_a) B_1) C_1))) (and (=> _let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_8) B_1))) (=> (not _let_9) (and (=> _let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B_1) _let_8))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 _let_1))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number X_a)) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_2 (tptp.zero_zero X_a))) (let ((_let_3 (tptp.ord_less X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 _let_2))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 C_1) _let_2)))) (let ((_let_7 (tptp.fun X_a X_a))) (let ((_let_8 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.times_times X_a) _let_1) C_1))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 C_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.inverse_divide X_a) B_1) C_1)) _let_1)) (and (=> _let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B_1) _let_8))) (=> (not _let_9) (and (=> _let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_8) B_1))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 _let_1))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number X_a)) (forall ((B_1 $$unsorted) (W_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 _let_1))) (let ((_let_5 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_5) _let_1)))) (let ((_let_7 (tptp.fun X_a X_a))) (let ((_let_8 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.times_times X_a) A_2) _let_5))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 _let_5)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.inverse_divide X_a) B_1) _let_5)) A_2)) (and (=> _let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_8))) (=> (not _let_9) (and (=> _let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_8) B_1))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 A_2))))))))))))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.complete_Sup_Sup _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_3 tptp.bool) (tptp.ord_less_eq _let_3) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less_eq _let_1) (tptp.hAPP _let_3 _let_1 _let_2 A_3)) (tptp.hAPP _let_3 _let_1 _let_2 B_2)))))))) (forall ((X_a $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) B_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) A_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((N $$unsorted) (M $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1))) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) (tptp.hAPP tptp.nat X_a _let_1 M)) (tptp.hAPP tptp.nat X_a _let_1 N))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number X_a)) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_2 A_2))) (let ((_let_5 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_6 (tptp.ord_less X_a))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_6 _let_5) _let_1)))) (let ((_let_8 (tptp.fun X_a X_a))) (let ((_let_9 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_8 (tptp.times_times X_a) A_2) _let_5))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_6 _let_1) _let_5)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_8 (tptp.inverse_divide X_a) B_1) _let_5))) (and (=> _let_10 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_9) B_1))) (=> (not _let_10) (and (=> _let_7 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_9))) (=> (not _let_7) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_4 _let_1)))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number X_a)) (forall ((W_1 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 _let_2))) (let ((_let_6 (tptp.ord_less X_a))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 C_1) _let_1)))) (let ((_let_8 (tptp.fun X_a X_a))) (let ((_let_9 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_8 (tptp.times_times X_a) _let_2) C_1))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_6 _let_1) C_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_8 (tptp.inverse_divide X_a) B_1) C_1))) (and (=> _let_10 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_9) B_1))) (=> (not _let_10) (and (=> _let_7 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B_1) _let_9))) (=> (not _let_7) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_5 _let_1)))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number X_a)) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_2 (tptp.zero_zero X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.ord_less X_a))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_5 C_1) _let_2)))) (let ((_let_7 (tptp.fun X_a X_a))) (let ((_let_8 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.times_times X_a) _let_1) C_1))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_5 _let_2) C_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.inverse_divide X_a) B_1) C_1)) _let_1)) (and (=> _let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B_1) _let_8))) (=> (not _let_9) (and (=> _let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_8) B_1))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 _let_2) _let_1))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number X_a)) (forall ((B_1 $$unsorted) (W_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1))) (let ((_let_5 (tptp.ord_less X_a))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_5 _let_4) _let_1)))) (let ((_let_7 (tptp.fun X_a X_a))) (let ((_let_8 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.times_times X_a) A_2) _let_4))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_5 _let_1) _let_4)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 (tptp.inverse_divide X_a) B_1) _let_4)) A_2)) (and (=> _let_9 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) _let_8))) (=> (not _let_9) (and (=> _let_6 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_8) B_1))) (=> (not _let_6) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_2))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number_ring X_a)) (forall ((R_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) R_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 R_1))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number_ring X_a)) (forall ((R_4 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 R_4)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) R_4) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) Y)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) Y)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) Y))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_3)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) _let_2) _let_2) (tptp.one_one tptp.int)))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4)))))) (forall ((X_a $$unsorted)) (=> (tptp.comple44059174attice X_a) (forall ((A_3 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.hAPP _let_1 X_a (tptp.complete_Sup_Sup X_a) A_3)) B_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comple44059174attice X_a) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_1) A_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) (tptp.hAPP _let_1 X_a (tptp.complete_Sup_Sup X_a) A_3)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comple44059174attice X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.complete_Sup_Sup X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.hAPP _let_2 X_a _let_1 A_3)) (tptp.hAPP _let_2 X_a _let_1 B_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comple44059174attice X_a) (forall ((V_1 $$unsorted) (U_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) V_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) U_1) A_3)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 U_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP _let_1 X_a (tptp.complete_Sup_Sup X_a) A_3)))))))))) (forall ((U $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) U)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) U) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) U)))))) (forall ((X_a $$unsorted)) (=> (tptp.comple1803745165norder X_a) (forall ((A_2 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_2) (tptp.hAPP _let_1 X_a (tptp.complete_Sup_Sup X_a) S))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) S)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_2) X_2)))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.linord1117847801e_zero X_a) (tptp.number_ring X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.minus_minus tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.inverse_divide tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.plus_plus tptp.real) A_1) B)) _let_1)) A_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 B) A_1)) _let_1))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.minus_minus tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.inverse_divide tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.plus_plus tptp.real) B) A_1)) _let_1)) A_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 B) A_1)) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) _let_2) _let_2) X)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) Y_1))) (let ((_let_3 (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (= (= X_1 (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real _let_3 Z))) (= (tptp.hAPP tptp.real tptp.real _let_3 X_1) (tptp.hAPP tptp.real tptp.real _let_2 Z))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((N $$unsorted) (Z_1 $$unsorted) (K_5 $$unsorted) (H_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (let ((_let_4 (tptp.semiring_1_of_nat tptp.real))) (let ((_let_5 (tptp.times_times tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.power_power X_a))) (let ((_let_8 (tptp.fun tptp.nat X_a))) (let ((_let_9 (tptp.hAPP X_a _let_8 _let_7 Z_1))) (let ((_let_10 (tptp.fun X_a X_a))) (let ((_let_11 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_10 (tptp.plus_plus X_a) Z_1) H_2))) (let ((_let_12 (tptp.minus_minus X_a))) (let ((_let_13 (tptp.ord_less_eq tptp.real))) (let ((_let_14 (tptp.fun tptp.real tptp.bool))) (=> (not (= (tptp.ti X_a H_2) (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_14 _let_13 (tptp.hAPP X_a tptp.real _let_1 Z_1)) K_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_14 _let_13 (tptp.hAPP X_a tptp.real _let_1 _let_11)) K_5)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_14 _let_13 (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_10 _let_12 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_10 (tptp.inverse_divide X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_10 _let_12 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_8 _let_7 _let_11) N)) (tptp.hAPP tptp.nat X_a _let_9 N))) H_2)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_10 (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N)) (tptp.hAPP tptp.nat X_a _let_9 _let_3))))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.nat tptp.real _let_4 N)) (tptp.hAPP tptp.nat tptp.real _let_4 _let_3))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) K_5) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (tptp.hAPP X_a tptp.real _let_1 H_2)))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.norm_norm X_a))) (= (tptp.hAPP X_a tptp.real _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a tptp.real _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n2089651433ebra_1 X_a) (forall ((N $$unsorted)) (= (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N)) (tptp.hAPP tptp.nat tptp.real (tptp.semiring_1_of_nat tptp.real) N))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (= (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.zero_zero X_a)) (tptp.zero_zero tptp.real)))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X_1) (tptp.zero_zero tptp.real)) (= (tptp.ti X_a X_1) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n1866405975lgebra X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (= (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X)) (tptp.hAPP X_a tptp.real _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X)) (tptp.zero_zero tptp.real))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n2089651433ebra_1 X_a) (= (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.one_one X_a)) (tptp.one_one tptp.real)))) (forall ((X_a $$unsorted)) (=> (tptp.real_n1866405975lgebra X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (= (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X) N)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP X_a tptp.real _let_1 X)) N)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.real_normed_field X_a)) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (= (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_1) B)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP X_a tptp.real _let_1 A_1)) (tptp.hAPP X_a tptp.real _let_1 B))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.norm_norm tptp.complex))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.complex tptp.real _let_1 (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.plus_plus tptp.complex) B) A_1))) (tptp.hAPP tptp.complex tptp.real _let_1 B))) (tptp.hAPP tptp.complex tptp.real _let_1 A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted) (Y $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 C) (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) C) (tptp.hAPP X_a tptp.real _let_1 Y)))) (= (tptp.ti X_a X) (tptp.zero_zero X_a)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X_1)) (tptp.zero_zero tptp.real))) (= (tptp.ti X_a X_1) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X_1))) (not (= (tptp.ti X_a X_1) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X)) (tptp.hAPP X_a tptp.real _let_1 Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y $$unsorted) (S_3 $$unsorted) (X $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 X)) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 Y)) S_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_4) S_3))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_1) B)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP X_a tptp.real _let_1 A_1)) (tptp.hAPP X_a tptp.real _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP X_a tptp.real _let_1 X)) (tptp.hAPP X_a tptp.real _let_1 Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((Y $$unsorted) (S_3 $$unsorted) (X $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 X)) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 Y)) S_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) R_4) S_3))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) B))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP X_a tptp.real _let_1 A_1)) (tptp.hAPP X_a tptp.real _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n2089651433ebra_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X) N))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP X_a tptp.real _let_1 X)) N))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP X_a tptp.real _let_1 A_1)) (tptp.hAPP X_a tptp.real _let_1 B))) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP X_a tptp.real _let_1 A_1)) (tptp.hAPP X_a tptp.real _let_1 B))) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.norm_norm X_a))) (let ((_let_4 (tptp.plus_plus X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 C) D)))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP X_a tptp.real _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C))) (tptp.hAPP X_a tptp.real _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.setS A_2) P_4))))))) (forall ((K $$unsorted) (L $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K) L)) (exists ((N_2 $$unsorted)) (= L (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K) N_2))))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real F A_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F B_1)))) (let ((_let_5 (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real _let_4 _let_3)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 B_1) A_2))))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 _let_3) (tptp.hAPP tptp.real tptp.real _let_5 A_2)) (tptp.hAPP tptp.real tptp.real _let_4 (tptp.hAPP tptp.real tptp.real _let_5 B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (H_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (let ((_let_4 (tptp.times_times X_a))) (let ((_let_5 (tptp.hAPP X_a _let_2 _let_4 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_5 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 C) D))) H_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)) H_2))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C)) H_2)) D))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X_2) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X_2) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_4) B_4))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 A_4)) (tptp.hAPP X_a tptp.real _let_1 B_4))) K_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X_2) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_4) B_4))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 A_4)) (tptp.hAPP X_a tptp.real _let_1 B_4))) K_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X_2) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y $$unsorted)) (exists ((K_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X_2) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (exists ((K_2 $$unsorted)) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_4) B_4))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 A_4)) (tptp.hAPP X_a tptp.real _let_1 B_4))) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y $$unsorted)) (exists ((K_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X_2) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X $$unsorted)) (exists ((K_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_card X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 A_3)) (tptp.hAPP _let_1 tptp.nat _let_2 B_2))) (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_card X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) B_2) A_3)) (= (tptp.hAPP _let_2 tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) A_3) B_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_card X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_2)))))))) (forall ((X_a $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_finite_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.finite_finite X_a) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.finite_finite_1 X_a) A_3))))) (forall ((X_a $$unsorted)) (=> (tptp.finite_finite X_a) (forall ((A_3 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.finite_finite_1 X_a) A_3))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_2)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) A_3) B_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 A_3))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_3) (tptp.zero_zero tptp.nat))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.finite_card X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_2 tptp.nat _let_1 A_3)) (tptp.hAPP _let_2 tptp.nat _let_1 B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) A_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) A_3)))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.finite_card X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_3 A_3)) (tptp.hAPP _let_1 tptp.nat _let_3 B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_card X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 B_2)) (tptp.hAPP _let_1 tptp.nat _let_2 A_3))) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) A_3)) (=> (forall ((M_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) M_3) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) M_3)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) A_3)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)))) (= (tptp.one_one tptp.nat) _let_1)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_3) _let_1)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.real tptp.arctan X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1)) (tptp.hAPP tptp.real tptp.real tptp.arctan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) X) (tptp.hAPP tptp.real tptp.real _let_3 (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real _let_3 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))))))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.member X_a) A_3) (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) C_2))) (not (forall ((X_4 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.member X_a) A_3) X_4)) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_4) C_2)))))))))))) (forall ((Ma $$unsorted) (No_1 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real F N_2)) (tptp.hAPP tptp.nat tptp.real F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real F Ma)) (tptp.hAPP tptp.nat tptp.real F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) No_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.arctan X)) (tptp.hAPP tptp.real tptp.real tptp.arctan Y))))))) (= (tptp.hAPP tptp.real tptp.real tptp.arctan _let_37) _let_37) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.arctan X)) (tptp.hAPP tptp.real tptp.real tptp.arctan Y))))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) N)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) N)))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.ord X_a) (tptp.real_normed_vector X_b)) (forall ((X_3 $$unsorted) (M_1 $$unsorted)) (=> (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) M_1) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP X_a X_b X_3 M_1)) (tptp.hAPP X_a X_b X_3 N_2)))) (tptp.one_one tptp.real))))) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_b))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) M_1) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_b tptp.real _let_1 (tptp.hAPP X_a X_b X_3 N_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP X_b tptp.real _let_1 (tptp.hAPP X_a X_b X_3 M_1)))))))))))) (forall ((Y $$unsorted) (X $$unsorted) (U $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.ord_less tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.inverse_divide tptp.real) U) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1))))) (let ((_let_9 (tptp.abs_abs tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real _let_9 X)) _let_8)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real _let_9 Y)) _let_8)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 X) _let_2)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 Y) _let_2)))) U)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.inverse_divide tptp.real) X) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1)))))) (tptp.one_one tptp.real)))))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) N)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Ma $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) Ma))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) K))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 K))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Ma $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) Ma)) K)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Ma) K)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((L_4 $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (=> (= (tptp.hAPP X_a X_a _let_1 L_4) (tptp.hAPP X_a X_a _let_1 K_4)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) L_4) K_4))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.inverse_divide X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N))) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_2) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.ordere142940540dd_abs X_a) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.linordered_idom X_a) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 _let_3) _let_3) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((R_4 $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) R_4) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) R_4))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) A_1))) (= (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) A_1)) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_2)) _let_1)) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_2))) (not (= (tptp.ti X_a A_2) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) A_1)) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (let ((_let_4 (tptp.hAPP X_a X_a _let_3 B))) (let ((_let_5 (tptp.hAPP X_a X_a _let_3 A_1))) (let ((_let_6 (tptp.ord_less X_a))) (let ((_let_7 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 _let_6 _let_5) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 _let_6 _let_4) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 _let_5) _let_4)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.inverse_divide X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) X) X)) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X))) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor _let_37) _let_40) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X)) (tptp.hAPP tptp.real tptp.nat tptp.natfloor Y))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) N))) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor _let_136) _let_179) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ring_abs X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.zero_zero X_a))) (let ((_let_5 (tptp.ord_less_eq X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (let ((_let_7 (tptp.hAPP X_a _let_6 _let_5 _let_4))) (=> (and (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_7 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_6 _let_5 A_1) _let_4))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_7 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_6 _let_5 B) _let_4)))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) X)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) X) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (let ((_let_4 (tptp.plus_plus X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 C) D)))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_4 (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) C))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.minus_minus X_a) A_1) B))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (A_2 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.minus_minus X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_4 X_1) A_2))) R_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_4 A_2) R_1)) X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_2) R_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) Y)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X)) Y) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y)))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)) (tptp.one_one X_a)))) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling _let_37) _let_40) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X)) (tptp.hAPP tptp.real tptp.nat tptp.natceiling Y))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) N))) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling _let_136) _let_179) (forall ((X $$unsorted) (Y $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.abs_abs tptp.real))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 C) _let_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) C) (tptp.hAPP tptp.real tptp.real _let_2 Y)))) (= X _let_1)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.real_n2089651433ebra_1 X_a)) (forall ((W $$unsorted)) (= (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W)) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) W)))))) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X)) (tptp.one_one tptp.real))) X)))) (forall ((U $$unsorted) (V $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.abs_abs tptp.real))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (= X Y) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real _let_2 U)) V)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) U)) Y))) V))))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor X) (tptp.zero_zero tptp.nat)))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((N $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)) N)) (tptp.one_one X_a))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP X_a tptp.real _let_1 A_1)) (tptp.hAPP X_a tptp.real _let_1 B)))) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_1) B)))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling X) (tptp.zero_zero tptp.nat)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)) _let_1) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)))))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.one_one tptp.real)) X_1)))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X_1)) (tptp.one_one tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X_1) (tptp.one_one tptp.real))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor A_1)) (tptp.hAPP tptp.real tptp.nat tptp.natfloor B))) (tptp.hAPP tptp.real tptp.nat tptp.natfloor (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) A_1) B)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) _let_1))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) (tptp.one_one tptp.real))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X)) (tptp.one_one tptp.nat))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) Y)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.one_one tptp.real))) (let ((_let_3 (tptp.plus_plus tptp.real))) (let ((_let_4 (tptp.abs_abs tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_4 X)) _let_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real _let_4 Y)) _let_2)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_3 (tptp.hAPP tptp.real tptp.real tptp.arctan X)) (tptp.hAPP tptp.real tptp.real tptp.arctan Y)) (tptp.hAPP tptp.real tptp.real tptp.arctan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_3 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) _let_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) X) Y))))))))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) (tptp.one_one tptp.real))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X)) (tptp.one_one tptp.nat))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) N_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) N_1)) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N_1)) X_1)))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) N_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X_1)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) N_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N_1))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) B)) (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) Y_2))) D_3)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_1) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y_2) B)))))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) B)) (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) Y_2))) D_3)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_1) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y_2) B)))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.one_one tptp.real))) (let ((_let_5 (tptp.abs_abs tptp.real))) (let ((_let_6 (tptp.ord_less_eq tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real _let_5 X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) _let_4) _let_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.plus_plus tptp.real) _let_4) X))) X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.times_times tptp.real) _let_2) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1)))))))))))))) (= _let_189 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_33 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_33 _let_132 _let_188) (tptp.hAPP tptp.real tptp.real tptp.arctan (tptp.hAPP tptp.real tptp.real _let_137 (tptp.hAPP tptp.int tptp.real _let_30 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_4)))))) (tptp.hAPP tptp.real tptp.real tptp.arctan (tptp.hAPP tptp.real tptp.real _let_137 (tptp.hAPP tptp.int tptp.real _let_30 (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_20))))))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2))) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_a $$unsorted) (B_2 $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)))))))) (not (= tptp.pi _let_37)) (forall ((M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) M))) (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) _let_1) _let_1))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.dvd_dvd tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 B) A_1)) (= (tptp.hAPP tptp.int tptp.int _let_1 A_1) (tptp.hAPP tptp.int tptp.int _let_1 B)))))))) (forall ((D $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) D)) D))) (forall ((D $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) D)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.abs_abs tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) M) N)) _let_1) (= (tptp.hAPP tptp.int tptp.int _let_2 M) _let_1))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_130 tptp.pi)) (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_243 _let_37))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_242 tptp.pi)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) X_1) _let_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X_1) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X))) (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.ln X)) X)))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y_1)) (= (= (tptp.hAPP tptp.real tptp.real tptp.ln X_1) (tptp.hAPP tptp.real tptp.real tptp.ln Y_1)) (= X_1 Y_1)))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 Y_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.ln X_1)) (tptp.hAPP tptp.real tptp.real tptp.ln Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.div_div tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) Y) X)) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 X) Y)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 X)) (tptp.hAPP tptp.int tptp.int _let_1 Y)))))))) (= (tptp.hAPP tptp.real tptp.real tptp.ln _let_136) _let_37) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (=> (= (tptp.hAPP tptp.real tptp.real tptp.ln X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) _let_1)) (= X _let_1))))) (forall ((Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) Z)) (tptp.one_one tptp.int))) (= (tptp.ti tptp.int Z) (tptp.zero_zero tptp.int)))) (forall ((D $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (not (= (tptp.ti tptp.int I_1) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.dvd_dvd tptp.int) D) I_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 D)) (tptp.hAPP tptp.int tptp.int _let_1 I_1)))))))) (forall ((X $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X)) N)))) (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) W) Z_1))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 W))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 Z_1)))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.ti tptp.int Z))) (let ((_let_2 (tptp.one_one tptp.int))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) Z) _let_2) (or (= _let_1 _let_2) (= _let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 Y_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.ln X_1)) (tptp.hAPP tptp.real tptp.real tptp.ln Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real tptp.ln X))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real tptp.ln X))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 (tptp.hAPP tptp.real tptp.real tptp.ln X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) X_1)))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_1) X_1)) (= (= (tptp.hAPP tptp.real tptp.real tptp.ln X_1) _let_1) (= X_1 (tptp.one_one tptp.real)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 _let_3) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.ln X_1)) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) (tptp.one_one tptp.real))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.ln X)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 (tptp.hAPP tptp.real tptp.real tptp.ln X))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) X)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)) (not (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)))))))))) (forall ((X_a $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_2))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_a $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) X_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) A_3))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_2))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) A_3)))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_2 (tptp.minus_minus _let_1) A_3) B_2) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_2 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) (tptp.hAPP _let_1 _let_1 _let_3 A_3))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_2 (tptp.combb tptp.bool tptp.bool X_a) tptp.fNot) (tptp.hAPP _let_1 _let_1 _let_3 B_2))))))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 _let_4) B_2) _let_4)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) (tptp.one_one tptp.real))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X_1)) N_1))) (or (not (= (tptp.ti tptp.int X_1) _let_1)) (= N_1 (tptp.zero_zero tptp.nat)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.abs_abs tptp.int))) (let ((_let_3 (tptp.power_power tptp.int))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 X) _let_1)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 X)) _let_1))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (=> (not (= (tptp.ti tptp.int Ma) (tptp.zero_zero tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) Ma) N_1)) Ma)) (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) N_1) (tptp.one_one tptp.int))))) (forall ((Z $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) Z) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) Z))) Ma)))) (forall ((Ma $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Ma)) Z)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) Ma) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) Z)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)))))))) (forall ((X_a $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP _let_1 _let_3 _let_2 A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_4 C_2))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 _let_3) (tptp.hAPP tptp.real tptp.real tptp.ln X))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_3) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) X)))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_3) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 _let_3) (tptp.hAPP tptp.real tptp.real tptp.ln X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) X_1)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 Y)) (= (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln X)) (tptp.hAPP tptp.real tptp.real tptp.ln Y)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.one_one tptp.real)) X))) X)))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 Y)) (= (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln X)) (tptp.hAPP tptp.real tptp.real tptp.ln Y)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.one_one tptp.real)) X))) X))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.power_power tptp.int))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (= (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 A_2) _let_2) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 B_1) _let_2)) (= (tptp.hAPP tptp.int tptp.int _let_1 A_2) (tptp.hAPP tptp.int tptp.int _let_1 B_1)))))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.abs_abs tptp.int))) (let ((_let_3 (tptp.power_power tptp.int))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 A_1) _let_1)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 A_1)) _let_1))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_55 _let_125 _let_31) tptp.pi)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_243 _let_188)) (not (= _let_35 _let_31)) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) A_1) _let_1)))) (forall ((X $$unsorted) (Z_1 $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.zero_zero tptp.int)) D)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 Z_1))) (tptp.one_one tptp.int))) D))) Z_1)))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.zero_zero tptp.int)) D)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 Z_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X) Z_1))) (tptp.one_one tptp.int))) D)))))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_55 _let_125 _let_35) _let_31)) (not (= _let_35 _let_37)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_55 _let_240 _let_35) _let_31)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_130 _let_35)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_242 _let_35)) (forall ((Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real tptp.arctan Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (= (tptp.hAPP tptp.real tptp.real tptp.arctan _let_136) _let_189) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)) A_3)))) (forall ((X_a $$unsorted) (D_2 $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted) (C_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_3) C_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 D_2) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_2) D_2))))))))))) (forall ((X_a $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.minus_minus _let_1))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.ord_less_eq _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_5 _let_4 B_2) C_2)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 B_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_3 _let_2 C_2) A_3)) (tptp.ti _let_1 A_3)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) X) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) _let_1) X))))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (not (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (or (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)))))) (forall ((X_a $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 _let_2 (tptp.ord_less _let_1) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) B_2) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 C_2)))))))) (forall ((X_a $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) C_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) C_2)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) _let_1) X))) X))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) tptp.zOdd)) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) Y_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 N_2) X_1))))) X_1))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) X)) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 N_2) X))))) X))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.one_one tptp.real))) (let ((_let_5 (tptp.ord_less_eq tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) _let_4) _let_2))) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 X) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.plus_plus tptp.real) _let_4) X))) X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.times_times tptp.real) _let_2) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1)))))))))))))) (forall ((K $$unsorted) (F $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) (tptp.one_one tptp.nat)))) (tptp.hAPP tptp.nat tptp.int F I_2)))) (tptp.one_one tptp.int))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int F (tptp.zero_zero tptp.nat))) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) (tptp.hAPP tptp.nat tptp.int F N_1))) (exists ((I_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) N_1)) (= (tptp.hAPP tptp.nat tptp.int F I_2) (tptp.ti tptp.int K)))))))))) (forall ((K $$unsorted) (F $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) I_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) (tptp.one_one tptp.nat)))) (tptp.hAPP tptp.nat tptp.int F I_2)))) (tptp.one_one tptp.int))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int F (tptp.zero_zero tptp.nat))) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) (tptp.hAPP tptp.nat tptp.int F N_1))) (exists ((I_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) N_1)) (= (tptp.hAPP tptp.nat tptp.int F I_2) (tptp.ti tptp.int K)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) (tptp.hAPP X_a X_a _let_1 A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (A_6 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.div_mod X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_6) B)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_6)) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (= (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X)) (tptp.hAPP X_a tptp.real _let_1 X)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) (tptp.hAPP X_a X_a _let_1 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) (tptp.hAPP X_a X_a _let_1 A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_2)) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B_1)) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_1)) (tptp.hAPP X_a X_a _let_3 A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X)) Y) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.inverse_divide X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_1))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.ti X_a A_2))) (= (= (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2) _let_1) (= _let_1 (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.ti X_a A_2))) (= (= _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) (= _let_1 (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) (= _let_1 (tptp.ti X_a A_2))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.group_add X_a) (= (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) (tptp.hAPP X_a X_a _let_1 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B_1) (tptp.hAPP X_a X_a _let_1 A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_2)) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B_1)) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B_1)) (tptp.hAPP X_a X_a _let_3 A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 A_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.idom X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ti X_a A_2))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_2) A_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 B_1) B_1)) (or (= _let_1 (tptp.ti X_a B_1)) (= _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) B_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X)) Y) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) B) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Xa_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) Xa_1))) (let ((_let_2 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 X)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1))) (let ((_let_2 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W)) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.int X_a _let_1 W))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (= (tptp.ti X_a A_2) (tptp.hAPP X_a X_a _let_1 B_1)) (= (tptp.ti X_a B_1) (tptp.hAPP X_a X_a _let_1 A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (= (tptp.hAPP X_a X_a _let_1 A_2) (tptp.ti X_a B_1)) (= (tptp.hAPP X_a X_a _let_1 B_1) (tptp.ti X_a A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (= (tptp.hAPP X_a X_a _let_1 A_2) (tptp.hAPP X_a X_a _let_1 B_1)) (= (tptp.ti X_a A_2) (tptp.ti X_a B_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.int X_a _let_1 W))) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W))) Z_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) X_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) Y_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X_1)) Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.ti X_a B))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) B)) (tptp.ti X_a B))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.arctan (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.arctan X))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_2))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.zero_zero X_a)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_2))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.zero_zero X_a)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X_1) Y_1) (tptp.zero_zero X_a)) (= (tptp.ti X_a Y_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (= (tptp.ti X_a A_2) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) B_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) A_1) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) A_1) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_1) B) (tptp.zero_zero X_a)) (= (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1) (tptp.ti X_a B)))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.zero_zero X_a)) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP X_a X_a _let_1 (tptp.one_one X_a))) X)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ti X_a X_1))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X_1) X_1) _let_1) (or (= _let_2 _let_1) (= _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) X) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) X) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) B)))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.group_add X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.minus_minus X_a) A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_1))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (=> (not (= (tptp.ti X_a B) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_2)) B_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1)) B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_2)) B_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) B_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.abs_abs X_a))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) N)) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.div_div X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) Y) X)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X)) Y) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_div X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.div_div X_a) X))) (let ((_let_2 (tptp.uminus_uminus X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) Y) X)) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 Y))))))))) (forall ((U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 U) U))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 X) X)))))) (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X_1) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) A_2)) (tptp.zero_zero tptp.real)) (= X_1 A_2))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X_1) Y_1) (tptp.zero_zero tptp.real)) (= Y_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X_1)))) (forall ((X_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X_1)) R_1)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) R_1)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) R_1))))))) (forall ((R_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) R_4) S_3) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) R_4) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) S_3))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) X) Y) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.real))) (let ((_let_2 (tptp.plus_plus tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.abs_abs tptp.real))) (= (tptp.hAPP tptp.real tptp.real _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) (tptp.hAPP tptp.real tptp.real _let_1 Y))) (tptp.hAPP tptp.real tptp.real _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) (tptp.hAPP tptp.real tptp.real _let_1 X))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1))) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) N) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 (tptp.one_one X_a))) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 A_1) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.abs_if X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.zero_zero X_a))))) (and (=> _let_2 (= _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1))) (=> (not _let_2) (= _let_1 (tptp.ti X_a A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.idom X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ti X_a X_1))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (let ((_let_3 (tptp.power_power X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (= (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 X_1) _let_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_4 _let_3 Y_1) _let_2)) (or (= _let_1 (tptp.ti X_a Y_1)) (= _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) Y_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)) Z_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) Z_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.one_one X_a))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.number_ring X_a)) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) X) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X_1) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X_1)) Y_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X_1) Y_1)) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y_1) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X_1))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X_1) Y_1)) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y_1) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X_1))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X_1) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X_1)) Y_1)))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) A_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) A_1) (tptp.zero_zero tptp.real))))) (and (=> _let_2 (= _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) A_1))) (=> (not _let_2) (= _let_1 A_1)))))) (forall ((R_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) R_4))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) R_4) (tptp.zero_zero tptp.real))))) (and (=> _let_2 (= _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) R_4))) (=> (not _let_2) (= _let_1 R_4)))))) (forall ((X $$unsorted) (Y $$unsorted) (L_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real _let_1 M))) (let ((_let_3 (tptp.plus_plus tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.abs_abs tptp.real))) (let ((_let_6 (tptp.hAPP tptp.real tptp.real _let_1 L_4))) (let ((_let_7 (tptp.hAPP tptp.real _let_4 _let_3 X))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real _let_7 Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 _let_6) _let_2)))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real _let_5 (tptp.hAPP tptp.real tptp.real _let_7 _let_6))) (tptp.hAPP tptp.real tptp.real _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 Y) _let_2))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.linordered_idom X_a)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) X))) (let ((_let_2 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) _let_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1) (tptp.zero_zero X_a))))) (and (=> _let_3 (= _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) _let_1))) (=> (not _let_3) (= _let_2 _let_1))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.number_ring X_a)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)) X) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.one_one X_a)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) _let_1) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_11004092258visors X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ti X_a A_2))) (= (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_2) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) _let_1) (or (= _let_2 _let_1) (= _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_1)) _let_1) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)))))))) (forall ((U $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 U) _let_1))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.ord_less tptp.real) X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) _let_1) X))) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) _let_1) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) X) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.ln _let_3) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) _let_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) X) _let_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) _let_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)) _let_1))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_55 _let_240 (tptp.hAPP tptp.real tptp.real _let_219 _let_237)) tptp.pi)) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.one_one X_a)))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N))) _let_1))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_55 _let_240 (tptp.hAPP tptp.real tptp.real _let_219 _let_35)) _let_37)) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real tptp.arctan Y))) (let ((_let_3 (tptp.ord_less tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) _let_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 _let_2) _let_1)))))))) (forall ((Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hAPP tptp.real tptp.real tptp.arctan Y)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.minus_minus tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_5 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_4))) (let ((_let_6 (tptp.ord_less_eq tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) _let_1) _let_5))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.times_times tptp.real) _let_5) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_4))))) (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 _let_1) X)))))))))))))) (forall ((K $$unsorted) (F $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) I_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) I_2) N_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.nat tptp.int F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) (tptp.one_one tptp.nat)))) (tptp.hAPP tptp.nat tptp.int F I_2)))) (tptp.one_one tptp.int)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int F Ma)) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 K) (tptp.hAPP tptp.nat tptp.int F N_1))) (exists ((I_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Ma) I_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 I_2) N_1)) (= (tptp.hAPP tptp.nat tptp.int F I_2) (tptp.ti tptp.int K))))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real tptp.arcsin Y))) (let ((_let_4 (tptp.ord_less tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.int tptp.real _let_1 tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 Y) (tptp.one_one tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_2)) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 _let_3) _let_2))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real tptp.arcsin Y))) (let ((_let_4 (tptp.ord_less_eq tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.int tptp.real _let_1 tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 Y) (tptp.one_one tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_2)) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 _let_3) _let_2))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real _let_1 tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hAPP tptp.real tptp.real tptp.arcsin Y))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real _let_1 tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.arcsin Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 N))) (tptp.hAPP tptp.nat tptp.int _let_1 M))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (tptp.hAPP tptp.nat tptp.int _let_1 M))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.uminus_uminus _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 A_3)) (tptp.hAPP _let_1 _let_1 _let_4 B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.uminus_uminus _let_1))) (let ((_let_3 (tptp.ord_less_eq _let_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_4 _let_3 (tptp.hAPP _let_1 _let_1 _let_2 B_2)) (tptp.hAPP _let_1 _let_1 _let_2 A_3))))))))) (= (tptp.hAPP tptp.int tptp.int _let_140 tptp.pls) tptp.pls) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int _let_1 K_4))))) (= (tptp.hAPP tptp.int tptp.int _let_140 _let_1) _let_1) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 Z_1)) W) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Z_1) W))))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.number_number_of tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int _let_2 W)) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int _let_1 W)))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 Z_1) W)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 Z_1)) (tptp.hAPP tptp.int tptp.int _let_1 W))))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int _let_1 Z_1)) (tptp.ti tptp.int Z_1)))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) B_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) Ma))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 Ma)))))) (forall ((D_1 $$unsorted) (Ta $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 D_1) Ta)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) D_1)) Ta)))))) (forall ((D_1 $$unsorted) (Ta $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Ta)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) Ta)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.div_div tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 A_1) (tptp.hAPP tptp.int tptp.int _let_1 B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 A_1)) B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_div tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 A_1)) (tptp.hAPP tptp.int tptp.int _let_3 B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.div_mod tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 A_1) (tptp.hAPP tptp.int tptp.int _let_1 B)) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 A_1)) B))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 A_1)) (tptp.hAPP tptp.int tptp.int _let_3 B)) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B))))))) (forall ((X $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.div_mod tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 X) M))) M) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 X)) M)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) X_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.complex tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_1 (tptp.minus_minus tptp.complex) X) Y) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_1 (tptp.plus_plus tptp.complex) X) (tptp.hAPP tptp.complex tptp.complex (tptp.uminus_uminus tptp.complex) Y))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) Z_1)) Z_1) (tptp.zero_zero tptp.int))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.semiring_1_of_nat tptp.int))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_2 N_1)) (tptp.hAPP tptp.nat tptp.int _let_2 Ma)) (and (= N_1 _let_1) (= Ma _let_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 N)) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 M))))))) _let_241 (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.div_mod tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (=> (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) K_4)) L_4) _let_1)) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 K_4) L_4) _let_1))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) K_4))) (=> (not (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) L_4)) _let_1)) (not (= (tptp.hAPP tptp.int tptp.int _let_2 L_4) _let_1)))))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) tptp.min_1) K_4) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) K_4))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) Z_1) W) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) Z_1) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) Z_1) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) Z_1) W)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W)))))))) (= (tptp.hAPP tptp.int tptp.int _let_140 tptp.min_1) _let_3) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.nat tptp.int _let_2 N_1)) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int _let_2 Ma)))) (and (= N_1 _let_1) (= Ma _let_1)))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))) (tptp.zero_zero tptp.int)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))) (tptp.zero_zero tptp.nat))) (forall ((I_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) I_1))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) I_1) (tptp.zero_zero tptp.int))))) (and (=> _let_2 (= _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) I_1))) (=> (not _let_2) (= _let_1 (tptp.ti tptp.int I_1))))))) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.number_number_of tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 V)) (tptp.hAPP tptp.int tptp.int _let_2 W)) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) V) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) A_1))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_2 B))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) B)))) (let ((_let_5 (tptp.zero_zero tptp.int))) (let ((_let_6 (= _let_3 _let_5))) (and (=> _let_6 (= _let_4 _let_5)) (=> (not _let_6) (= _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) _let_3) B))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_mod tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) A_1)) B))) (let ((_let_5 (tptp.zero_zero tptp.int))) (let ((_let_6 (= _let_3 _let_5))) (and (=> _let_6 (= _let_4 _let_5)) (=> (not _let_6) (= _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) B) _let_3))))))))))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) A_1))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted) (C $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.minus_minus X_a) C) (tptp.hAPP tptp.int X_a _let_1 W))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W)))) C)))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (tptp.zero_zero tptp.int)))) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.int))) (let ((_let_3 (tptp.fun tptp.nat tptp.int))) (let ((_let_4 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_4 A_1)) _let_1) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 A_1) _let_1)))))))) (forall ((Z_4 $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Z_1) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) Z_1) Z_4)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 Z_1))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 Z_4))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) A_1))) (let ((_let_3 (tptp.uminus_uminus tptp.int))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_2 B)))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int _let_3 B)))) (let ((_let_6 (tptp.zero_zero tptp.int))) (let ((_let_7 (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) A_1) B) _let_6))) (=> (not (= (tptp.ti tptp.int B) _let_6)) (and (=> _let_7 (= _let_5 _let_4)) (=> (not _let_7) (= _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) _let_4) (tptp.one_one tptp.int)))))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.div_div tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.uminus_uminus tptp.int))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B)))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 A_1)) B))) (let ((_let_6 (tptp.zero_zero tptp.int))) (let ((_let_7 (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_mod tptp.int) A_1) B) _let_6))) (=> (not (= (tptp.ti tptp.int B) _let_6)) (and (=> _let_7 (= _let_5 _let_4)) (=> (not _let_7) (= _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) _let_4) (tptp.one_one tptp.int)))))))))))))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1))) (let ((_let_2 (tptp.power_power tptp.int))) (let ((_let_3 (tptp.fun tptp.nat tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_4 tptp.bool) (tptp.member tptp.int) X_1) tptp.zEven)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) A_2)) _let_1) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 A_2) _let_1))))))))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1))) (let ((_let_2 (tptp.power_power tptp.int))) (let ((_let_3 (tptp.fun tptp.nat tptp.int))) (let ((_let_4 (tptp.uminus_uminus tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_5 tptp.bool) (tptp.member tptp.int) X_1) tptp.zOdd)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_4 A_2)) _let_1) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 A_2) _let_1))))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Q_2 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.hAPP tptp.bool (tptp.fun tptp.int _let_2) (tptp.if tptp.int) (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.fequal tptp.int) R_1) _let_3)))) (let ((_let_5 (tptp.uminus_uminus tptp.int))) (let ((_let_6 (tptp.hAPP tptp.int tptp.int _let_5 Q_2))) (let ((_let_7 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_8 (tptp.product_prod tptp.int tptp.int))) (let ((_let_9 (tptp.fun tptp.int _let_8))) (let ((_let_10 (tptp.fun _let_8 tptp.bool))) (let ((_let_11 (tptp.fun tptp.int _let_10))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP tptp.int _let_10 (tptp.hAPP tptp.int _let_11 tptp.divmod_int_rel A_2) B_1) (tptp.hAPP tptp.int _let_8 (tptp.hAPP tptp.int _let_9 _let_7 Q_2) R_1))) (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP tptp.int _let_10 (tptp.hAPP tptp.int _let_11 tptp.divmod_int_rel (tptp.hAPP tptp.int tptp.int _let_5 A_2)) B_1) (tptp.hAPP tptp.int _let_8 (tptp.hAPP tptp.int _let_9 _let_7 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 _let_6) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 _let_6) (tptp.one_one tptp.int)))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 _let_3) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B_1) R_1)))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.int X_a _let_1 V)) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) W)))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X) (tptp.zero_zero tptp.int))) (exists ((N_2 $$unsorted)) (= (tptp.ti tptp.int X) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.inverse_divide tptp.real))) (=> (not (= X (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.arctan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_2 (tptp.one_one tptp.real)) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.sgn_sgn tptp.real) X)) tptp.pi)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (tptp.hAPP tptp.real tptp.real tptp.arctan X))))))) (forall ((X_a $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 B_2)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_2))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real tptp.arcsin X)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) _let_1) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.ln X)) X)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) _let_2 (tptp.combb tptp.bool tptp.bool X_a) tptp.fNot) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)) A_3))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.uminus_uminus _let_1))) (= (tptp.hAPP _let_1 _let_1 _let_2 (tptp.hAPP _let_1 _let_1 _let_2 A_3)) (tptp.ti _let_1 A_3))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.uminus_uminus _let_1))) (= (= (tptp.hAPP _let_1 _let_1 _let_2 A_3) (tptp.hAPP _let_1 _let_1 _let_2 B_2)) (= (tptp.ti _let_1 A_3) (tptp.ti _let_1 B_2)))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3))))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X)) (tptp.hAPP tptp.real tptp.real tptp.cos X))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.sgn_sgn X_a))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) X_1) _let_1) (= (tptp.ti X_a X_1) _let_1)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.real_normed_vector X_a) (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) A_2) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.sgn_if X_a) (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.real_n1866405975lgebra X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.sgn_sgn X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 X)) (tptp.hAPP X_a X_a _let_1 Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.sgn_sgn X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.real_n2089651433ebra_1 X_a) (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.sgn_sgn X_a))) (let ((_let_2 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 X)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 X)))))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real tptp.cos X)) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_37) _let_136) (forall ((X $$unsorted)) (not (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real tptp.arctan X)) (tptp.zero_zero tptp.real)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.sgn_sgn tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((K_4 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.abs_abs X_a) K_4) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) K_4) (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) K_4)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) X)) (tptp.hAPP X_a X_a (tptp.abs_abs X_a) X)) (tptp.ti X_a X))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) tptp.pi)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos X)) (tptp.hAPP tptp.real tptp.real tptp.cos Y))))))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) (tptp.hAPP tptp.real tptp.real tptp.cos X)))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real tptp.cos X))) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.real tptp.cos tptp.pi) _let_183) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) tptp.pi)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.cos X)))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real (tptp.sgn_sgn tptp.real) X) (tptp.one_one tptp.real)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) A_2) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) A_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) A_1)) (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) A_1) (tptp.one_one X_a)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 (tptp.zero_zero tptp.real)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 X) tptp.pi)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos X)) (tptp.hAPP tptp.real tptp.real tptp.cos Y)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) tptp.pi)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos Y)) (tptp.hAPP tptp.real tptp.real tptp.cos X))))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) X) (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.sgn_sgn tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real (tptp.sgn_sgn tptp.real) X))) (let ((_let_3 (tptp.zero_zero tptp.real))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_3) X)))) (let ((_let_5 (= X _let_3))) (and (=> _let_5 (= _let_2 _let_3)) (=> (not _let_5) (and (=> _let_4 (= _let_2 _let_1)) (=> (not _let_4) (= _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)))))))))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real (tptp.sgn_sgn tptp.real) A_1))) (let ((_let_3 (tptp.zero_zero tptp.real))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_3) A_1)))) (let ((_let_5 (= A_1 _let_3))) (and (=> _let_5 (= _let_2 _let_3)) (=> (not _let_5) (and (=> _let_4 (= _let_2 _let_1)) (=> (not _let_4) (= _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)))))))))))) (not (= _let_239 _let_37)) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (= (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) A_2) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.one_one X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_2) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) A_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.sgn_if X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) X))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_3) X)))) (let ((_let_5 (= (tptp.ti X_a X) _let_3))) (and (=> _let_5 (= _let_2 _let_3)) (=> (not _let_5) (and (=> _let_4 (= _let_2 _let_1)) (=> (not _let_4) (= _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) _let_1)))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) tptp.pi)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 X) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos Y)) (tptp.hAPP tptp.real tptp.real tptp.cos X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) X)))) (let ((_let_2 (= (tptp.ti X_a X) (tptp.zero_zero X_a)))) (and (=> _let_2 (= _let_1 (tptp.zero_zero tptp.real))) (=> (not _let_2) (= _let_1 (tptp.one_one tptp.real))))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_55 _let_125 _let_239) _let_37)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_55 _let_240 _let_239) _let_37)) (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_35) _let_37) (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_237) _let_136) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) tptp.pi))) (tptp.hAPP tptp.real tptp.real tptp.cos X)))) (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_235) _let_138) (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_236) _let_234) (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_189) _let_232) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) _let_1) X))) (tptp.one_one tptp.real))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 (tptp.hAPP tptp.real tptp.real tptp.cos X))))))))) (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_230) _let_37) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_3)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real tptp.cos X))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_3)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real tptp.cos X))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) (tptp.one_one tptp.real))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) tptp.pi)) (= (tptp.hAPP tptp.real tptp.real tptp.cos X_2) Y) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y_2) tptp.pi)) (= (tptp.hAPP tptp.real tptp.real tptp.cos Y_2) Y)) (= Y_2 X_2)))))))))))))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_2) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (= (tptp.hAPP tptp.real tptp.real tptp.cos X_2) _let_1) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y_2) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (= (tptp.hAPP tptp.real tptp.real tptp.cos Y_2) _let_1)) (= Y_2 X_2))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real tptp.tan X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1)))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real _let_4 X))) (let ((_let_6 (tptp.zero_zero tptp.real))) (=> (not (= (tptp.hAPP tptp.real tptp.real tptp.cos X) _let_6)) (=> (not (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_5) _let_6)) (= (tptp.hAPP tptp.real tptp.real tptp.tan _let_5) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real _let_4 _let_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.minus_minus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) _let_2) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1)))))))))))))) (forall ((X_5 $$unsorted) (Y_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.inverse_divide tptp.real) X_5) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X_5) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y_4) _let_1)))))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real tptp.arccos _let_5)) _let_5))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.tan (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.tan X))))) (= (tptp.hAPP tptp.real tptp.real tptp.tan _let_37) _let_37) (forall ((Y $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.tan (tptp.hAPP tptp.real tptp.real tptp.arctan Y)) Y)) (= (tptp.hAPP tptp.real tptp.real tptp.tan tptp.pi) _let_37) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.tan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) tptp.pi)) (tptp.hAPP tptp.real tptp.real tptp.tan X))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.tan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N)) tptp.pi))) (tptp.hAPP tptp.real tptp.real tptp.tan X)))) (forall ((I_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.sgn_sgn tptp.int) I_1))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_3) I_1)))) (let ((_let_5 (= (tptp.ti tptp.int I_1) _let_3))) (and (=> _let_5 (= _let_2 _let_3)) (=> (not _let_5) (and (=> _let_4 (= _let_2 _let_1)) (=> (not _let_4) (= _let_2 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) tptp.pi)) (= (tptp.hAPP tptp.real tptp.real tptp.arccos (tptp.hAPP tptp.real tptp.real tptp.cos X)) X)))))) (forall ((Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) Y)) (tptp.one_one tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real tptp.arccos Y)) Y))) (= (tptp.hAPP tptp.real tptp.real tptp.tan _let_235) _let_233) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real tptp.arccos Y)))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) (tptp.one_one tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real tptp.arccos Y)) Y)))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.arccos Y)) tptp.pi))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 tptp.pi)) X)) (= (tptp.hAPP tptp.real tptp.real tptp.arccos (tptp.hAPP tptp.real tptp.real tptp.cos X)) (tptp.hAPP tptp.real tptp.real _let_1 X)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.tan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) tptp.pi))) (tptp.hAPP tptp.real tptp.real tptp.tan X)))) (= (tptp.hAPP tptp.real tptp.real tptp.tan _let_189) _let_136) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.tan Y))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real tptp.tan X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.plus_plus tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 X) Y))) (let ((_let_6 (tptp.zero_zero tptp.real))) (=> (not (= (tptp.hAPP tptp.real tptp.real tptp.cos X) _let_6)) (=> (not (= (tptp.hAPP tptp.real tptp.real tptp.cos Y) _let_6)) (=> (not (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_5) _let_6)) (= (tptp.hAPP tptp.real tptp.real tptp.tan _let_5) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 _let_2) _let_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.minus_minus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.times_times tptp.real) _let_2) _let_1)))))))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.cos Y))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real tptp.cos X))) (let ((_let_3 (tptp.times_times tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.zero_zero tptp.real))) (=> (not (= _let_2 _let_5)) (=> (not (= _let_1 _let_5)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.minus_minus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real tptp.tan X)) (tptp.hAPP tptp.real tptp.real tptp.tan Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.plus_plus tptp.real) X) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 _let_2) _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 (tptp.hAPP tptp.real tptp.real tptp.tan X))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.arccos Y))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y) (tptp.one_one tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) tptp.pi))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_3)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.tan Y)) (tptp.hAPP tptp.real tptp.real tptp.tan X)))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 Y_1))) (let ((_let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_5 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_4)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_5 Y_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 _let_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_5 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) _let_4)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.tan Y_1)) (tptp.hAPP tptp.real tptp.real tptp.tan X_1)))))))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.arccos Y))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y) (tptp.one_one tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) tptp.pi))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.inverse_divide tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) (tptp.hAPP tptp.real tptp.real tptp.tan Y)) (tptp.hAPP tptp.real tptp.real tptp.tan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) Y)))))) (= (tptp.hAPP tptp.real tptp.real tptp.tan _let_236) (tptp.hAPP tptp.real tptp.real _let_137 _let_233)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) tptp.pi)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.tan X)) _let_1)))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.arctan Y))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_3 (tptp.ord_less tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_2)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 _let_1) _let_2)) (= (tptp.hAPP tptp.real tptp.real tptp.tan _let_1) Y))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.arctan (tptp.hAPP tptp.real tptp.real tptp.tan X)) X))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.arccos Y))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y) (tptp.one_one tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) tptp.pi)) (= (tptp.hAPP tptp.real tptp.real tptp.cos _let_1) Y)))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X)) (tptp.one_one tptp.real))) (exists ((Z_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) Z_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Z_2) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.tan Z_2) X)))))))) (forall ((Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) Y)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) X_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (= (tptp.hAPP tptp.real tptp.real tptp.tan X_2) Y)))))) (forall ((Y $$unsorted)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_2) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.tan X_2) Y) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y_2) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.tan Y_2) Y)) (= Y_2 X_2)))))))))))) (forall ((Y $$unsorted)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_2) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.tan X_2) Y))))))) (forall ((Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Y)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) (tptp.hAPP tptp.real tptp.real tptp.tan X_2))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) _let_1) X))) (let ((_let_4 (tptp.inverse_divide tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_4 tptp.pi) _let_1))) (let ((_let_6 (tptp.ord_less tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_5)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 _let_6 X) _let_5)) (= (tptp.hAPP tptp.real tptp.real tptp.tan X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_4 (tptp.hAPP tptp.real tptp.real tptp.sin _let_3)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.cos _let_3)) (tptp.one_one tptp.real)))))))))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) tptp.pi) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1)) M))))) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1))) (tptp.zero_zero tptp.real))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real tptp.arccos X)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) _let_1) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) X))) (= (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) _let_1) _let_1))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.real _let_1 N_1) (tptp.hAPP tptp.nat tptp.real _let_1 Ma)) (= N_1 Ma)))) (= (tptp.hAPP tptp.real tptp.real tptp.sin _let_37) _let_37) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) N)) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) N)) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) tptp.pi) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))) (tptp.zero_zero tptp.real))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) tptp.pi)) (tptp.zero_zero tptp.real))) _let_238 _let_238 (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X)) (tptp.one_one tptp.real)))) (forall ((N_1 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1) (tptp.zero_zero tptp.real)) (= N_1 (tptp.zero_zero tptp.nat)))) (= (tptp.hAPP tptp.nat tptp.real _let_43 _let_40) _let_37) (forall ((N $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) (tptp.zero_zero tptp.real))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N_1)) (tptp.hAPP tptp.nat tptp.real _let_1 Ma))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) Ma))))) (= (tptp.hAPP tptp.real tptp.real tptp.sin tptp.pi) _let_37) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N_1)) (tptp.hAPP tptp.nat tptp.real _let_1 Ma))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) Ma))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 M)) (tptp.hAPP tptp.nat tptp.real _let_1 N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) M) N)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 M)) (tptp.hAPP tptp.nat tptp.real _let_1 N))))) (= (tptp.hAPP tptp.nat tptp.real _let_43 _let_179) _let_136) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 M)) N) (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 M)) N)))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) tptp.pi)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 (tptp.hAPP tptp.real tptp.real tptp.sin X))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) tptp.pi)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 (tptp.hAPP tptp.real tptp.real tptp.sin X))))))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) (tptp.zero_zero tptp.real))) (= N_1 (tptp.zero_zero tptp.nat)))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) (tptp.hAPP tptp.real tptp.real tptp.sin X)))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N))))) (forall ((X $$unsorted)) (=> (= (tptp.hAPP tptp.real tptp.real tptp.cos X) (tptp.one_one tptp.real)) (= (tptp.hAPP tptp.real tptp.real tptp.sin X) (tptp.zero_zero tptp.real)))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X))) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.nat tptp.real _let_43 _let_206) _let_136) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.plus_plus tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_3 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin X)) (tptp.hAPP tptp.real tptp.real tptp.cos Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos X)) (tptp.hAPP tptp.real tptp.real tptp.sin Y)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.minus_minus tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_3 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos Y)) (tptp.hAPP tptp.real tptp.real tptp.sin X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin Y)) (tptp.hAPP tptp.real tptp.real tptp.cos X)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.minus_minus tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_3 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin X)) (tptp.hAPP tptp.real tptp.real tptp.cos Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos X)) (tptp.hAPP tptp.real tptp.real tptp.sin Y)))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N)) (tptp.one_one tptp.real))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) tptp.pi) X)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X)))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) tptp.pi)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X)))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) M) N)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 M)) (tptp.hAPP tptp.nat tptp.real _let_1 N)))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) N) X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N)) (tptp.hAPP tptp.nat tptp.real _let_1 X)))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.tan X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X)) (tptp.hAPP tptp.real tptp.real tptp.cos X)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X))) X)))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) X)) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X) (tptp.hAPP tptp.real tptp.nat tptp.natfloor A_1))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) A_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X)) A_1)))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))) tptp.pi)) (tptp.zero_zero tptp.real))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.nat tptp.natfloor X))) (=> (= X (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) _let_1)) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) _let_1) N))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.sin X))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.hAPP tptp.real tptp.real tptp.cos X))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 _let_4) _let_4)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 _let_1) _let_1)) (tptp.one_one tptp.real))))))) (forall ((X $$unsorted)) (=> (= (tptp.hAPP tptp.real tptp.real tptp.sin X) (tptp.zero_zero tptp.real)) (= (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real tptp.cos X)) (tptp.one_one tptp.real)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos Y)) (tptp.hAPP tptp.real tptp.real tptp.cos X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin Y)) (tptp.hAPP tptp.real tptp.real tptp.sin X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos X)) (tptp.hAPP tptp.real tptp.real tptp.cos Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin X)) (tptp.hAPP tptp.real tptp.real tptp.sin Y))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos X)) (tptp.hAPP tptp.real tptp.real tptp.cos Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin X)) (tptp.hAPP tptp.real tptp.real tptp.sin Y))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N_1)) (tptp.one_one tptp.real))) (tptp.hAPP tptp.nat tptp.real _let_1 Ma)))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 Ma)) (tptp.one_one tptp.real))))))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) A_2) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) A_2)) X_1))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.tan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) tptp.pi)) (tptp.zero_zero tptp.real))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X_1)) A_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) A_2)))))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X))) (tptp.one_one tptp.real))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.tan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) tptp.pi))) (tptp.hAPP tptp.real tptp.real tptp.tan X)))) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) _let_1) X)) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) _let_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X)) A_1))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) (tptp.one_one tptp.real))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) A_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) _let_1) X)) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) _let_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X)) A_1))))) (forall ((X $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.real_1 tptp.nat))) (let ((_let_3 (tptp.times_times tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.inverse_divide tptp.real))) (let ((_let_6 (tptp.hAPP tptp.real _let_4 (tptp.plus_plus tptp.real) X))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.nat tptp.real _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) tptp.pi)) _let_1))) (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.nat tptp.real _let_2 M)) tptp.pi)) _let_1))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((X_3 $$unsorted)) (= (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_a X_b X_3 N_2))) K_2))))) (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_a X_b X_3 N_2))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_3)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((X_3 $$unsorted)) (= (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_a X_b X_3 N_2))) K_2))))) (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_a X_b X_3 N_2))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_3)))))))))) (forall ((N $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) D)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.dvd_dvd tptp.nat) D) N)) (= (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) N) D)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N)) (tptp.hAPP tptp.nat tptp.real _let_1 D)))))))) (forall ((N $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) N)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) (tptp.hAPP tptp.real tptp.real tptp.ln X))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) X) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X)) N)))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N)) (tptp.hAPP tptp.nat tptp.real _let_1 X))) (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) N) X)))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (and (=> _let_2 (= _let_1 (tptp.zero_zero tptp.real))) (=> (not _let_2) (= _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) V))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N)) (tptp.hAPP tptp.nat tptp.real _let_1 X))) (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) N) X)))) (tptp.one_one tptp.real)))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) A_1))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X)) A_1)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) (tptp.one_one tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real tptp.arcsin Y)) Y)))))) (forall ((Z_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor Z_1)) (tptp.one_one tptp.nat))) N)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) Z_1) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) _let_1) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor X) N)))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) A_1))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natceiling X)) A_1)))) (forall ((X $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.real_1 tptp.nat))) (let ((_let_3 (tptp.times_times tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.inverse_divide tptp.real))) (let ((_let_6 (tptp.hAPP tptp.real _let_4 (tptp.plus_plus tptp.real) X))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.nat tptp.real _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) tptp.pi)) _let_1))) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.nat tptp.real _let_2 M)) tptp.pi)) _let_1)))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 (tptp.hAPP tptp.real tptp.real tptp.sin X))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.real))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_2)) N)))) tptp.pi)) (tptp.hAPP tptp.int tptp.real _let_1 _let_2))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 tptp.min_1)) N)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real _let_3 X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 (tptp.hAPP tptp.real tptp.real tptp.sin X))) (tptp.hAPP tptp.real tptp.real tptp.cos X))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.plus_plus tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.ord_less_eq tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.zero_zero tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) X)) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) N)))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.cos Y))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real tptp.cos X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.plus_plus tptp.real))) (let ((_let_5 (tptp.zero_zero tptp.real))) (=> (not (= _let_2 _let_5)) (=> (not (= _let_1 _let_5)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 (tptp.hAPP tptp.real tptp.real tptp.tan X)) (tptp.hAPP tptp.real tptp.real tptp.tan Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 X) Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.times_times tptp.real) _let_2) _let_1))))))))))) (forall ((X $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.real _let_1 D))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.inverse_divide tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) D)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real _let_1 X)) _let_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.div_div tptp.nat) X) D))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.div_mod tptp.nat) X) D))) _let_2)))))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) tptp.pi)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) N))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) tptp.pi) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) N))) (= (tptp.hAPP tptp.real tptp.real tptp.sin _let_237) _let_37) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) tptp.pi))) (tptp.hAPP tptp.real tptp.real tptp.sin X)))) (= (tptp.hAPP tptp.real tptp.real tptp.sin _let_35) _let_136) (= (tptp.hAPP tptp.real tptp.real tptp.sin _let_236) _let_138) (= (tptp.hAPP tptp.real tptp.real tptp.sin _let_235) _let_234) (= (tptp.hAPP tptp.real tptp.real tptp.sin _let_189) _let_232) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.real_1 tptp.nat))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real _let_2 N)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1)) (tptp.hAPP tptp.nat tptp.real _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1)) N)))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.one_one tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Y)) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) X) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) Y))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) (tptp.hAPP tptp.real tptp.nat tptp.natfloor X)) Y))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) _let_1) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling X) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 (tptp.hAPP tptp.real tptp.real tptp.sin X))))))))) (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real _let_4 (tptp.times_times tptp.real) R_4))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_5 (tptp.hAPP tptp.real tptp.real tptp.cos A_1))) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_5 (tptp.hAPP tptp.real tptp.real tptp.sin A_1))) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 R_4) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sin X)) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.cos X)) _let_1)) (tptp.one_one tptp.real)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.cos X)) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sin X)) _let_1)) (tptp.one_one tptp.real)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sin X)) _let_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.cos X)) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.cos X)) _let_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sin X)) _let_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_3)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin Y)) (tptp.hAPP tptp.real tptp.real tptp.sin X)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos X) (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sin X) (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) X))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))) tptp.pi)) (tptp.one_one tptp.real))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) tptp.pi)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.sin X)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1)) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real tptp.cos X)) _let_2)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real tptp.sin X)) _let_2))))))))) (= (tptp.hAPP tptp.real tptp.real tptp.sin _let_230) _let_220) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X)) (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.arcsin (tptp.hAPP tptp.real tptp.real tptp.sin X)) X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real tptp.sin Y))) (let ((_let_3 (tptp.times_times tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real tptp.sin X)))) (let ((_let_6 (tptp.hAPP tptp.real tptp.real tptp.cos Y))) (let ((_let_7 (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real tptp.cos X)))) (let ((_let_8 (tptp.minus_minus tptp.real))) (let ((_let_9 (tptp.plus_plus tptp.real))) (let ((_let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_9 X) Y))) (let ((_let_11 (tptp.power_power tptp.real))) (let ((_let_12 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_9 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_12 _let_11 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_8 (tptp.hAPP tptp.real tptp.real tptp.sin _let_10)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_9 (tptp.hAPP tptp.real tptp.real _let_5 _let_6)) (tptp.hAPP tptp.real tptp.real _let_7 _let_2)))) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_12 _let_11 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_8 (tptp.hAPP tptp.real tptp.real tptp.cos _let_10)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_8 (tptp.hAPP tptp.real tptp.real _let_7 _let_6)) (tptp.hAPP tptp.real tptp.real _let_5 _let_2)))) _let_1)) (tptp.zero_zero tptp.real))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.power_power tptp.real))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (let ((_let_6 (tptp.plus_plus tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_6 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_6 (tptp.hAPP tptp.real tptp.real tptp.sin _let_2)) (tptp.hAPP tptp.real tptp.real tptp.sin X))) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.cos _let_2)) (tptp.hAPP tptp.real tptp.real tptp.cos X))) _let_1)) (tptp.zero_zero tptp.real))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) Y)) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real tptp.arccos Y)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) _let_1) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) Y) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.arcsin Y))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.number_number_of tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real _let_4 tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y) (tptp.one_one tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real _let_4 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) tptp.pi)) (= (tptp.hAPP tptp.real tptp.real tptp.sin _let_1) Y))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.arcsin Y))) (let ((_let_2 (tptp.number_number_of tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_4 (tptp.ord_less_eq tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.int tptp.real _let_2 tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 Y) (tptp.one_one tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_3)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 _let_1) _let_3)) (= (tptp.hAPP tptp.real tptp.real tptp.sin _let_1) Y)))))))))) (forall ((X_5 $$unsorted) (Y_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.inverse_divide tptp.real) X_5) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X_5) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y_4) _let_1)))))) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real tptp.arccos _let_5)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.minus_minus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 _let_5) _let_1)))))))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y) (tptp.one_one tptp.real))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_2) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.sin X_2) Y) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_1)) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 Y_2) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.sin Y_2) Y)) (= Y_2 X_2)))))))))))))))) (forall ((R_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) R_4)) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_2) (tptp.one_one tptp.nat)))) R_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) R_4) (tptp.hAPP tptp.nat tptp.real _let_1 N_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_1) Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) _let_1) X)) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.nat tptp.real _let_1 N_2)) Y)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.ord_less tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) Y)))))))))))))) (forall ((R_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) R_4)) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N_2)) R_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) R_4) (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (forall ((Y_2 $$unsorted)) (exists ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) Y_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_2)) X))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) N) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 _let_1) N)) _let_1))))))) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.real tptp.sin X_1) (tptp.zero_zero tptp.real)) (or (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_2)) (= X_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_2)) (= X_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.real tptp.cos X_1) (tptp.zero_zero tptp.real)) (or (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (and (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_2))) (= X_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (and (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_2))) (= X_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.nat))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) N_1)))) (not (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma))) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) N_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.nat))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 X_1)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) X_1) Y_1))) (or (and _let_3 _let_2) (and (not _let_3) (not _let_2)))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_228 _let_40)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc X_1))) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 X_1)))))) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_228 _let_179))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) X_1) Y_1))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y_1)))))) (forall ((N $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)) (tptp.zero_zero tptp.real)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 Y) N)))))))))))) (forall ((N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) N))) (let ((_let_4 (tptp.uminus_uminus X_a))) (let ((_let_5 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_4 X)) N))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N)))) (and (=> _let_6 (= _let_5 _let_3)) (=> (not _let_6) (= _let_5 (tptp.hAPP X_a X_a _let_4 _let_3))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X)) N) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X)) N) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) N)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) X)) N) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) N)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.nat))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y_1)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 X_1)))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) X_1) Y_1))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X_1) Y_1)) (and _let_3 _let_2) (and (not _let_3) (not _let_2)))))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X_1)))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) X_1))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X_1) N_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X_1)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.monoid_mult X_a) (tptp.linordered_ring X_a)) (forall ((X $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X) N))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_2) N_1))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X_1) N_1))) (or _let_2 (and (not _let_2) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X_1) N_1)) _let_1)) (and (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) _let_1))) (let ((_let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_2) X))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X)))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 _let_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) _let_1)) X) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_ring_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.one_one X_a)))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) X) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.abs_abs X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a _let_5 X)) (tptp.hAPP X_a X_a _let_5 Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 X) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 Y) N))))))))))))) (forall ((X_1 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X_1))) (exists ((Y_2 $$unsorted)) (= X_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) Y_2)))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X_1)) (exists ((Y_2 $$unsorted)) (= X_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) Y_2))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) X) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) W))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) _let_1)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.abs_abs X_a) X)) _let_1) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 X) _let_1))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (let ((_let_2 (tptp.div_div tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc X)) _let_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 X) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (let ((_let_2 (tptp.div_div tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc X)) _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 X) _let_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) X) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1)) _let_1)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) X) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) _let_1)))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) X_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1)) _let_1)))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) X_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))) _let_1)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X_1) Y_1))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Y_1)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc M))) (let ((_let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 _let_4) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) _let_4)) (= (tptp.hAPP tptp.nat tptp.nat _let_3 _let_5) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) _let_5) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1)))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X_1) N_1)) _let_1)) (and (not (= N_1 (tptp.zero_zero tptp.nat))) (or (and (not _let_2) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 X_1) _let_1))) (and _let_2 (= (tptp.ti X_a X_1) _let_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X_1) N_1))) (or (= N_1 (tptp.zero_zero tptp.nat)) (and _let_3 (not (= (tptp.ti X_a X_1) _let_1))) (and (not _let_3) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) W_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) _let_2)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X_1) _let_2))) (or _let_3 (and (not _let_3) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) W_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X_1) _let_4)) _let_1)) (and (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) _let_4))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X_1) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X)) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)) X) (tptp.one_one X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1))) (let ((_let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) X))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X)))) (and (=> _let_3 (= _let_2 (tptp.one_one X_a))) (=> (not _let_3) (= _let_2 _let_1))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.one_one tptp.nat))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X))) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.div_div tptp.nat) X) _let_1))) X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.div_div tptp.nat) X) _let_1)) X))))) (forall ((X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.even_odd_even tptp.int) X_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) W_1))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) _let_2)))) (let ((_let_4 (tptp.ord_less_eq X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X_1) _let_2)) _let_1)) (and (not (= _let_2 (tptp.zero_zero tptp.nat))) (or (and (not _let_3) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 _let_4 X_1) _let_1))) (and _let_3 (= (tptp.ti X_a X_1) _let_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((X_1 $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) W_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) _let_3)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) X_1) _let_3))) (or (= _let_3 (tptp.zero_zero tptp.nat)) (and _let_4 (not (= (tptp.ti X_a X_1) _let_1))) (and (not _let_4) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X_1)))))))))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N_1)))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) X_1)))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1)) (exists ((M_2 $$unsorted)) (= N_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M_2))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.even_odd_even tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) N_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))) (forall ((N_1 $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1))) (exists ((M_2 $$unsorted)) (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) M_2)))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.div_div tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat))) _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 N) _let_1))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.hAPP tptp.bool (tptp.fun tptp.real _let_5) (tptp.if tptp.real) (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1)) _let_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 (tptp.minus_minus tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N_1))))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 _let_1) N_1)) _let_1))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.div_div tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat))) _let_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 N) _let_1)))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) (let ((_let_3 (tptp.number_number_of tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 (tptp.div_mod tptp.nat) N) (tptp.hAPP tptp.int tptp.nat _let_3 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_2))) (tptp.hAPP tptp.int tptp.nat _let_3 (tptp.hAPP tptp.int tptp.int tptp.bit1 _let_1))) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))) (tptp.hAPP tptp.int tptp.nat _let_3 _let_2))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat))) (let ((_let_3 (tptp.one_one tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 (tptp.div_mod tptp.nat) N) (tptp.hAPP tptp.int tptp.nat _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) _let_3) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 (tptp.minus_minus tptp.nat) N) _let_3)) (tptp.hAPP tptp.int tptp.nat _let_2 _let_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) _let_1) X)) (=> (= (tptp.hAPP tptp.real tptp.real tptp.sin X) _let_1) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_2)) (= X (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) _let_1) X)) (=> (= (tptp.hAPP tptp.real tptp.real tptp.cos X) _let_1) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (and (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_2))) (= X (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))) (forall ((N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.power_power tptp.nat) N) (tptp.hAPP tptp.int tptp.nat _let_2 _let_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) X_2)) (tptp.one_one tptp.nat))))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.real tptp.sin_coeff X_2))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X_2)))) (and (=> _let_3 (= _let_2 (tptp.zero_zero tptp.real))) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) X_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) X_2)))))))))) (forall ((N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.number_number_of tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.power_power tptp.nat) N) (tptp.hAPP tptp.int tptp.nat _let_2 _let_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_2 (tptp.hAPP tptp.int tptp.int tptp.bit0 _let_1))) X_2)))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.real tptp.cos_coeff X_2))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) X_2)))) (and (=> _let_2 (= _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) X_2) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) X_2))))) (=> (not _let_2) (= _let_1 (tptp.zero_zero tptp.real))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 M) N))) (let ((_let_5 (tptp.hAPP tptp.nat tptp.nat _let_3 _let_4))) (let ((_let_6 (= M (tptp.zero_zero tptp.nat)))) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.nat tptp.nat _let_3 N))) (=> (not _let_6) (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) _let_4) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) (tptp.one_one tptp.nat))) N))))))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) M) N))) (let ((_let_4 (tptp.fact_fact tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat tptp.nat _let_4 _let_3))) (let ((_let_6 (= _let_3 (tptp.zero_zero tptp.nat)))) (and (=> _let_6 (= _let_5 _let_1)) (=> (not _let_6) (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) _let_3) (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) _let_3) _let_1))))))))))))) (forall ((N $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.nat))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 M)) (tptp.hAPP tptp.nat tptp.nat _let_1 N)))))))) (= (tptp.hAPP tptp.nat tptp.nat _let_227 _let_179) _let_179) (forall ((X_a $$unsorted)) (=> (tptp.semiring_char_0 X_a) (forall ((N $$unsorted)) (not (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)) (tptp.zero_zero X_a)))))) (= (tptp.hAPP tptp.nat tptp.nat _let_227 _let_40) _let_206) (= (tptp.hAPP tptp.nat tptp.nat _let_227 _let_206) _let_206) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.nat))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.zero_zero tptp.nat)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 M)) (tptp.hAPP tptp.nat tptp.nat _let_1 N))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc X))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 _let_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) _let_2) (tptp.hAPP tptp.nat tptp.nat _let_1 X)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) N) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (tptp.hAPP tptp.nat tptp.nat _let_1 M))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.one_one tptp.nat)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat)))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 _let_3) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) _let_3) (tptp.hAPP tptp.nat tptp.nat _let_1 N))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_1 N)) (tptp.hAPP tptp.nat tptp.nat _let_1 M)) (tptp.zero_zero tptp.nat))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 M))) (let ((_let_5 (= M (tptp.zero_zero tptp.nat)))) (and (=> _let_5 (= _let_4 _let_1)) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) M) _let_1)))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fact_fact tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.nat tptp.nat _let_2 N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) N) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1))) (let ((_let_3 (tptp.one_one tptp.real))) (let ((_let_4 (tptp.inverse_divide tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.power_power tptp.real))) (let ((_let_7 (tptp.fun tptp.nat tptp.real))) (let ((_let_8 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_9 (tptp.hAPP tptp.real _let_7 _let_6 X))) (let ((_let_10 (tptp.times_times tptp.real))) (let ((_let_11 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) _let_8))) (let ((_let_12 (tptp.ord_less_eq tptp.real))) (let ((_let_13 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_13 _let_12 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_13 _let_12 X) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_13 _let_12 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) _let_11)))) (tptp.hAPP tptp.nat tptp.real _let_9 _let_11))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.nat tptp.real _let_9 _let_8)) _let_2)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 _let_3) _let_2)) N)))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (= (tptp.hAPP tptp.int X_a _let_1 X_1) (tptp.one_one X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_1) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (= (tptp.one_one X_a) (tptp.hAPP tptp.int X_a _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) Y_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) X) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) _let_1) X)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.exp tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 Y)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (= (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) Y) X) (= (tptp.hAPP tptp.real tptp.real tptp.ln X) Y))) (forall ((U $$unsorted) (X $$unsorted)) (=> (= (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) U) X) (= (tptp.hAPP tptp.real tptp.real tptp.ln X) U))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X)) X)) (forall ((X_a $$unsorted)) (=> (and (tptp.divisi14063676e_zero X_a) (tptp.real_n1866405975lgebra X_a)) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (= (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP X_a tptp.real _let_1 A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n1866405975lgebra X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP X_a tptp.real _let_1 A_1)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.exp tptp.real))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 X_1)) (tptp.hAPP tptp.real tptp.real _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.exp tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 X)) (tptp.hAPP tptp.real tptp.real _let_3 Y))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X) Y))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.exp tptp.real))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 X_1)) (tptp.hAPP tptp.real tptp.real _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.hAPP X_a X_a _let_1 B))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (=> (tptp.division_ring X_a) (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (= (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) X_1) _let_1) (= (tptp.ti X_a X_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.divisi14063676e_zero X_a) (forall ((A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_inverse_zero X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (= (tptp.hAPP tptp.real tptp.real _let_84 _let_37) _let_37) (forall ((X_a $$unsorted)) (=> (tptp.divisi14063676e_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_1 A_1)) (tptp.ti X_a A_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.divisi14063676e_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (= (= (tptp.hAPP X_a X_a _let_1 A_2) (tptp.hAPP X_a X_a _let_1 B_1)) (= (tptp.ti X_a A_2) (tptp.ti X_a B_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.divisi14063676e_zero X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (=> (= (tptp.hAPP X_a X_a _let_1 A_1) (tptp.hAPP X_a X_a _let_1 B)) (= (tptp.ti X_a A_1) (tptp.ti X_a B))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.exp tptp.real))) (= (= (tptp.hAPP tptp.real tptp.real _let_1 X_1) (tptp.hAPP tptp.real tptp.real _let_1 Y_1)) (= X_1 Y_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.field_inverse_zero X_a) (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (tptp.divisi14063676e_zero X_a) (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) _let_1) _let_1)))) (forall ((X_a $$unsorted)) (=> (tptp.divisi14063676e_zero X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_2) _let_1) (= (tptp.ti X_a A_2) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (not (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.ti X_a A_1))) (let ((_let_2 (tptp.inverse_inverse X_a))) (=> (not (= _let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_2 A_1)) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1) _let_1) (= (tptp.ti X_a A_1) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ti X_a B))) (let ((_let_2 (tptp.ti X_a A_1))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.inverse_inverse X_a))) (=> (= (tptp.hAPP X_a X_a _let_4 A_1) (tptp.hAPP X_a X_a _let_4 B)) (=> (not (= _let_2 _let_3)) (=> (not (= _let_1 _let_3)) (= _let_2 _let_1))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X))) (= (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) _let_1) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.inverse_inverse tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.inverse_inverse X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 A_1)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.exp X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X)) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) (tptp.hAPP X_a X_a _let_1 X))))))) (forall ((X_a $$unsorted)) (=> (tptp.divisi14063676e_zero X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 A_1)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 A_1)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X $$unsorted)) (not (= (tptp.hAPP X_a X_a (tptp.exp X_a) X) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n1866405975lgebra X_a) (forall ((R_4 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 R_4) (tptp.hAPP X_a tptp.real _let_1 X))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) X))) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) R_4))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1))) (=> (not (= (tptp.ti X_a A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1)) _let_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 A_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 B) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 A_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1)) _let_1)) (=> (not (= (tptp.ti X_a A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.inverse_inverse X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (let ((_let_4 (tptp.inverse_inverse X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_4 A_1)) (tptp.hAPP X_a X_a _let_4 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_4)) (=> (not (= (tptp.ti X_a B) _let_4)) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 A_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) B) (tptp.one_one X_a)) (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1) (tptp.ti X_a B)))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.power_power X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 A_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 A_1)) N))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) Z)) (= (tptp.ti X_a Z) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.uminus_uminus X_a))) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 A_1)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.inverse_divide X_a) A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) B))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.inverse_inverse X_a))) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 A_1)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 A_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) (tptp.one_one X_a)) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) (tptp.one_one X_a)) A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.one_one X_a)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) X) Y) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) Y))))) (forall ((R $$unsorted) (S_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) R) S_5) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) R) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) S_5))))) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X)) (tptp.zero_zero tptp.real))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X)))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X)))) (forall ((X $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X)) (tptp.zero_zero tptp.real))))) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X_1) (tptp.one_one tptp.real)) (= X_1 (tptp.zero_zero tptp.real)))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) (tptp.zero_zero X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 A_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) B) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 B)) (tptp.hAPP X_a X_a _let_1 A_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.inverse_inverse X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.zero_zero X_a)) A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.inverse_inverse X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) (tptp.hAPP X_a X_a _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) B) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) A_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) X_1)) _let_1)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X_1) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) X_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) X_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (let ((_let_3 (tptp.plus_plus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.hAPP X_a X_a _let_1 A_1))) (let ((_let_6 (tptp.times_times X_a))) (let ((_let_7 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_7)) (=> (not (= (tptp.ti X_a B) _let_7)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 _let_5) _let_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_6 _let_5) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) B))) _let_2)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (let ((_let_3 (tptp.hAPP X_a X_a _let_1 A_1))) (let ((_let_4 (tptp.plus_plus X_a))) (let ((_let_5 (tptp.fun X_a X_a))) (let ((_let_6 (tptp.times_times X_a))) (let ((_let_7 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_7)) (=> (not (= (tptp.ti X_a B) _let_7)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 _let_3) _let_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 A_1) B)) _let_3)) _let_2)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1)) (tptp.one_one X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((A_1 $$unsorted)) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1)) A_1) (tptp.one_one X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1)) A_1) (tptp.one_one X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.hAPP X_a X_a _let_1 A_1))) (let ((_let_6 (tptp.times_times X_a))) (let ((_let_7 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_7)) (=> (not (= (tptp.ti X_a B) _let_7)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 _let_5) _let_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_6 _let_5) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 B) A_1))) _let_2)))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (= (tptp.hAPP X_a X_a (tptp.exp X_a) (tptp.zero_zero X_a)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((A_1 $$unsorted)) (=> (not (= (tptp.ti X_a A_1) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) (tptp.one_one X_a)) A_1)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.exp X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.times_times X_a) (tptp.hAPP X_a X_a _let_1 X)) (tptp.hAPP X_a X_a _let_1 Y)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.exp X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) (tptp.hAPP X_a X_a _let_2 X)) (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.plus_plus X_a) X) Y)))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (=> (and (tptp.field X_a) (tptp.number_ring X_a)) (= (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) _let_1) _let_1)))) (forall ((X_b $$unsorted)) (=> (and (tptp.division_ring X_b) (tptp.number X_b)) (forall ((W $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) W))) (= (tptp.hAPP X_b X_b (tptp.inverse_inverse X_b) _let_1) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.inverse_divide X_b) (tptp.one_one X_b)) _let_1)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.exp X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.minus_minus X_a) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.inverse_divide X_a) (tptp.hAPP X_a X_a _let_1 X)) (tptp.hAPP X_a X_a _let_1 Y)))))))) (forall ((Y $$unsorted) (U $$unsorted) (X1_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.inverse_inverse tptp.real))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.ord_less tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.hAPP tptp.real _let_5 _let_4 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_6 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_6 X1_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X1_1) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) U))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X)) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X1_1)) U))))))))))))) (forall ((Y $$unsorted) (U $$unsorted) (X1_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.inverse_inverse tptp.real))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.ord_less tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.hAPP tptp.real _let_5 _let_4 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_6 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_6 X1_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X1_1) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) U))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) (tptp.hAPP tptp.real tptp.real _let_1 X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 U) (tptp.hAPP tptp.real tptp.real _let_1 X1_1)))))))))))))) (forall ((X $$unsorted)) (=> (not (= X (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) X)) X) (tptp.one_one tptp.real)))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X_1)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X_1)) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) (tptp.zero_zero tptp.real))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X_1)) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) (tptp.zero_zero tptp.real))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X_1)))))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.one_one tptp.real)) X)) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.exp tptp.real))) (= (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) X)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real _let_1 X)) N)))) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln X_1)) X_1) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_1)))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln X)) X))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.ring_char_0 X_a)) (forall ((W $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 W)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.pls))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.ring_char_0 X_a)) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (let ((_let_2 (tptp.iszero X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W_1)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 (tptp.hAPP tptp.int X_a _let_1 W_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_2) B_1))) (let ((_let_5 (tptp.inverse_inverse X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_5 A_2)) (tptp.hAPP X_a X_a _let_5 B_1))) (and (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_3) _let_4)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_4) _let_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.zero_zero X_a))) (let ((_let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_2) B_1))) (let ((_let_5 (tptp.inverse_inverse X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_5 A_2)) (tptp.hAPP X_a X_a _let_5 B_1))) (and (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) _let_3) _let_4)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 _let_4) _let_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) X_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) (tptp.zero_zero X_a)) X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X_1) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord1117847801e_zero X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) X_1)) _let_1)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) X_1) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) X_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) (tptp.zero_zero X_a)) A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_1) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 _let_1) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.division_ring X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.hAPP X_a X_a _let_1 A_1))) (let ((_let_6 (tptp.times_times X_a))) (let ((_let_7 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_7)) (=> (not (= (tptp.ti X_a B) _let_7)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 _let_5) _let_2) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_6 _let_5) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) B))) _let_2))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)))))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) _let_1) X) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) _let_1))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N)))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) X)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.one_one tptp.real)) X)) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.inverse_divide tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) (tptp.one_one tptp.real))) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.ln Y)) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.ln X)) X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((H_2 $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.inverse_divide X_a))) (let ((_let_6 (tptp.hAPP X_a X_a _let_1 A_1))) (let ((_let_7 (tptp.times_times X_a))) (let ((_let_8 (tptp.zero_zero X_a))) (=> (not (= (tptp.ti X_a A_1) _let_8)) (=> (not (= (tptp.ti X_a B) _let_8)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 _let_6) _let_2)) H_2) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_7 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_7 _let_6) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 A_1) B)) H_2))) _let_2)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (= (tptp.hAPP tptp.int X_a _let_1 X_1) (tptp.hAPP tptp.int X_a _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_1) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) Y_1)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.inverse_inverse tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.sqrt X))) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.real tptp.real _let_1 X))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (= (tptp.zero_zero X_a) (tptp.hAPP tptp.int X_a _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) tptp.pls) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) Y_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (= (tptp.hAPP tptp.int X_a _let_1 X_1) (tptp.zero_zero X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.iszero X_a) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_1) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) tptp.pls)))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.plus_plus tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.ord_less_eq tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 X) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 _let_1) X)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real tptp.cos X))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (=> (not (= _let_2 (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real tptp.tan X)) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) _let_2)) _let_1)))))))) (forall ((Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.one_one tptp.real)) Y)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) Y) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X_2) Y))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (exists ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))) X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 tptp.log _let_1) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) (tptp.one_one tptp.real)))) (tptp.hAPP tptp.real tptp.real tptp.ln _let_1))) (tptp.hAPP tptp.real tptp.real tptp.ln X))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_4 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_4 X_1) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_3) (tptp.deriv tptp.real) tptp.arccos) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) _let_1) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.exp X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun X_a _let_2) (tptp.deriv X_a) _let_1) X_1) (tptp.hAPP X_a X_a _let_1 X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((E_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun X_a _let_1) (tptp.deriv X_a) F) X_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 E_3)) (= (tptp.ti X_a D_2) (tptp.ti X_a E_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun X_a _let_1) (tptp.deriv X_a) F) X_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 X_3)) (=> (= (tptp.ti X_a X_3) (tptp.ti X_a Y_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 Y_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((E_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun X_a _let_1) (tptp.deriv X_a) F) X_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 D_2)) (=> (= (tptp.ti X_a D_2) (tptp.ti X_a E_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 E_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((C_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP _let_1 (tptp.fun X_a _let_2) (tptp.deriv X_a) (tptp.hAPP X_a _let_1 (tptp.times_times X_a) C_1)) X_1) C_1))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) tptp.sin) X_1) (tptp.hAPP tptp.real tptp.real tptp.cos X_1))))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.log A_1) (tptp.one_one tptp.real)) (tptp.zero_zero tptp.real))) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.log A_1) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln X)) (tptp.hAPP tptp.real tptp.real tptp.ln A_1))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) tptp.cos) X_1) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X_1)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) tptp.ln) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) X_1)))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) A_1)) (=> (not (= A_1 _let_1)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.log A_1) A_1) _let_1))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.log A_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) A_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_4 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_4 Y_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 X_1)) (tptp.hAPP tptp.real tptp.real _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1))))))))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.ln X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.log (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) (tptp.one_one tptp.real))) X))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) tptp.ln) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.one_one tptp.real)) X_1))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.log A_2))) (let ((_let_4 (tptp.ord_less tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real _let_2 _let_4 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_4 (tptp.one_one tptp.real)) A_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_5 X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_5 Y_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 X_1)) (tptp.hAPP tptp.real tptp.real _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1)))))))))))) (forall ((B $$unsorted) (N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.log B))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) N)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) (tptp.hAPP tptp.real tptp.real _let_2 X))))))) (forall ((Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.log A_1))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 A_1)) (=> (not (= A_1 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 Y)) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real _let_2 Y))))))))))) (forall ((Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.log A_1))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 A_1)) (=> (not (= A_1 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 Y)) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real _let_2 Y))))))))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.log A_1))) (let ((_let_2 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 A_1)) (=> (not (= A_1 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 X)) (= (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) X)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real _let_1 X))))))))) (forall ((X $$unsorted) (B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (let ((_let_3 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 A_1)) (=> (not (= A_1 _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 B)) (=> (not (= B _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 X)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.log A_1) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln B)) (tptp.hAPP tptp.real tptp.real tptp.ln A_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.log B) X)))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) tptp.sqrt) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1))) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.cos X_1))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (not (= _let_1 (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) tptp.tan) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) _let_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) tptp.arctan) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))) (forall ((D_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_4 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sqrt X_1)))) (let ((_let_5 (tptp.inverse_divide tptp.real))) (let ((_let_6 (tptp.zero_zero tptp.real))) (let ((_let_7 (tptp.ord_less tptp.real))) (=> (not (= X_1 _let_6)) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_7 _let_6) X_1)) (= D_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_5 _let_4) _let_3))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_7 X_1) _let_6)) (= D_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_5 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_4)) _let_3))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) tptp.sqrt) X_1) D_2))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_4 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_4 X_1) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_3) (tptp.deriv tptp.real) tptp.arcsin) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) _let_1) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.log (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real _let_2 X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) (tptp.one_one tptp.real)))) (tptp.hAPP tptp.real tptp.real tptp.ln X))))))) (forall ((V_1 $$unsorted) (K $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.plus_plus tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.inverse_divide tptp.real))) (=> (not (= A_2 B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) V_1) X_2) K)))) (= (tptp.hAPP tptp.real tptp.real V_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 A_2) B_1)) _let_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real V_1 A_2)) (tptp.hAPP tptp.real tptp.real V_1 B_1))) _let_1))))))))) (forall ((D_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) F) X_1) L)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_1) D_1)) (=> (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X_1) Y_2))) D_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real F X_1)) (tptp.hAPP tptp.real tptp.real F Y_2)))))) (= L _let_1))))))) (forall ((D_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) F) X_1) L)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_1) D_1)) (=> (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X_1) Y_2))) D_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real F Y_2)) (tptp.hAPP tptp.real tptp.real F X_1)))))) (= L _let_1))))))) (forall ((D_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) F) X_1) L)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_1) D_1)) (=> (forall ((Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X_1) Y_2))) D_1)) (= (tptp.hAPP tptp.real tptp.real F X_1) (tptp.hAPP tptp.real tptp.real F Y_2)))) (= L _let_1))))))) (forall ((F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_1) L)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) L)) (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((H_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) H_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 H_1) D_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X_1) H_1))) (tptp.hAPP tptp.real tptp.real F X_1)))))))))))))) (forall ((F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_1) L)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) L) (tptp.zero_zero tptp.real))) (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((H_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) H_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 H_1) D_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F X_1)) (tptp.hAPP tptp.real tptp.real F (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X_1) H_1))))))))))))))) (forall ((F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_1) L)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) L) (tptp.zero_zero tptp.real))) (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((H_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) H_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 H_1) D_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X_1) H_1))) (tptp.hAPP tptp.real tptp.real F X_1)))))))))))))) (forall ((F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_1) L)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) L)) (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((H_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) H_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 H_1) D_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F X_1)) (tptp.hAPP tptp.real tptp.real F (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X_1) H_1))))))))))))))) (forall ((F $$unsorted) (K $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (not (= A_2 B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) K)))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F B_1)) (tptp.hAPP tptp.real tptp.real F A_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 B_1) A_2)) K)))))) (forall ((F $$unsorted) (K $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (not (= A_2 B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) K)))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F B_1)) (tptp.hAPP tptp.real tptp.real F A_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 B_1) A_2)) K))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 tptp.root N_1))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.ord_less tptp.real) X_1) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.deriv tptp.real) _let_3) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real _let_3 X_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1))))))))))))))) (forall ((D_2 $$unsorted) (X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 tptp.root N_1))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.zero_zero tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real _let_2 X_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_4))))))) (let ((_let_6 (= D_2 _let_5))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1)))) (let ((_let_8 (tptp.zero_zero tptp.real))) (let ((_let_9 (tptp.ord_less tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_4) N_1)) (=> (not (= X_1 _let_8)) (=> (=> _let_7 (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_9 _let_8) X_1)) _let_6)) (=> (=> _let_7 (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_9 X_1) _let_8)) (= D_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_5)))) (=> (=> (not _let_7) _let_6) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_3) (tptp.deriv tptp.real) _let_2) X_1) D_2))))))))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) _let_1) _let_1))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) X) X)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (= (tptp.hAPP tptp.real tptp.real _let_1 X_1) (tptp.hAPP tptp.real tptp.real _let_1 Y_1)) (= X_1 Y_1))))) (forall ((X $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 tptp.root M))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 tptp.root N))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 N)) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real _let_3 X)) (tptp.hAPP tptp.real tptp.real _let_3 (tptp.hAPP tptp.real tptp.real _let_2 X)))))))))) (forall ((Y $$unsorted) (X $$unsorted) (N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N))) (=> (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) Y) N) X) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) X) Y)))) (forall ((X $$unsorted) (N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) X)) N) X))) (forall ((X $$unsorted) (N $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) N)) X))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 X_1)) (tptp.hAPP tptp.real tptp.real _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 Y))))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) X_1) _let_1) (= X_1 _let_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 X_1)) (tptp.hAPP tptp.real tptp.real _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) Y_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 Y))))))))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 tptp.root N))) (let ((_let_3 (tptp.times_times tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_3 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_3 (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real _let_2 Y)))))))) (forall ((X $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N)) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root M) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N) X)))))))) (forall ((X $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) K_4)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X)) K_4))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) _let_1) _let_1)))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) X_1) _let_1) (= X_1 _let_1))))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 tptp.root N))) (let ((_let_3 (tptp.inverse_divide tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_3 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_3 (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real _let_2 Y)))))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N))) (let ((_let_2 (tptp.uminus_uminus tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X))))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N))) (let ((_let_2 (tptp.abs_abs tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X))))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N))) (let ((_let_2 (tptp.inverse_inverse tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (= (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X))))))) (forall ((Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y_1)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) X_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1)))))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) X))))))) (forall ((Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y_1)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) X_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1)))))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) X))))))) (forall ((Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.one_one tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y_1)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) X_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1)))))))) (forall ((X $$unsorted) (N_5 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 N) N_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.one_one tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N_5) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N) X)))))))))))) (forall ((Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.one_one tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_1 Y_1)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_1) X_1)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1)))))))) (forall ((X $$unsorted) (N_5 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 N) N_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.one_one tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N_5) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N) X)))))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root _let_1) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) _let_1)) X)))) (forall ((X_5 $$unsorted) (N_6 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_6)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_1) X_5)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) _let_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N_6) X_5)))))))) (forall ((Y $$unsorted) (X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 Y)))))))))) (forall ((Y $$unsorted) (X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 tptp.root N))) (let ((_let_3 (tptp.times_times tptp.real))) (let ((_let_4 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_4 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_4 Y)) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_3 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_3 (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real _let_2 Y))))))))))) (forall ((X $$unsorted) (N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N)) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root M) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N) X))))))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) N)) X)))) (forall ((X $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) X)) N) X)))) (forall ((X $$unsorted) (Y $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) Y)) (=> (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) Y) N) X) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) X) Y))))) (forall ((X $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N) X)) N) X)))) (forall ((X $$unsorted) (N_5 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 N) N_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N_5) X))))))))))))) (forall ((X $$unsorted) (N_5 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.ord_less tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 N) N_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 tptp.root N_5) X))))))))))))) _let_226 (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) tptp.root N))) (let ((_let_2 (tptp.inverse_inverse tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real _let_2 X)) (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X)))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 tptp.root N_1))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) N_1))) (=> (not (= X_1 (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_3) (tptp.deriv tptp.real) _let_2) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real _let_2 X_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))))))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 tptp.root N_1))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.deriv tptp.real) _let_3) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.real tptp.real _let_3 X_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1)))))))))))))) (forall ((Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Y)) (exists ((X_2 $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X_2) Y)))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) X)) (exists ((N_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_2))) X)))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 K_4))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.pdivmod K_4) L_4))) (let ((_let_6 (tptp.zero_zero tptp.int))) (let ((_let_7 (= (tptp.ti tptp.int L_4) _let_6))) (and (=> _let_7 (= _let_5 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 (tptp.product_Pair tptp.int tptp.int) _let_6) _let_2))) (=> (not _let_7) (= _let_5 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.posDivAlg _let_2) (tptp.hAPP tptp.int tptp.int _let_1 L_4))))))))))))) (forall ((F $$unsorted) (F_2 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) A_2) B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 X_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) (tptp.hAPP tptp.real tptp.real F_2 X_2))))))) (exists ((Z_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.ord_less tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 A_2) Z_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 Z_2) B_1)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F B_1)) (tptp.hAPP tptp.real tptp.real F A_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 B_1) A_2)) (tptp.hAPP tptp.real tptp.real F_2 Z_2)))))))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 L_4))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_1 K_4))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.product_prod tptp.int tptp.int))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (= (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 tptp.pdivmod K_4) L_4) (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.div_div tptp.int) _let_3) _let_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.div_mod tptp.int) _let_3) _let_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) X)) (exists ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) X)) (exists ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_2)) X)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) Y) (tptp.zero_zero tptp.real))) (exists ((R_2 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_2))) (and (= X (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos A_4))) (= Y (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin A_4)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Y)) (exists ((R_2 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_2))) (and (= X (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos A_4))) (= Y (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin A_4)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) A_3) B_2)) (exists ((B_4 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) B_4) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) B_2) A_3)))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) K_4))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.z3mod K_4) L_4))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) L_4)))) (and (=> _let_4 (= _let_3 (tptp.hAPP tptp.int tptp.int _let_2 L_4))) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) L_4)))))))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) K_4))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.z3div K_4) L_4))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) L_4)))) (and (=> _let_5 (= _let_4 (tptp.hAPP tptp.int tptp.int _let_3 L_4))) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_1 L_4)))))))))))) (forall ((X_a $$unsorted) (C_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((X_4 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_4) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) X_4) C_2)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) A_3)) C_2)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) (tptp.zero_zero tptp.real))))) (= (tptp.hAPP tptp.real tptp.real F X_1) (tptp.hAPP tptp.real tptp.real F Y_1)))) (forall ((X $$unsorted)) (exists ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) X) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_2))))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_4) L_4)) (exists ((N_2 $$unsorted)) (= L_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K_4) N_2))))) (forall ((X_a $$unsorted)) (=> (tptp.comple44059174attice X_a) (forall ((Z $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) Z))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.hAPP _let_1 X_a (tptp.complete_Sup_Sup X_a) A_3)) Z))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 X) Y)) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((X $$unsorted)) (exists ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((X $$unsorted)) (exists ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_2))))))) (forall ((P_1 $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.zero_zero tptp.nat)))) (=> (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 X1))) (exists ((N_2 $$unsorted)) (and (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))))))) (forall ((Real1 $$unsorted) (Real2 $$unsorted) (Real1_2 $$unsorted) (Real2_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.complex))) (= (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 Real1) Real2) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 Real1_2) Real2_2)) (and (= Real1 Real1_2) (= Real2 Real2_2))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (= (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 A_2) B_1) (tptp.zero_zero tptp.complex)) (and (= A_2 _let_1) (= B_1 _let_1))))) (= _let_208 (tptp.hAPP tptp.real tptp.complex _let_224 _let_37)) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (W_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 A_2) B_1) (tptp.hAPP tptp.int tptp.complex (tptp.number_number_of tptp.complex) W_1)) (and (= A_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) W_1)) (= B_1 (tptp.zero_zero tptp.real))))) (= _let_207 (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_223 tptp.complex_1 _let_136) _let_37)) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 A_2) B_1) (tptp.one_one tptp.complex)) (and (= A_2 (tptp.one_one tptp.real)) (= B_1 (tptp.zero_zero tptp.real))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.plus_plus tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_3 tptp.complex_1 A_1) B)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_3 tptp.complex_1 C) D)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_3 tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 B) D))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.uminus_uminus tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.complex_1 A_1) B)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.complex_1 (tptp.hAPP tptp.real tptp.real _let_1 A_1)) (tptp.hAPP tptp.real tptp.real _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.minus_minus tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_3 tptp.complex_1 A_1) B)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_3 tptp.complex_1 C) D)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_3 tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 B) D))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 B))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 _let_1 A_1))) (let ((_let_5 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_5 tptp.complex_1 A_1) B)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_5 tptp.complex_1 C) D)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_5 tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real _let_4 C)) (tptp.hAPP tptp.real tptp.real _let_3 D))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real _let_4 D)) (tptp.hAPP tptp.real tptp.real _let_3 C)))))))))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.real tptp.real tptp.cos A_1)) (tptp.hAPP tptp.real tptp.real tptp.sin A_1))) (tptp.one_one tptp.real))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 A_1) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 B) _let_1)))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.inverse_inverse tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_7 tptp.complex_1 A_1) B)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_7 tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_6 A_1) _let_5)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) B)) _let_5))))))))))) (forall ((Real1_1 $$unsorted) (Real2_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.nat tptp.complex_size (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 Real1_1) Real2_1)) (tptp.zero_zero tptp.nat))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_1) Y)) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.complex tptp.real tptp.arg (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 _let_1) Y))) _let_1)))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) Y) _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.complex tptp.real tptp.arg (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 _let_1) Y))) _let_1)))) (forall ((Real1_1 $$unsorted) (Real2_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.nat (tptp.size_size tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 Real1_1) Real2_1)) (tptp.zero_zero tptp.nat))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.complex tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_1 (tptp.inverse_divide tptp.complex) X) Y) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_1 (tptp.times_times tptp.complex) X) (tptp.hAPP tptp.complex tptp.complex (tptp.inverse_inverse tptp.complex) Y))))) (forall ((Y $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (=> (not (= Y _let_1)) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.complex tptp.real tptp.arg (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 _let_1) Y))) _let_1)))) (= (tptp.hAPP tptp.nat tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.nat tptp.complex) (tptp.power_power tptp.complex) tptp.ii) _let_6) _let_222) (forall ((X_a $$unsorted) (F1 $$unsorted) (Real1 $$unsorted) (Real2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real X_a))) (= (tptp.hAPP tptp.complex X_a (tptp.hAPP (tptp.fun tptp.real _let_1) (tptp.fun tptp.complex X_a) (tptp.complex_rec X_a) F1) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 Real1) Real2)) (tptp.hAPP tptp.real X_a (tptp.hAPP tptp.real _let_1 F1 Real1) Real2)))) (forall ((X_a $$unsorted) (F1 $$unsorted) (Real1 $$unsorted) (Real2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real X_a))) (= (tptp.hAPP tptp.complex X_a (tptp.hAPP (tptp.fun tptp.real _let_1) (tptp.fun tptp.complex X_a) (tptp.complex_case X_a) F1) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 Real1) Real2)) (tptp.hAPP tptp.real X_a (tptp.hAPP tptp.real _let_1 F1 Real1) Real2)))) (not (= tptp.ii _let_208)) (not (= tptp.ii _let_207)) (forall ((W $$unsorted)) (not (= tptp.ii (tptp.hAPP tptp.int tptp.complex (tptp.number_number_of tptp.complex) W)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) tptp.ii))) (= (tptp.hAPP tptp.complex tptp.complex _let_1 (tptp.hAPP tptp.complex tptp.complex _let_1 X)) (tptp.hAPP tptp.complex tptp.complex (tptp.uminus_uminus tptp.complex) X)))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.inverse_inverse tptp.complex) tptp.ii) _let_212) _let_225 (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 X_1) Y_1) tptp.ii) (and (= X_1 (tptp.zero_zero tptp.real)) (= Y_1 (tptp.one_one tptp.real))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 A_1) B)) tptp.ii) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) B)) A_1)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) tptp.ii) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 A_1) B)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) B)) A_1)))) (= _let_221 _let_222) (= _let_221 _let_218) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 Y) _let_1)))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.of_real tptp.complex))) (let ((_let_8 (tptp.fun tptp.complex tptp.complex))) (let ((_let_9 (tptp.hAPP tptp.complex _let_8 (tptp.times_times tptp.complex) tptp.ii))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.inverse_inverse tptp.complex) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_8 (tptp.plus_plus tptp.complex) (tptp.hAPP tptp.real tptp.complex _let_7 X)) (tptp.hAPP tptp.complex tptp.complex _let_9 (tptp.hAPP tptp.real tptp.complex _let_7 Y)))) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_8 (tptp.minus_minus tptp.complex) (tptp.hAPP tptp.real tptp.complex _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_6 X) _let_5))) (tptp.hAPP tptp.complex tptp.complex _let_9 (tptp.hAPP tptp.real tptp.complex _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_6 Y) _let_5))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dvd X_a) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.dvd_dvd X_a) B) A_1)) (not (forall ((K_1 $$unsorted)) (not (= (tptp.ti X_a A_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) B) K_1))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card _let_1) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) A_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_3))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) A_3) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) B_2))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) A_3)) (tptp.ti _let_1 A_3))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) A_3) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) A_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (= (tptp.hAPP tptp.real X_a _let_1 X_1) (tptp.hAPP tptp.real X_a _let_1 Y_1)) (= X_1 Y_1)))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (= (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) A_3) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc _let_1 _let_1 tptp.bool) (tptp.ord_less_eq _let_1)) A_3))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) A_3) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) A_3) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) B_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.real X_a (tptp.of_real X_a) X_1) (tptp.zero_zero X_a)) (= X_1 (tptp.zero_zero tptp.real)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (= (tptp.hAPP tptp.real X_a (tptp.of_real X_a) (tptp.zero_zero tptp.real)) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (= (tptp.hAPP tptp.real X_a (tptp.of_real X_a) (tptp.zero_zero tptp.real)) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.real X_a _let_1 X)) (tptp.hAPP tptp.real X_a _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.real_algebra_1 X_a)) (forall ((W $$unsorted)) (= (tptp.hAPP tptp.real X_a (tptp.of_real X_a) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) W)) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (= (tptp.hAPP tptp.real X_a (tptp.of_real X_a) (tptp.one_one tptp.real)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.real X_a _let_1 X)) (tptp.hAPP tptp.real X_a _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.real X_a _let_1 X)) (tptp.hAPP tptp.real X_a _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP tptp.real X_a _let_1 X)) N)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Xa_2 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 X_1) Y_1) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) Xa_2)) (and (= X_1 Xa_2) (= Y_1 (tptp.zero_zero tptp.real))))) (forall ((R_4 $$unsorted)) (= (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 R_4) (tptp.zero_zero tptp.real)))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.real_field X_a)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) (tptp.hAPP tptp.real X_a _let_1 X)) (tptp.hAPP tptp.real X_a _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.real X_a _let_1 X)) (tptp.hAPP tptp.real X_a _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.real X_a _let_1 X)) (tptp.hAPP tptp.real X_a _let_1 Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X)) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.real X_a _let_1 X))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X)) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.real X_a _let_1 X))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n2089651433ebra_1 X_a) (forall ((R_4 $$unsorted)) (= (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.real X_a (tptp.of_real X_a) R_4)) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) R_4))))) (forall ((X_a $$unsorted)) (=> (and (tptp.divisi14063676e_zero X_a) (tptp.real_div_algebra X_a)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) X)) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) (tptp.hAPP tptp.real X_a _let_1 X))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP X_a X_a (tptp.exp X_a) (tptp.hAPP tptp.real X_a _let_1 X)) (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real X_a (tptp.of_real X_a) (tptp.hAPP tptp.nat tptp.real (tptp.semiring_1_of_nat tptp.real) N)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n2089651433ebra_1 X_a) (forall ((R_4 $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) (tptp.hAPP tptp.real X_a _let_1 R_4)) (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.sgn_sgn tptp.real) R_4))))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex (tptp.sgn_sgn tptp.complex) Z_1) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.inverse_divide tptp.complex) Z_1) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) Z_1))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.pow X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_3 tptp.bool) (tptp.ord_less_eq _let_3) (tptp.hAPP _let_2 _let_3 _let_1 A_3)) (tptp.hAPP _let_2 _let_3 _let_1 B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_field X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (=> (not (= Y (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) (tptp.hAPP tptp.real X_a _let_1 X)) (tptp.hAPP tptp.real X_a _let_1 Y)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) (tptp.hAPP _let_2 _let_1 (tptp.complete_Sup_Sup _let_1) A_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_div_algebra X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (=> (not (= X (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) X)) (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) (tptp.hAPP tptp.real X_a _let_1 X)))))))) (forall ((X $$unsorted) (Y $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_3 tptp.complex_1 X) Y)) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_3 tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 X) R_4)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 Y) R_4))))))) (forall ((R_4 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_4))) (let ((_let_2 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.complex_1 X) Y)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.complex_1 (tptp.hAPP tptp.real tptp.real _let_1 X)) (tptp.hAPP tptp.real tptp.real _let_1 Y)))))) (forall ((X $$unsorted) (Y $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.plus_plus tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 X) Y)) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) R_4)) Y)))) (forall ((R_4 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.plus_plus tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 X) Y)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) R_4) X)) Y)))) (= _let_221 (tptp.hAPP tptp.real tptp.complex _let_214 _let_183)) (forall ((R_4 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4)) tptp.ii) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.zero_zero tptp.real)) R_4))) (forall ((R_4 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) tptp.ii) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.zero_zero tptp.real)) R_4))) (= (tptp.hAPP tptp.real tptp.complex _let_214 _let_220) _let_218) (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.real tptp.real tptp.cos A_1)) (tptp.hAPP tptp.real tptp.real tptp.sin A_1)))) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) R_4))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.real X_a (tptp.of_real X_a) X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) X_2)) K_2)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.real X_a (tptp.of_real X_a) X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) X_2)) K_2)))))))) (= (tptp.hAPP tptp.complex tptp.complex tptp.expi (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_217 _let_216 (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_217 _let_216 (tptp.hAPP tptp.int tptp.complex _let_215 _let_4)) (tptp.hAPP tptp.real tptp.complex _let_214 tptp.pi))) tptp.ii)) _let_207) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.complex tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex tptp.expi (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_1 (tptp.plus_plus tptp.complex) A_1) B)) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_1 (tptp.times_times tptp.complex) (tptp.hAPP tptp.complex tptp.complex tptp.expi A_1)) (tptp.hAPP tptp.complex tptp.complex tptp.expi B))))) (= (tptp.hAPP tptp.complex tptp.complex tptp.expi _let_208) _let_207) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (exists ((K_2 $$unsorted)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.real X_a (tptp.of_real X_a) X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) X_2)) K_2))))))) (forall ((Z_1 $$unsorted)) (exists ((R_2 $$unsorted) (A_4 $$unsorted)) (= Z_1 (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_2)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.real tptp.real tptp.cos A_4)) (tptp.hAPP tptp.real tptp.real tptp.sin A_4)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_5 $$unsorted)) (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_2) X_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) T_5)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) Z_1))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X) Y)) (=> (forall ((W_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 X) W_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 W_2) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) W_2) Z_1))))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) Y) Z_1)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) B_1) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) C_1) (tptp.hAPP X_a X_b F B_1))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_a X_b F Y_2)) (tptp.hAPP X_a X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) C_1) (tptp.hAPP X_a X_b F A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_5 $$unsorted)) (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_2) T_5))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_5 $$unsorted)) (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Z_2) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) T_5) X_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((T_5 $$unsorted)) (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) Z_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) T_5) X_2)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) C_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) B_1) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_a X_b F B_1))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F Y_2)) (tptp.hAPP X_a X_b F X_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool _let_1 (tptp.hAPP X_a X_b F A_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F B_1)) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b F Y_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_1 (tptp.ord_less X_b) (tptp.hAPP X_a X_b F A_2)) C_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((F $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_a X_b F B_1)) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b F Y_2))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_2 _let_1 (tptp.hAPP X_a X_b F A_2)) C_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.ord X_b)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F B_1)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) C_1) B_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_b X_a F Y_2)) (tptp.hAPP X_b X_a F X_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) (tptp.hAPP X_b X_a F C_1)) A_2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.order X_a) (tptp.order X_b)) (forall ((C_1 $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_b X_a F B_1)) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) C_1) B_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F Y_2)) (tptp.hAPP X_b X_a F X_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_b X_a F C_1)) A_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (F $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) A_2) (tptp.hAPP X_b X_a F B_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) B_1) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_b X_a F X_2)) (tptp.hAPP X_b X_a F Y_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) A_2) (tptp.hAPP X_b X_a F C_1)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.order X_b) (tptp.order X_a)) (forall ((C_1 $$unsorted) (A_2 $$unsorted) (F $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) A_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_b X_a F B_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) B_1) C_1)) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_b X_a F X_2)) (tptp.hAPP X_b X_a F Y_2))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_b X_a F C_1)))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a (tptp.fun tptp.nat X_a)))) (let ((_let_2 (tptp.fun X_a (tptp.fun X_a X_a)))) (=> (tptp.power X_a) (= (tptp.power_power X_a) (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_a (tptp.fun _let_2 _let_1) (tptp.power_1 X_a) (tptp.one_one X_a)) (tptp.times_times X_a))))))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) B_1))) (exists ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) Y_2))))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F A_2)) (tptp.hAPP tptp.real tptp.real F B_1)))))))) (forall ((X_a $$unsorted) (One $$unsorted) (Times $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a (tptp.fun X_a X_a)))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_1 (tptp.hAPP _let_3 _let_2 (tptp.hAPP X_a (tptp.fun _let_3 _let_2) (tptp.power_1 X_a) One) Times) A_2) (tptp.zero_zero tptp.nat)) (tptp.ti X_a One)))))) (forall ((X_a $$unsorted) (One $$unsorted) (Times $$unsorted) (A_2 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.hAPP X_a _let_1 (tptp.hAPP _let_4 _let_2 (tptp.hAPP X_a (tptp.fun _let_4 _let_2) (tptp.power_1 X_a) One) Times) A_2))) (= (tptp.hAPP tptp.nat X_a _let_5 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 Times A_2) (tptp.hAPP tptp.nat X_a _let_5 N_1))))))))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) B_1))) (exists ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) Y_2) (tptp.zero_zero tptp.real)))))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F B_1)) (tptp.hAPP tptp.real tptp.real F A_2)))))))) (forall ((I $$unsorted) (P_1 $$unsorted) (K $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 K)) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) K) I_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I_2) (tptp.one_one tptp.int))))))) (=> (forall ((I_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) I_2) K)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I_2) (tptp.one_one tptp.int))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I)))))) (forall ((P_1 $$unsorted) (P1 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_1)) (=> (forall ((X_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_1) D_1))))))) (=> (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X_2) Z_2)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P1 X_2)))))) (=> (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P1 X1))) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X1)))))))) (forall ((P_1 $$unsorted) (P_2 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_1)) (=> (forall ((X_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_1) D_1))))))) (=> (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Z_2) X_2)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X_2)))))) (=> (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X1))) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X1)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 tptp.coprime X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 tptp.coprime (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.times_times tptp.nat) X) Y)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 X) _let_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 Y) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1)) (tptp.one_one tptp.int))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))) (forall ((D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime D))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B))))) (forall ((D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime D))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1))))) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime D))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) A_1) B))))))) (forall ((D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime D_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) A_2) B_1))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1)))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime N_1) N_1)) (= N_1 (tptp.one_one tptp.nat)))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime A_1) (tptp.one_one tptp.nat)))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime (tptp.one_one tptp.nat)) A_1))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime A_2) B_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime B_1) A_2))))) (forall ((E_1 $$unsorted) (B $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 D) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 E_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime D) E_1)))))))) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.power_power tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 tptp.coprime A_1) B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 tptp.coprime (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) N)))))))) (forall ((N $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime D))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) A_1) N)))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.nat tptp.natfloor X) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X)))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) A_1))) (forall ((A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime A_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (= (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) (tptp.zero_zero X_a)) (tptp.zero_zero tptp.int)))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.hAPP X_a tptp.int _let_1 Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.hAPP X_a tptp.int _let_1 Y)))))))) (forall ((D_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime D_1) (tptp.zero_zero tptp.nat))) (= D_1 (tptp.one_one tptp.nat)))) (forall ((D_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime (tptp.zero_zero tptp.nat)) D_1)) (= D_1 (tptp.one_one tptp.nat)))) (forall ((N $$unsorted) (M $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 N) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 tptp.coprime M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N)) R_4)))))))) (forall ((D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) D))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) A_1) B))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime D) A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 B))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (= (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) (tptp.one_one X_a)) (tptp.one_one tptp.int)))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime A_2) B_1)) (forall ((D_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) D_3))) (= (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1))) (= D_3 (tptp.one_one tptp.nat))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((V $$unsorted)) (= (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N) (tptp.one_one tptp.nat))) N))) (forall ((A_2 $$unsorted) (N_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_3 (tptp.power_power tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 A_2) _let_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 B_1) _let_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime A_2) B_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((N $$unsorted)) (= (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))))) (forall ((N $$unsorted)) (=> (not (= N (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N) (tptp.one_one tptp.nat))) N)))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.nat tptp.real _let_1 N)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X)) N))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1)) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_1) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1)) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_1) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1)) (tptp.one_one tptp.int))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_1) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.one_one tptp.int)) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.one_one X_a)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted) (V_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((V_1 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_1)) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V_1)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X) (tptp.one_one X_a))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.one_one tptp.int))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X) (tptp.one_one X_a))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.one_one tptp.int))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.real tptp.int _let_1 A_1)) (tptp.hAPP tptp.real tptp.int _let_1 B))) (tptp.hAPP tptp.real tptp.int _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) A_1) B))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 N)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) X) (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N)))) (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X)) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((V_1 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_1)) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V_1)) (tptp.one_one X_a))) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted) (V_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V_1)) (tptp.one_one X_a)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) X_1)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime A_2) B_1)) (exists ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 A_2))) (let ((_let_5 (tptp.hAPP tptp.nat _let_3 _let_2 B_1))) (let ((_let_6 (tptp.minus_minus tptp.nat))) (or (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_6 (tptp.hAPP tptp.nat tptp.nat _let_4 X_2)) (tptp.hAPP tptp.nat tptp.nat _let_5 Y_2)) _let_1) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_6 (tptp.hAPP tptp.nat tptp.nat _let_5 X_2)) (tptp.hAPP tptp.nat tptp.nat _let_4 Y_2)) _let_1))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime A_1) B)) (=> (not (= B (tptp.one_one tptp.nat))) (exists ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) X_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) Y_2)) (tptp.one_one tptp.nat))))))))) (forall ((V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.int tptp.nat _let_1 V)) (tptp.one_one tptp.nat)))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) V) tptp.pls)))) (and (=> _let_3 (= _let_2 (tptp.zero_zero tptp.nat))) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.pred V))))))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.int tptp.int tptp.succ (tptp.hAPP tptp.int tptp.int tptp.pred X)) (tptp.ti tptp.int X))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int tptp.pred (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int tptp.pred (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.pred K_4)))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) K) L)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred K)) L))))) (= (tptp.hAPP tptp.int tptp.int tptp.pred tptp.pls) tptp.min_1) (= (tptp.hAPP tptp.int tptp.int tptp.pred tptp.min_1) (tptp.hAPP tptp.int tptp.int tptp.bit0 tptp.min_1)) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int tptp.pred K_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) K_4) (tptp.one_one tptp.int)))) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.pred (tptp.hAPP tptp.int tptp.int _let_1 K_4)))))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) K_4) tptp.min_1) (tptp.hAPP tptp.int tptp.int tptp.pred K_4))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) tptp.min_1) K_4) (tptp.hAPP tptp.int tptp.int tptp.pred K_4))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 K_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 L_4)) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int tptp.pred K_4)) L_4)))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int tptp.pred W)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.one_one X_a))) (tptp.hAPP tptp.int X_a _let_1 W))))))) (forall ((V_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (= (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1) (tptp.zero_zero tptp.nat)))) (forall ((M $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) tptp.pls) V)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.int tptp.nat _let_1 V)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 M) (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.pred V))))))))) (forall ((X_a $$unsorted) (R1_1 $$unsorted) (R2_1 $$unsorted)) (let ((_let_1 (tptp.accp X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_3 tptp.bool) (tptp.ord_less_eq _let_3) R1_1) R2_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_3 _let_2 _let_1 R2_1)) (tptp.hAPP _let_3 _let_2 _let_1 R1_1)))))))) (forall ((Z_1 $$unsorted)) (exists ((A_4 $$unsorted) (R_2 $$unsorted)) (= Z_1 (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_2)) (tptp.hAPP tptp.complex tptp.complex tptp.expi A_4))))) (forall ((X_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) tptp.resSet Ma) X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) X_3)))))) (forall ((Ma $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) tptp.resSet Ma) X_3)) (forall ((Y1 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.member tptp.int))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Y1) X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 Y2) X_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong Y1) Y2) Ma))) (= (tptp.ti tptp.int Y1) (tptp.ti tptp.int Y2)))))))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) tptp.resSet P_4) (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))))) (forall ((X_a $$unsorted) (R_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP (tptp.fun X_a _let_1) _let_1 (tptp.accp X_a) R_1) A_2)) (exists ((X_2 $$unsorted)) (and (= (tptp.ti X_a A_2) (tptp.ti X_a X_2)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 R_1 Xa) X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP (tptp.fun X_a _let_1) _let_1 (tptp.accp X_a) R_1) Xa)))))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (R_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a _let_1) _let_1 (tptp.accp X_a) R_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 R_1 A_2) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_2 A_2))))))) (forall ((Nat_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat tptp.nat_size (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.nat_size Nat_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (forall ((Nat_1 $$unsorted)) (let ((_let_1 (tptp.size_size tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_1 Nat_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))) (= (tptp.hAPP tptp.code_code_numeral tptp.nat tptp.code_c271388182l_size _let_209) _let_40) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.size_size tptp.nat) N) N)) (= (tptp.hAPP tptp.nat tptp.nat _let_213 _let_40) _let_40) (= (tptp.hAPP tptp.nat tptp.nat tptp.nat_size _let_40) _let_40) (forall ((Code_numeral_2 $$unsorted)) (= (tptp.hAPP tptp.code_code_numeral tptp.nat tptp.code_c271388182l_size (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral tptp.code_S1047413653umeral Code_numeral_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.code_code_numeral tptp.nat tptp.code_c271388182l_size Code_numeral_2)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.norm_norm tptp.complex))) (= (tptp.hAPP tptp.complex tptp.real _let_1 (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) Z_1) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z_1))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.complex tptp.real _let_1 Z_1)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.uminus X_a) (forall ((A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (= (tptp.hAPP X_b X_a (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3) X_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_b X_a A_3 X_1))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.inverse_inverse tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.complex tptp.complex _let_1 X)) (tptp.hAPP tptp.complex tptp.complex _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.complex))) (= (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z) _let_1) (= Z _let_1)))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj _let_208) _let_208) (forall ((W $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.complex (tptp.number_number_of tptp.complex) W))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj _let_1) _let_1))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.complex))) (let ((_let_2 (tptp.fun tptp.complex tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 X) Y)) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X)) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Y)))))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj _let_207) _let_207) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.complex tptp.complex _let_1 X)) (tptp.hAPP tptp.complex tptp.complex _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.complex))) (let ((_let_2 (tptp.fun tptp.complex tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 X) Y)) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X)) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Y)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj X_1) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Y_1)) (= X_1 Y_1))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z_1)) Z_1)) (forall ((Code_numeral $$unsorted) (Code_numeral_5 $$unsorted)) (= (= (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral tptp.code_S1047413653umeral Code_numeral) (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral tptp.code_S1047413653umeral Code_numeral_5)) (= Code_numeral Code_numeral_5))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.complex (tptp.semiring_1_of_nat tptp.complex) N))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj _let_1) _let_1))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.norm_norm tptp.complex))) (= (tptp.hAPP tptp.complex tptp.real _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z_1)) (tptp.hAPP tptp.complex tptp.real _let_1 Z_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.complex))) (let ((_let_2 (tptp.fun tptp.complex tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 X) Y)) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X)) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Y)))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power tptp.complex))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.nat tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 X) N)) (tptp.hAPP tptp.nat tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X)) N))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.inverse_divide tptp.complex))) (let ((_let_2 (tptp.fun tptp.complex tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 X) Y)) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_2 _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X)) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Y)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) X))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj _let_1) _let_1))) (forall ((Code_numeral_4 $$unsorted)) (not (= (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral tptp.code_S1047413653umeral Code_numeral_4) (tptp.zero_zero tptp.code_code_numeral)))) (forall ((Code_numeral_3 $$unsorted)) (not (= (tptp.zero_zero tptp.code_code_numeral) (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral tptp.code_S1047413653umeral Code_numeral_3)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 A_1))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.real tptp.complex _let_1 B)) (tptp.hAPP tptp.real tptp.complex _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) B))))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj tptp.ii) _let_212) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) X) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_sem1668676832m_mult X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_1))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_1 X)) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (= (= (tptp.hAPP X_a X_a _let_1 X_1) (tptp.hAPP X_a X_a _let_1 Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral (tptp.hAPP tptp.code_code_numeral (tptp.fun tptp.code_code_numeral tptp.code_code_numeral) (tptp.minus_minus tptp.code_code_numeral) (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral tptp.code_S1047413653umeral N)) (tptp.one_one tptp.code_code_numeral)) N)) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X_1)) (tptp.hAPP X_a X_a _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 Y)) (tptp.hAPP X_a X_a _let_1 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Y) (tptp.hAPP X_a X_a _let_1 X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) (tptp.hAPP X_a X_a _let_1 Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 Y)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 X)) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 Y)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a _let_1 X)) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 Y) (tptp.hAPP X_a X_a _let_1 X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 X) (tptp.hAPP X_a X_a _let_1 Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.boolean_algebra X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X_1)) (tptp.hAPP X_a X_a _let_3 Y_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) X_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.minus X_b) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_b (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2) X_2) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP X_a X_b A_3 X_2)) (tptp.hAPP X_a X_b B_2 X_2))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.minus X_a) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (= (tptp.hAPP X_b X_a (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP X_b X_a A_3 X_1)) (tptp.hAPP X_b X_a B_2 X_1))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.uminus X_b) (forall ((A_3 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_b (tptp.hAPP _let_1 _let_1 (tptp.uminus_uminus _let_1) A_3) X_2) (tptp.hAPP X_b X_b (tptp.uminus_uminus X_b) (tptp.hAPP X_a X_b A_3 X_2))))))) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm tptp.complex))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.complex tptp.real _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.complex tptp.real _let_1 X_2)) K_2))))))) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm tptp.complex))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.complex tptp.real _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.complex tptp.real _let_1 X_2)) K_2))))))) (exists ((K_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm tptp.complex))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.complex tptp.real _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.complex tptp.real _let_1 X_2)) K_2)))))) (forall ((Code_numeral_2 $$unsorted)) (let ((_let_1 (tptp.size_size tptp.code_code_numeral))) (= (tptp.hAPP tptp.code_code_numeral tptp.nat _let_1 (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral tptp.code_S1047413653umeral Code_numeral_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.code_code_numeral tptp.nat _let_1 Code_numeral_2)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.complex tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_1 (tptp.minus_minus tptp.complex) Z_1) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z_1)) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex _let_1 (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.complex tptp.real tptp.im Z_1)))) tptp.ii)))) (forall ((Y $$unsorted)) (=> (not (= Y (tptp.zero_zero tptp.code_code_numeral))) (not (forall ((Code_numeral_1 $$unsorted)) (not (= Y (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral tptp.code_S1047413653umeral Code_numeral_1))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 X) Y)) Y)) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex tptp.cnj X)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im X)))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) Z_1)) (tptp.zero_zero tptp.real))) (= (tptp.hAPP tptp.complex tptp.real tptp.im tptp.ii) _let_136) (= (tptp.hAPP tptp.complex tptp.real tptp.im _let_208) _let_37) (= (tptp.hAPP tptp.complex tptp.real tptp.im _let_207) _let_37) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.plus_plus tptp.complex) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im X)) (tptp.hAPP tptp.complex tptp.real tptp.im Y)))) (forall ((V $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.int tptp.complex (tptp.number_number_of tptp.complex) V)) (tptp.zero_zero tptp.real))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex (tptp.uminus_uminus tptp.complex) X)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im X)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.minus_minus tptp.complex) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im X)) (tptp.hAPP tptp.complex tptp.real tptp.im Y)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.nat tptp.complex (tptp.semiring_1_of_nat tptp.complex) N)) (tptp.zero_zero tptp.real))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im X))) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X)))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) Z_1) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z_1))) (tptp.zero_zero tptp.real))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex (tptp.sgn_sgn tptp.complex) Z_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im Z_1)) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) Z_1)))) (= (tptp.hAPP tptp.code_code_numeral tptp.nat _let_210 _let_209) _let_40) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X_2)) K_2)))))) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X_2)) K_2)))))) (exists ((K_2 $$unsorted)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X_2)) K_2))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP tptp.complex tptp.real tptp.im X))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.hAPP tptp.complex tptp.real tptp.re X))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_6 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 _let_5) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 _let_2) _let_1)))) (let ((_let_8 (tptp.inverse_divide tptp.real))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.inverse_inverse tptp.complex) X) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_6 _let_8 _let_5) _let_7)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_6 _let_8 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_2)) _let_7)))))))))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) Z_1) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z_1)) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.complex tptp.real tptp.re Z_1)) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.complex tptp.real tptp.im Z_1)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP tptp.complex tptp.real tptp.im X))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex (tptp.inverse_inverse tptp.complex) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.complex tptp.real tptp.re X)) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_4 _let_3 _let_2) _let_1)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 X) Y)) X)) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) Z_1)) Z_1)) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex tptp.cnj X)) (tptp.hAPP tptp.complex tptp.real tptp.re X))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= X_1 Y_1) (and (= (tptp.hAPP tptp.complex tptp.real tptp.re X_1) (tptp.hAPP tptp.complex tptp.real tptp.re Y_1)) (= (tptp.hAPP tptp.complex tptp.real tptp.im X_1) (tptp.hAPP tptp.complex tptp.real tptp.im Y_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (= (tptp.hAPP tptp.complex tptp.real tptp.re X) (tptp.hAPP tptp.complex tptp.real tptp.re Y)) (=> (= (tptp.hAPP tptp.complex tptp.real tptp.im X) (tptp.hAPP tptp.complex tptp.real tptp.im Y)) (= X Y)))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re X)) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X)))) (= (tptp.hAPP tptp.complex tptp.real tptp.re tptp.ii) _let_37) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.complex tptp.real tptp.re Z_1)) (tptp.hAPP tptp.complex tptp.real tptp.im Z_1)) Z_1)) (= (tptp.hAPP tptp.complex tptp.real tptp.re _let_208) _let_37) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.plus_plus tptp.complex) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re X)) (tptp.hAPP tptp.complex tptp.real tptp.re Y)))) (= (tptp.hAPP tptp.complex tptp.real tptp.re _let_207) _let_136) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex (tptp.uminus_uminus tptp.complex) X)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re X)))) (forall ((V $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.int tptp.complex (tptp.number_number_of tptp.complex) V)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) V))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.minus_minus tptp.complex) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re X)) (tptp.hAPP tptp.complex tptp.real tptp.re Y)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.nat tptp.complex (tptp.semiring_1_of_nat tptp.complex) N)) (tptp.hAPP tptp.nat tptp.real (tptp.semiring_1_of_nat tptp.real) N))) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re X))) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X)))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex (tptp.sgn_sgn tptp.complex) Z_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re Z_1)) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) Z_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.complex tptp.real tptp.re X)) (tptp.hAPP tptp.complex tptp.real tptp.im Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.complex tptp.real tptp.im X)) (tptp.hAPP tptp.complex tptp.real tptp.re Y))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.complex tptp.real tptp.re X)) (tptp.hAPP tptp.complex tptp.real tptp.re Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.complex tptp.real tptp.im X)) (tptp.hAPP tptp.complex tptp.real tptp.im Y))))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z_1) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.complex tptp.real tptp.re Z_1)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.im Z_1))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) Z_1) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) Z_1) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.plus_plus tptp.complex) X) Y) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.complex tptp.real tptp.re X)) (tptp.hAPP tptp.complex tptp.real tptp.re Y))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.complex tptp.real tptp.im X)) (tptp.hAPP tptp.complex tptp.real tptp.im Y))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.real))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.uminus_uminus tptp.complex) X) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.complex tptp.real tptp.re X))) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.complex tptp.real tptp.im X)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.complex tptp.real tptp.re Y))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.complex tptp.real tptp.im X)))) (let ((_let_5 (tptp.hAPP tptp.complex tptp.real tptp.im Y))) (let ((_let_6 (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.complex tptp.real tptp.re X)))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) X) Y) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real _let_6 _let_1)) (tptp.hAPP tptp.real tptp.real _let_4 _let_5))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.real tptp.real _let_6 _let_5)) (tptp.hAPP tptp.real tptp.real _let_4 _let_1))))))))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.plus_plus tptp.complex) Z_1) (tptp.hAPP tptp.complex tptp.complex tptp.cnj Z_1)) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.complex tptp.real tptp.re Z_1))))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) Z_1) (tptp.hAPP tptp.real tptp.real tptp.sqrt (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.complex tptp.real tptp.re Z_1)) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.complex tptp.real tptp.im Z_1)) _let_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.hAPP tptp.complex tptp.real tptp.re X))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex (tptp.inverse_inverse tptp.complex) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.inverse_divide tptp.real) _let_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 _let_4) _let_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.complex tptp.real tptp.im X)) _let_1)))))))))) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X_2)) K_2)))))) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X_2)) K_2)))))) (exists ((K_2 $$unsorted)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X_2)) K_2))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex tptp.expi Z_1) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) (tptp.hAPP tptp.complex tptp.real tptp.re Z_1)))) (tptp.hAPP tptp.real tptp.complex tptp.cis (tptp.hAPP tptp.complex tptp.real tptp.im Z_1))))) (forall ((N $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) A_1)) (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.nat tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.nat tptp.complex) (tptp.power_power tptp.complex) (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)) N)))) (forall ((N $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) A_1)) (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.nat tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.nat tptp.complex) (tptp.power_power tptp.complex) (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)) N)))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)) (tptp.hAPP tptp.real tptp.real tptp.cos A_1))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)) (tptp.hAPP tptp.real tptp.real tptp.sin A_1))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)) (tptp.hAPP tptp.real tptp.complex tptp.cis B)) (tptp.hAPP tptp.real tptp.complex tptp.cis (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) A_1) B)))) (= (tptp.hAPP tptp.real tptp.complex tptp.cis _let_37) _let_207) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex (tptp.inverse_inverse tptp.complex) (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)) (tptp.hAPP tptp.real tptp.complex tptp.cis (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) A_1)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.inverse_divide tptp.complex) (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)) (tptp.hAPP tptp.real tptp.complex tptp.cis B)) (tptp.hAPP tptp.real tptp.complex tptp.cis (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) A_1) B)))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.complex tptp.cis A_1) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.real tptp.real tptp.cos A_1)) (tptp.hAPP tptp.real tptp.real tptp.sin A_1)))) (forall ((A_1 $$unsorted) (N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.nat tptp.complex) (tptp.power_power tptp.complex) (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)) N) (tptp.hAPP tptp.real tptp.complex tptp.cis (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) A_1)))) (forall ((N $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.complex tptp.cis (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) A_1)) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)) (tptp.hAPP tptp.real tptp.complex tptp.cis (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.nat tptp.real _let_1 N)) A_1)))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) tptp.bezw X) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) (tptp.one_one tptp.int)) (tptp.zero_zero tptp.int))))) (forall ((X_a $$unsorted) (S $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.finite_finite_1 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 T_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 S))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) S) T_3))))))))) (forall ((Y $$unsorted) (X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((X_a $$unsorted) (S $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.finite_finite_1 X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) S) T_3)) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 S))) (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 T_3)))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((Y $$unsorted) (X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X) Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X) Y))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Y) Z_1)))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (R_3 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.in_rel X_a X_b) R_3) X_1) Y_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_1) Y_1)) R_3))))))) (forall ((M $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 B))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_1 A_1))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.divmod_int A_1) B))) (let ((_let_7 (tptp.zero_zero tptp.int))) (let ((_let_8 (tptp.fun tptp.int tptp.bool))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_8 (tptp.ord_less tptp.int) _let_7) B)))) (let ((_let_10 (tptp.hAPP tptp.int _let_8 (tptp.ord_less_eq tptp.int) _let_7))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_10 A_1)))) (let ((_let_12 (= (tptp.ti tptp.int A_1) _let_7))) (let ((_let_13 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_10 B)))) (and (=> _let_11 (and (=> _let_13 (= _let_6 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.posDivAlg A_1) B))) (=> (not _let_13) (and (=> _let_12 (= _let_6 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 (tptp.product_Pair tptp.int tptp.int) _let_7) _let_7))) (=> (not _let_12) (= _let_6 (tptp.hAPP _let_4 _let_4 tptp.negateSnd (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.negDivAlg _let_3) _let_2)))))))) (=> (not _let_11) (and (=> _let_9 (= _let_6 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.negDivAlg A_1) B))) (=> (not _let_9) (= _let_6 (tptp.hAPP _let_4 _let_4 tptp.negateSnd (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 tptp.posDivAlg _let_3) _let_2))))))))))))))))))))) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime _let_40))) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime _let_179))) (forall ((Q_3 $$unsorted) (P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime Q_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_5) Q_3)) (= P_5 Q_3))))) (forall ((Q_3 $$unsorted) (P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime Q_3)) (=> (not (= P_5 Q_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime P_5) Q_3)))))) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime _let_206))) (forall ((P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) P_5)))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_4)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) A_2) B_1))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) A_1) B))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B))))))) (forall ((M $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M) N))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N))))))) (forall ((P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) P_5) Q_3))) (or (= P_5 _let_1) (= Q_3 _let_1))))) (forall ((X $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 X) N))) (let ((_let_4 (tptp.dvd_dvd tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 P_5) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 P_5) N)) _let_3)))))))))) (forall ((X $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) X) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 X)))))) (forall ((A_1 $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) A_1) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1)))))) (forall ((P_4 $$unsorted) (N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) P_4) N_1))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_4)) (= N_1 (tptp.one_one tptp.nat))))) (forall ((P_5 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime A_1) B)) (not (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 B)))))))) (forall ((N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) P_5) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime P_5) N)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime A_2) B_1)) (forall ((P_6 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_6))) (not (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_6)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1)))))))) (forall ((A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime A_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) A_1))))) (forall ((P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) P_5)))) (forall ((P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_5) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))))) (forall ((M $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (not (= N (tptp.zero_zero tptp.nat))) (=> (= N (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) P_5) M)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)))))) (forall ((P_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_4)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.one_one tptp.nat)) P_4)) (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) M_2) P_4)) (or (= M_2 (tptp.one_one tptp.nat)) (= M_2 P_4))))))) (forall ((D_1 $$unsorted) (K $$unsorted) (P_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_4)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) D_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) P_4) K))) (exists ((I_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) I_2) K)) (= D_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) P_4) I_2))))))) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.power_power tptp.nat) P_5) N)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 P_5) B))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) A_1) B))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 A_1)))))))))) (forall ((X $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.zero_zero tptp.nat)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 X) P_5)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime X) P_5)))))))) (forall ((N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (or (= N (tptp.one_one tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) P_5) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 tptp.coprime P_5) N)))))) (forall ((Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) Q_3))) (= (tptp.hAPP _let_1 _let_1 tptp.negateSnd (tptp.hAPP tptp.int _let_1 _let_2 R_4)) (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) R_4)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (Qr_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.uminus_uminus tptp.int))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.divmod_int_rel (tptp.hAPP tptp.int tptp.int _let_4 A_1)) (tptp.hAPP tptp.int tptp.int _let_4 B)) Qr_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.divmod_int_rel A_1) B) (tptp.hAPP _let_1 _let_1 tptp.negateSnd Qr_1))))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime _let_6)) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (not (= (tptp.ti tptp.int B) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.divmod_int_rel A_1) B) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.divmod_int A_1) B))))))) (forall ((M $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) M) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)))))) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.power_power tptp.nat) P_5) N)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 tptp.coprime A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) A_1) B))) (or (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 A_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 B)))))))))) (forall ((P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_5)))) (forall ((P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (or (= P_5 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.even_odd_even tptp.nat) P_5)))))) (forall ((P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.divmod_int P_5) Q_3) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) P_5) Q_3)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) P_5) Q_3))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.code_code_numeral tptp.code_code_numeral))) (let ((_let_2 (tptp.product_prod tptp.code_code_numeral tptp.code_code_numeral))) (let ((_let_3 (tptp.fun tptp.code_code_numeral _let_2))) (= (tptp.hAPP tptp.code_code_numeral _let_2 (tptp.hAPP tptp.code_code_numeral _let_3 tptp.code_d418564891umeral N) M) (tptp.hAPP tptp.code_code_numeral _let_2 (tptp.hAPP tptp.code_code_numeral _let_3 (tptp.product_Pair tptp.code_code_numeral tptp.code_code_numeral) (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral (tptp.hAPP tptp.code_code_numeral _let_1 (tptp.div_div tptp.code_code_numeral) N) M)) (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral (tptp.hAPP tptp.code_code_numeral _let_1 (tptp.div_mod tptp.code_code_numeral) N) M))))))) (forall ((M $$unsorted) (R_4 $$unsorted) (S_3 $$unsorted) (T_5 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.product_prod tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N)) (=> (= (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.xzgcd M) N) (tptp.hAPP _let_3 _let_4 (tptp.hAPP tptp.int (tptp.fun _let_3 _let_4) (tptp.product_Pair tptp.int _let_3) R_4) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) (tptp.product_Pair tptp.int tptp.int) S_3) T_5))) (= (tptp.ti tptp.int R_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 S_3) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 T_5) N)))))))))) (forall ((M $$unsorted) (N $$unsorted) (R_5 $$unsorted) (S_4 $$unsorted) (S_3 $$unsorted) (T_6 $$unsorted) (T_5 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) R_5) R_4)))) (let ((_let_3 (tptp.minus_minus tptp.int))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (let ((_let_5 (tptp.product_prod tptp.int _let_4))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (let ((_let_9 (tptp.fun tptp.int _let_8))) (let ((_let_10 (tptp.fun tptp.int _let_9))) (let ((_let_11 (tptp.fun tptp.int _let_10))) (let ((_let_12 (tptp.hAPP tptp.int _let_11 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_11) tptp.xzgcda M) N))) (let ((_let_13 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 (tptp.hAPP tptp.int _let_9 (tptp.hAPP tptp.int _let_10 _let_12 R_5) R_4) S_4) S_3) T_6) T_5))) (let ((_let_14 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) R_4) (tptp.zero_zero tptp.int))))) (and (=> _let_14 (= _let_13 (tptp.hAPP _let_4 _let_5 (tptp.hAPP tptp.int (tptp.fun _let_4 _let_5) (tptp.product_Pair tptp.int _let_4) R_5) (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) (tptp.product_Pair tptp.int tptp.int) S_4) T_6)))) (=> (not _let_14) (= _let_13 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 (tptp.hAPP tptp.int _let_9 (tptp.hAPP tptp.int _let_10 _let_12 R_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) R_5) R_4)) S_3) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 S_4) (tptp.hAPP tptp.int tptp.int _let_2 S_3))) T_5) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 T_6) (tptp.hAPP tptp.int tptp.int _let_2 T_5))))))))))))))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int (tptp.product_prod tptp.int tptp.int)))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (let ((_let_9 (tptp.fun tptp.int _let_8))) (= (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 tptp.xzgcd M) N) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 (tptp.hAPP tptp.int _let_9 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_9) tptp.xzgcda M) N) M) N) _let_1) _let_2) _let_2) _let_1)))))))))))) (forall ((M $$unsorted) (N $$unsorted) (R_5 $$unsorted) (S_4 $$unsorted) (S_3 $$unsorted) (T_6 $$unsorted) (T_5 $$unsorted) (Rn $$unsorted) (Sn_1 $$unsorted) (Tn_1 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.plus_plus tptp.int))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (let ((_let_5 (tptp.product_prod tptp.int _let_4))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (let ((_let_9 (tptp.fun tptp.int _let_8))) (let ((_let_10 (tptp.fun tptp.int _let_9))) (let ((_let_11 (tptp.fun tptp.int _let_10))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) R_4)) (=> (= (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 (tptp.hAPP tptp.int _let_9 (tptp.hAPP tptp.int _let_10 (tptp.hAPP tptp.int _let_11 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_11) tptp.xzgcda M) N) R_5) R_4) S_4) S_3) T_6) T_5) (tptp.hAPP _let_4 _let_5 (tptp.hAPP tptp.int (tptp.fun _let_4 _let_5) (tptp.product_Pair tptp.int _let_4) Rn) (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) (tptp.product_Pair tptp.int tptp.int) Sn_1) Tn_1))) (=> (= (tptp.ti tptp.int R_5) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 S_4) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 T_6) N))) (=> (= (tptp.ti tptp.int R_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 S_3) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 T_5) N))) (= (tptp.ti tptp.int Rn) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Sn_1) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 Tn_1) N))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime X) Y))) (exists ((P_6 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_6))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_6)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y))))))) (forall ((X $$unsorted) (K_4 $$unsorted) (N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (not (= N (tptp.zero_zero tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 X) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 P_5) K_4)) (exists ((I_2 $$unsorted)) (= X (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) P_5) I_2))))))))) (forall ((N $$unsorted)) (=> (not (= N (tptp.one_one tptp.nat))) (exists ((P_6 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_6)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_6) N)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) M) N))) (let ((_let_3 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.nat _let_4 tptp.divmod_nat M) N) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.nat _let_4 (tptp.product_Pair tptp.nat tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) _let_2) N))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) _let_2) N))))))))))) (forall ((A_1 $$unsorted) (P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) P_5) A_1))) (exists ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) X_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 P_5) Y_2)) (tptp.one_one tptp.nat))))))))) (forall ((N $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) N)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime N)))) (exists ((M_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 M_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_3 K_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M_2) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 K_1) N)) (= N (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) M_2) K_1))))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 tptp.divmod_nat M) _let_1) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.product_Pair tptp.nat tptp.nat) _let_1) M)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M) N)) (= (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat _let_2 tptp.divmod_nat M) N) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.product_Pair tptp.nat tptp.nat) (tptp.zero_zero tptp.nat)) M)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 tptp.divmod_nat M) N) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.product_Pair tptp.nat tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) M) N))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) A_1))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 R_4))) (let ((_let_4 (tptp.product_Pair tptp.nat tptp.nat))) (let ((_let_5 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.nat _let_7 (tptp.hAPP tptp.nat _let_8 tptp.divmod_nat_rel B) C) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP tptp.nat _let_6 _let_4 Q_3) R_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) C)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.nat _let_7 (tptp.hAPP tptp.nat _let_8 tptp.divmod_nat_rel (tptp.hAPP tptp.nat tptp.nat _let_2 B)) C) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP tptp.nat _let_6 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_2 Q_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) _let_3) C))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) _let_3) C))))))))))))))) (forall ((C $$unsorted) (A_1 $$unsorted) (B $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) B))) (let ((_let_3 (tptp.product_Pair tptp.nat tptp.nat))) (let ((_let_4 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun _let_4 tptp.bool))) (let ((_let_7 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_6) tptp.divmod_nat_rel A_1))) (let ((_let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.nat _let_6 _let_7 B) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat _let_5 _let_3 Q_3) R_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_8 B)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_8 C)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.nat _let_6 _let_7 (tptp.hAPP tptp.nat tptp.nat _let_2 C)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat _let_5 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) Q_3) C)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) Q_3) C))) R_4)))))))))))))))) (forall ((B $$unsorted) (Bq $$unsorted) (Br $$unsorted) (A_1 $$unsorted) (C $$unsorted) (Aq $$unsorted) (Ar $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Ar) Br))) (let ((_let_4 (tptp.product_Pair tptp.nat tptp.nat))) (let ((_let_5 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.fun _let_5 tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.nat _let_7 (tptp.hAPP tptp.nat _let_8 tptp.divmod_nat_rel A_1) C) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP tptp.nat _let_6 _let_4 Aq) Ar))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.nat _let_7 (tptp.hAPP tptp.nat _let_8 tptp.divmod_nat_rel B) C) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP tptp.nat _let_6 _let_4 Bq) Br))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) C)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.nat _let_7 (tptp.hAPP tptp.nat _let_8 tptp.divmod_nat_rel (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B)) C) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP tptp.nat _let_6 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Aq) Bq)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.div_div tptp.nat) _let_3) C))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.div_mod tptp.nat) _let_3) C)))))))))))))))) (forall ((Qr_2 $$unsorted) (M $$unsorted) (N $$unsorted) (Qr_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) tptp.divmod_nat_rel M) N))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 Qr_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 Qr_2)) (= Qr_1 Qr_2))))))) (forall ((M $$unsorted) (N $$unsorted) (Qr_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) tptp.divmod_nat_rel M) N) Qr_1)) (= (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) tptp.divmod_nat M) N) Qr_1))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) tptp.divmod_nat_rel M) N) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) tptp.divmod_nat M) N)))))) (forall ((M $$unsorted) (N $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) tptp.divmod_nat_rel M) N) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.product_Pair tptp.nat tptp.nat) Q_3) R_4))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) M) N) Q_3))))) (forall ((M $$unsorted) (N $$unsorted) (Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) tptp.divmod_nat_rel M) N) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.product_Pair tptp.nat tptp.nat) Q_3) R_4))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M) N) R_4))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_3) tptp.divmod_nat_rel M) N) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.product_Pair tptp.nat tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) M) N)))))))) (forall ((M $$unsorted) (N $$unsorted)) (not (forall ((Q_4 $$unsorted) (R_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) tptp.divmod_nat_rel M) N) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.product_Pair tptp.nat tptp.nat) Q_4) R_2))))))))) (forall ((N $$unsorted)) (exists ((P_6 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_6)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) N) P_6))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W))) (let ((_let_2 (tptp.uminus_uminus tptp.int))) (let ((_let_3 (tptp.one_one tptp.int))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) _let_3) _let_1) (tptp.hAPP _let_4 tptp.int (tptp.product_fst tptp.int tptp.int) (tptp.hAPP _let_4 _let_4 tptp.negateSnd (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.negDivAlg (tptp.hAPP tptp.int tptp.int _let_2 _let_3)) (tptp.hAPP tptp.int tptp.int _let_2 _let_1))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B) (tptp.hAPP _let_1 tptp.int (tptp.product_fst tptp.int tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.divmod_int A_1) B))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) _let_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_2) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B) (tptp.hAPP _let_1 tptp.int (tptp.product_fst tptp.int tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.negDivAlg A_1) B)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) _let_2) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B) (tptp.hAPP _let_1 tptp.int (tptp.product_fst tptp.int tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.posDivAlg A_1) B))))))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) _let_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) _let_2) _let_1) (tptp.hAPP _let_3 tptp.int (tptp.product_fst tptp.int tptp.int) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.posDivAlg _let_2) _let_1)))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 _let_3) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 B) _let_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B) (tptp.hAPP _let_2 tptp.int (tptp.product_fst tptp.int tptp.int) (tptp.hAPP _let_2 _let_2 tptp.negateSnd (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.negDivAlg (tptp.hAPP tptp.int tptp.int _let_1 A_1)) (tptp.hAPP tptp.int tptp.int _let_1 B))))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) A_1) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) B) _let_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B) (tptp.hAPP _let_2 tptp.int (tptp.product_fst tptp.int tptp.int) (tptp.hAPP _let_2 _let_2 tptp.negateSnd (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.posDivAlg (tptp.hAPP tptp.int tptp.int _let_1 A_1)) (tptp.hAPP tptp.int tptp.int _let_1 B)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 tptp.bezw Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) X) Y)))) (let ((_let_5 (tptp.hAPP _let_2 tptp.int (tptp.product_snd tptp.int tptp.int) _let_4))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_8 (tptp.fun tptp.int _let_2))) (let ((_let_9 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 tptp.bezw X) Y))) (let ((_let_10 (= Y (tptp.zero_zero tptp.nat)))) (and (=> _let_10 (= _let_9 (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_8 _let_7 (tptp.one_one tptp.int)) (tptp.zero_zero tptp.int)))) (=> (not _let_10) (= _let_9 (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_8 _let_7 _let_5) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 (tptp.minus_minus tptp.int) (tptp.hAPP _let_2 tptp.int (tptp.product_fst tptp.int tptp.int) _let_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 (tptp.times_times tptp.int) _let_5) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) X) Y))))))))))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 tptp.bezw Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) X) Y)))) (let ((_let_5 (tptp.hAPP _let_2 tptp.int (tptp.product_snd tptp.int tptp.int) _let_4))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) Y)) (= (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 tptp.bezw X) Y) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.product_Pair tptp.int tptp.int) _let_5) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 (tptp.minus_minus tptp.int) (tptp.hAPP _let_2 tptp.int (tptp.product_fst tptp.int tptp.int) _let_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 (tptp.times_times tptp.int) _let_5) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) X) Y)))))))))))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W))) (let ((_let_2 (tptp.uminus_uminus tptp.int))) (let ((_let_3 (tptp.one_one tptp.int))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) _let_3) _let_1) (tptp.hAPP _let_4 tptp.int (tptp.product_snd tptp.int tptp.int) (tptp.hAPP _let_4 _let_4 tptp.negateSnd (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.negDivAlg (tptp.hAPP tptp.int tptp.int _let_2 _let_3)) (tptp.hAPP tptp.int tptp.int _let_2 _let_1))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B) (tptp.hAPP _let_1 tptp.int (tptp.product_snd tptp.int tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.divmod_int A_1) B))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.ord_less tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_1) _let_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 _let_2) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B) (tptp.hAPP _let_1 tptp.int (tptp.product_snd tptp.int tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.negDivAlg A_1) B)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.zero_zero tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_2) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less_eq tptp.int) _let_2) B)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B) (tptp.hAPP _let_1 tptp.int (tptp.product_snd tptp.int tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.posDivAlg A_1) B))))))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W))) (let ((_let_2 (tptp.one_one tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) _let_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) _let_2) _let_1) (tptp.hAPP _let_3 tptp.int (tptp.product_snd tptp.int tptp.int) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.posDivAlg _let_2) _let_1)))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 _let_3) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 B) _let_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B) (tptp.hAPP _let_2 tptp.int (tptp.product_snd tptp.int tptp.int) (tptp.hAPP _let_2 _let_2 tptp.negateSnd (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.negDivAlg (tptp.hAPP tptp.int tptp.int _let_1 A_1)) (tptp.hAPP tptp.int tptp.int _let_1 B))))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.zero_zero tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less tptp.int) A_1) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) B) _let_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) A_1) B) (tptp.hAPP _let_2 tptp.int (tptp.product_snd tptp.int tptp.int) (tptp.hAPP _let_2 _let_2 tptp.negateSnd (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.posDivAlg (tptp.hAPP tptp.int tptp.int _let_1 A_1)) (tptp.hAPP tptp.int tptp.int _let_1 B)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (G $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun _let_1 tptp.nat))) (let ((_let_5 (tptp.fun X_b tptp.nat))) (= (tptp.hAPP _let_1 tptp.nat (tptp.hAPP _let_5 _let_4 (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_5 _let_4) (tptp.product_prod_size X_a X_b) F) G) P_4) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP X_a tptp.nat F (tptp.hAPP _let_1 X_a (tptp.product_fst X_a X_b) P_4))) (tptp.hAPP X_b tptp.nat G (tptp.hAPP _let_1 X_b (tptp.product_snd X_a X_b) P_4)))) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.hAPP X_b (tptp.fun X_a _let_1) (tptp.product_Pair X_b X_a) X_1) Y_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_3 P_1 Y_1) X_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_3 P_1 (tptp.hAPP _let_1 X_a (tptp.product_snd X_b X_a) _let_2)) (tptp.hAPP _let_1 X_b (tptp.product_fst X_b X_a) _let_2)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (Q_2 $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) P_4) Q_2))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 P_4)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_1 Q_2)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.hAPP _let_1 X_a (tptp.product_fst X_a X_b) _let_2))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool Q_1 (tptp.hAPP _let_1 X_b (tptp.product_snd X_a X_b) _let_2))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_div tptp.nat) M) N) (tptp.hAPP _let_1 tptp.nat (tptp.product_fst tptp.nat tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) tptp.divmod_nat M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M) N) (tptp.hAPP _let_1 tptp.nat (tptp.product_snd tptp.nat tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) tptp.divmod_nat M) N))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (Qr $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP _let_2 tptp.nat (tptp.product_snd tptp.nat tptp.nat) Qr))) (let ((_let_4 (tptp.ord_less_eq tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (let ((_let_6 (tptp.ord_less tptp.nat))) (let ((_let_7 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_6 _let_1) N_1)))) (let ((_let_8 (= N_1 _let_1))) (let ((_let_9 (tptp.hAPP _let_2 tptp.nat (tptp.product_fst tptp.nat tptp.nat) Qr))) (let ((_let_10 (tptp.fun tptp.nat tptp.nat))) (let ((_let_11 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.nat _let_11 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_11) tptp.divmod_nat_rel Ma) N_1) Qr)) (and (= Ma (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_10 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_10 (tptp.times_times tptp.nat) _let_9) N_1)) _let_3)) (=> _let_8 (= _let_9 _let_1)) (=> (not _let_8) (and (=> _let_7 (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 _let_1) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_6 _let_3) N_1)))) (=> (not _let_7) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_6 N_1) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 _let_4 _let_3) _let_1)))))))))))))))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.product_prod tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.real _let_4 (tptp.hAPP tptp.real _let_5 (tptp.hAPP (tptp.fun _let_3 tptp.bool) (tptp.fun tptp.real _let_5) tptp.bolzano_bisect P_1) A_2) B_1) N_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) B_1)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP _let_3 tptp.real (tptp.product_snd tptp.real tptp.real) _let_6)) (tptp.hAPP _let_3 tptp.real (tptp.product_fst tptp.real tptp.real) _let_6)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 B_1) A_2)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N_1))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (T_5 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (= (tptp.ti _let_1 T_5) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) (tptp.hAPP _let_1 X_a (tptp.product_fst X_a X_b) T_5)) (tptp.hAPP _let_1 X_b (tptp.product_snd X_a X_b) T_5))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (= (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) (tptp.hAPP _let_1 X_a (tptp.product_fst X_a X_b) P_5)) (tptp.hAPP _let_1 X_b (tptp.product_snd X_a X_b) P_5)) (tptp.ti _let_1 P_5)))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) B_1)) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1) N_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_1 tptp.real (tptp.product_fst tptp.real tptp.real) _let_4)) (tptp.hAPP _let_1 tptp.real (tptp.product_snd tptp.real tptp.real) _let_4)))))))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (= (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.product_Pair tptp.real tptp.real) A_2) B_1)))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) B_1)) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1))) (let ((_let_5 (tptp.product_fst tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_1 tptp.real _let_5 (tptp.hAPP tptp.nat _let_1 _let_4 N_2))) (tptp.hAPP _let_1 tptp.real _let_5 (tptp.hAPP tptp.nat _let_1 _let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))))))))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) B_1)) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1))) (let ((_let_5 (tptp.product_snd tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_1 tptp.real _let_5 (tptp.hAPP tptp.nat _let_1 _let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))) (tptp.hAPP _let_1 tptp.real _let_5 (tptp.hAPP tptp.nat _let_1 _let_4 N_2)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted)) (= (forall ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a X_b) tptp.bool P_1 X1))) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_4) B_4))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_8 $$unsorted) (B_7 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (= (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_2) B_1) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_8) B_7)) (and (= (tptp.ti X_a A_2) (tptp.ti X_a A_8)) (= (tptp.ti X_b B_1) (tptp.ti X_b B_7)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted) (A_6 $$unsorted) (B_5 $$unsorted)) (let ((_let_1 (tptp.product_Pair X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun X_b _let_2))) (=> (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_1) B) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a _let_3 _let_1 A_6) B_5)) (not (=> (= (tptp.ti X_a A_1) (tptp.ti X_a A_6)) (not (= (tptp.ti X_b B) (tptp.ti X_b B_5)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_a))) (= (tptp.hAPP _let_1 X_a (tptp.product_snd X_b X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP X_b (tptp.fun X_a _let_1) (tptp.product_Pair X_b X_a) A_1) B)) (tptp.ti X_a B)))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X $$unsorted) (Y $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ti X_a A_1))) (let ((_let_2 (tptp.product_prod X_b X_a))) (=> (= (tptp.hAPP _let_2 X_a (tptp.product_snd X_b X_a) (tptp.hAPP X_a _let_2 (tptp.hAPP X_b (tptp.fun X_a _let_2) (tptp.product_Pair X_b X_a) X) Y)) _let_1) (= (tptp.ti X_a Y) _let_1))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (= (tptp.hAPP _let_1 X_a (tptp.product_fst X_a X_b) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_1) B)) (tptp.ti X_a A_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X $$unsorted) (Y $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.ti X_a A_1))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (= (tptp.hAPP _let_2 X_a (tptp.product_fst X_a X_b) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) X) Y)) _let_1) (= (tptp.ti X_a X) _let_1))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.product_snd X_a X_b))) (let ((_let_3 (tptp.product_fst X_a X_b))) (=> (= (tptp.hAPP _let_1 X_a _let_3 P_5) (tptp.hAPP _let_1 X_a _let_3 Q_3)) (=> (= (tptp.hAPP _let_1 X_b _let_2 P_5) (tptp.hAPP _let_1 X_b _let_2 Q_3)) (= (tptp.ti _let_1 P_5) (tptp.ti _let_1 Q_3)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Sa $$unsorted) (Ta $$unsorted)) (let ((_let_1 (tptp.product_snd X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.product_fst X_a X_b))) (= (= (tptp.ti _let_2 Sa) (tptp.ti _let_2 Ta)) (and (= (tptp.hAPP _let_2 X_a _let_3 Sa) (tptp.hAPP _let_2 X_a _let_3 Ta)) (= (tptp.hAPP _let_2 X_b _let_1 Sa) (tptp.hAPP _let_2 X_b _let_1 Ta)))))))) (forall ((N_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1) N_1))) (let ((_let_5 (tptp.product_Pair tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_1))) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.real tptp.real))) (let ((_let_2 (tptp.product_prod tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 _let_1 A_4))) (let ((_let_5 (tptp.ord_less_eq tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 _let_4 B_4))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 _let_1 B_4) C_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 A_4) B_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 B_4) C_4)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 _let_4 C_4)))))))))))))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real _let_6 _let_5 A_2) B_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) B_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP _let_1 tptp.real (tptp.product_fst tptp.real tptp.real) _let_4)) (tptp.hAPP _let_1 tptp.real (tptp.product_snd tptp.real tptp.real) _let_4))))))))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.real tptp.real))) (let ((_let_2 (tptp.product_prod tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 _let_1 A_4))) (let ((_let_5 (tptp.ord_less_eq tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 _let_4 B_4))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 _let_1 B_4) C_4))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 A_4) B_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 B_4) C_4))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 _let_4 C_4))))))))))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.product_Pair tptp.real tptp.real) A_2) B_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) B_1)) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1) N_2))) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.product_Pair tptp.real tptp.real) (tptp.hAPP _let_1 tptp.real (tptp.product_fst tptp.real tptp.real) _let_4)) (tptp.hAPP _let_1 tptp.real (tptp.product_snd tptp.real tptp.real) _let_4))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_a))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) P_1 (tptp.hAPP _let_1 X_a (tptp.product_snd X_b X_a) P_4)) (tptp.hAPP _let_1 X_b (tptp.product_fst X_b X_a) P_4))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) P_1 Y_2) X_2)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (Y $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.product_prod X_a _let_1))) (not (= (tptp.ti _let_2 Y) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_a (tptp.fun _let_1 _let_2) (tptp.product_Pair X_a _let_1) A_4) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) B_4) C_4))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.product_prod X_a _let_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_a (tptp.fun _let_1 _let_2) (tptp.product_Pair X_a _let_1) A_4) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) B_4) C_4))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b X_c)) tptp.bool P_1 X_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (Y $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted) (D_3 $$unsorted)) (let ((_let_1 (tptp.product_prod X_c X_d))) (let ((_let_2 (tptp.product_prod X_b _let_1))) (let ((_let_3 (tptp.product_prod X_a _let_2))) (not (= (tptp.ti _let_3 Y) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_a (tptp.fun _let_2 _let_3) (tptp.product_Pair X_a _let_2) A_4) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_2) (tptp.product_Pair X_b _let_1) B_4) (tptp.hAPP X_d _let_1 (tptp.hAPP X_c (tptp.fun X_d _let_1) (tptp.product_Pair X_c X_d) C_4) D_3))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (X_f $$unsorted) (X_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted) (D_3 $$unsorted) (E $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.product_prod X_e X_f))) (let ((_let_2 (tptp.product_prod X_d _let_1))) (let ((_let_3 (tptp.product_prod X_c _let_2))) (let ((_let_4 (tptp.product_prod X_b _let_3))) (let ((_let_5 (tptp.product_prod X_a _let_4))) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool P_1 (tptp.hAPP _let_4 _let_5 (tptp.hAPP X_a (tptp.fun _let_4 _let_5) (tptp.product_Pair X_a _let_4) A_4) (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_b (tptp.fun _let_3 _let_4) (tptp.product_Pair X_b _let_3) B_4) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_c (tptp.fun _let_2 _let_3) (tptp.product_Pair X_c _let_2) C_4) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_d (tptp.fun _let_1 _let_2) (tptp.product_Pair X_d _let_1) D_3) (tptp.hAPP X_f _let_1 (tptp.hAPP X_e (tptp.fun X_f _let_1) (tptp.product_Pair X_e X_f) E) F_3))))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b (tptp.product_prod X_c (tptp.product_prod X_d (tptp.product_prod X_e X_f))))) tptp.bool P_1 X_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (X_f $$unsorted) (Y $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted) (D_3 $$unsorted) (E $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.product_prod X_e X_f))) (let ((_let_2 (tptp.product_prod X_d _let_1))) (let ((_let_3 (tptp.product_prod X_c _let_2))) (let ((_let_4 (tptp.product_prod X_b _let_3))) (let ((_let_5 (tptp.product_prod X_a _let_4))) (not (= (tptp.ti _let_5 Y) (tptp.hAPP _let_4 _let_5 (tptp.hAPP X_a (tptp.fun _let_4 _let_5) (tptp.product_Pair X_a _let_4) A_4) (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_b (tptp.fun _let_3 _let_4) (tptp.product_Pair X_b _let_3) B_4) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_c (tptp.fun _let_2 _let_3) (tptp.product_Pair X_c _let_2) C_4) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_d (tptp.fun _let_1 _let_2) (tptp.product_Pair X_d _let_1) D_3) (tptp.hAPP X_f _let_1 (tptp.hAPP X_e (tptp.fun X_f _let_1) (tptp.product_Pair X_e X_f) E) F_3))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (X_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted) (D_3 $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.product_prod X_d X_e))) (let ((_let_2 (tptp.product_prod X_c _let_1))) (let ((_let_3 (tptp.product_prod X_b _let_2))) (let ((_let_4 (tptp.product_prod X_a _let_3))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool P_1 (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_a (tptp.fun _let_3 _let_4) (tptp.product_Pair X_a _let_3) A_4) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_b (tptp.fun _let_2 _let_3) (tptp.product_Pair X_b _let_2) B_4) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c (tptp.fun _let_1 _let_2) (tptp.product_Pair X_c _let_1) C_4) (tptp.hAPP X_e _let_1 (tptp.hAPP X_d (tptp.fun X_e _let_1) (tptp.product_Pair X_d X_e) D_3) E))))))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b (tptp.product_prod X_c (tptp.product_prod X_d X_e)))) tptp.bool P_1 X_1)))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (Y $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted) (D_3 $$unsorted) (E $$unsorted)) (let ((_let_1 (tptp.product_prod X_d X_e))) (let ((_let_2 (tptp.product_prod X_c _let_1))) (let ((_let_3 (tptp.product_prod X_b _let_2))) (let ((_let_4 (tptp.product_prod X_a _let_3))) (not (= (tptp.ti _let_4 Y) (tptp.hAPP _let_3 _let_4 (tptp.hAPP X_a (tptp.fun _let_3 _let_4) (tptp.product_Pair X_a _let_3) A_4) (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_b (tptp.fun _let_2 _let_3) (tptp.product_Pair X_b _let_2) B_4) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_c (tptp.fun _let_1 _let_2) (tptp.product_Pair X_c _let_1) C_4) (tptp.hAPP X_e _let_1 (tptp.hAPP X_d (tptp.fun X_e _let_1) (tptp.product_Pair X_d X_e) D_3) E))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (X_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted) (D_3 $$unsorted)) (let ((_let_1 (tptp.product_prod X_c X_d))) (let ((_let_2 (tptp.product_prod X_b _let_1))) (let ((_let_3 (tptp.product_prod X_a _let_2))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool P_1 (tptp.hAPP _let_2 _let_3 (tptp.hAPP X_a (tptp.fun _let_2 _let_3) (tptp.product_Pair X_a _let_2) A_4) (tptp.hAPP _let_1 _let_2 (tptp.hAPP X_b (tptp.fun _let_1 _let_2) (tptp.product_Pair X_b _let_1) B_4) (tptp.hAPP X_d _let_1 (tptp.hAPP X_c (tptp.fun X_d _let_1) (tptp.product_Pair X_c X_d) C_4) D_3))))))))) (tptp.hBOOL (tptp.hAPP (tptp.product_prod X_a (tptp.product_prod X_b (tptp.product_prod X_c X_d))) tptp.bool P_1 X_1)))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.product_prod X_b X_c))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 X_a) (tptp.product_prod_rec X_b X_c X_a) F1) (tptp.hAPP X_c _let_2 (tptp.hAPP X_b (tptp.fun X_c _let_2) (tptp.product_Pair X_b X_c) A_2) B_1)) (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_1 F1 A_2) B_1))))) (= _let_201 (tptp.hAPP tptp.int tptp.quickcheck_code_int _let_203 _let_3)) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.quickcheck_code_int (tptp.number_number_of tptp.quickcheck_code_int) _let_1))) (let ((_let_3 (tptp.fun tptp.quickcheck_code_int tptp.quickcheck_code_int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) _let_1)) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of (tptp.hAPP tptp.quickcheck_code_int tptp.quickcheck_code_int (tptp.hAPP tptp.quickcheck_code_int _let_3 (tptp.div_div tptp.quickcheck_code_int) K_4) _let_2))))) (let ((_let_6 (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of K_4))) (let ((_let_7 (tptp.zero_zero tptp.quickcheck_code_int))) (let ((_let_8 (= (tptp.hAPP tptp.quickcheck_code_int tptp.quickcheck_code_int (tptp.hAPP tptp.quickcheck_code_int _let_3 (tptp.div_mod tptp.quickcheck_code_int) K_4) _let_2) _let_7))) (let ((_let_9 (= K_4 _let_7))) (and (=> _let_9 (= _let_6 (tptp.zero_zero tptp.int))) (=> (not _let_9) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (= _let_6 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.plus_plus tptp.int) _let_5) (tptp.one_one tptp.int))))))))))))))))) (forall ((R_4 $$unsorted) (A_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.nat tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.nat tptp.complex) (tptp.power_power tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.rcis R_4) A_1)) N) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.rcis (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) R_4) N)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) A_1))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.quickcheck_code_int tptp.bool (tptp.hAPP tptp.quickcheck_code_int (tptp.fun tptp.quickcheck_code_int tptp.bool) (tptp.ord_less_eq tptp.quickcheck_code_int) N_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of N_1)) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of Ma))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.quickcheck_code_int tptp.bool (tptp.hAPP tptp.quickcheck_code_int (tptp.fun tptp.quickcheck_code_int tptp.bool) (tptp.ord_less tptp.quickcheck_code_int) N_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of N_1)) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of Ma))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of X_1) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of Y_1)) (= X_1 Y_1))) (forall ((K $$unsorted) (L $$unsorted)) (= (= (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of K) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of L)) (= K L))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of (tptp.hAPP tptp.int tptp.quickcheck_code_int (tptp.number_number_of tptp.quickcheck_code_int) K_4)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K_4))) (= _let_202 (tptp.hAPP tptp.int tptp.quickcheck_code_int _let_203 tptp.pls)) (forall ((R_4 $$unsorted)) (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.rcis R_4) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4))) (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.rcis R_4) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) R_4))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.complex tptp.cis A_1) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.rcis (tptp.one_one tptp.real)) A_1))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.rcis (tptp.zero_zero tptp.real)) A_1) (tptp.zero_zero tptp.complex))) (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.rcis R_4) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_4) (tptp.hAPP tptp.real tptp.real tptp.cos A_1)))) (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.rcis R_4) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_4) (tptp.hAPP tptp.real tptp.real tptp.sin A_1)))) (forall ((R1 $$unsorted) (A_1 $$unsorted) (R2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.rcis R1) A_1)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.rcis R2) B)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.rcis (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) R1) R2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) A_1) B)))))) (forall ((R1 $$unsorted) (A_1 $$unsorted) (R2 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.inverse_divide tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.rcis R1) A_1)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.rcis R2) B)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.rcis (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) R1) R2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) A_1) B)))))) (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (= (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.rcis R_4) A_1) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.times_times tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.of_real tptp.complex) R_4)) (tptp.hAPP tptp.real tptp.complex tptp.cis A_1)))) (forall ((R_4 $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.inverse_inverse tptp.complex) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.rcis R_4) A_1)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.rcis (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.one_one tptp.real)) R_4)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) A_1))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.quickcheck_code_int tptp.quickcheck_code_int))) (let ((_let_2 (tptp.product_prod tptp.quickcheck_code_int tptp.quickcheck_code_int))) (let ((_let_3 (tptp.fun tptp.quickcheck_code_int _let_2))) (= (tptp.hAPP tptp.quickcheck_code_int _let_2 (tptp.hAPP tptp.quickcheck_code_int _let_3 tptp.quickc495462417de_int N) M) (tptp.hAPP tptp.quickcheck_code_int _let_2 (tptp.hAPP tptp.quickcheck_code_int _let_3 (tptp.product_Pair tptp.quickcheck_code_int tptp.quickcheck_code_int) (tptp.hAPP tptp.quickcheck_code_int tptp.quickcheck_code_int (tptp.hAPP tptp.quickcheck_code_int _let_1 (tptp.div_div tptp.quickcheck_code_int) N) M)) (tptp.hAPP tptp.quickcheck_code_int tptp.quickcheck_code_int (tptp.hAPP tptp.quickcheck_code_int _let_1 (tptp.div_mod tptp.quickcheck_code_int) N) M))))))) (forall ((I_1 $$unsorted)) (= (tptp.hAPP tptp.quickcheck_code_int tptp.nat tptp.quickcheck_nat_of I_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of I_1)))) (forall ((P_1 $$unsorted) (A0 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP (tptp.fun tptp.int _let_1) _let_1 (tptp.accp tptp.int) tptp.quickc1265749348ro_rel) A0)) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP (tptp.fun tptp.int _let_2) _let_2 (tptp.accp tptp.int) tptp.quickc1265749348ro_rel) I_2)) (=> (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) I_2) _let_1))) (=> (not (= (tptp.ti tptp.int I_2) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) I_2) (tptp.one_one tptp.int)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 I_2))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 A0)))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) X))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) _let_1) X)))) (and (=> _let_3 (= _let_2 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X))))) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.product_prod _let_1 _let_1))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.bool) (tptp.member _let_2) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_2) (tptp.product_Pair _let_1 _let_1) A_3) B_2)) (tptp.finite_psubset X_a))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.sum_sum X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.hAPP _let_2 tptp.nat (tptp.finite_card _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.sum_Plus X_a X_b) A_3) B_2)))) (let ((_let_6 (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) B_2))))) (and (=> _let_6 (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_4 tptp.nat (tptp.finite_card X_a) A_3)) (tptp.hAPP _let_3 tptp.nat (tptp.finite_card X_b) B_2)))) (=> (not _let_6) (= _let_5 (tptp.zero_zero tptp.nat))))))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 M) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 M)) (tptp.hAPP tptp.int tptp.int _let_1 N)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.sum_sum X_a X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 _let_2) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun X_a tptp.bool) (tptp.fun _let_1 _let_3) (tptp.sum_Plus X_a X_b) A_3) B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_2))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.sum_sum X_a X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 _let_2) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_4 _let_3) (tptp.sum_Plus X_a X_b) A_3) B_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.sum_sum X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.sum_Plus X_a X_b) A_3) B_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.sum_sum X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 _let_3) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.sum_Plus X_a X_b) A_3) B_2))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_2))))))))) (= (tptp.hAPP tptp.int tptp.int _let_205 _let_2) _let_2) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 M) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 M)) (tptp.hAPP tptp.int tptp.int _let_1 N))))))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) M) _let_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) M) _let_1)))) (= (tptp.hAPP tptp.int tptp.int _let_205 _let_1) _let_2) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) X)))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) _let_1) N)) (not (= (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) N) _let_1))))) (forall ((M $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) M)))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) X))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) N))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.one_one tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) N))))))) (forall ((M $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.zero_zero tptp.int)) K_4)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 M)) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) M) K_4))))))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 (tptp.one_one tptp.int)) M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_2 M) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) M) (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) N)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.sum_sum X_a X_b))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_2)) (= (tptp.hAPP _let_4 tptp.nat (tptp.finite_card _let_3) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.sum_Plus X_a X_b) A_3) B_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_3)) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) B_2)))))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) X))))) (forall ((M $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fact_fact tptp.int))) (let ((_let_4 (tptp.ord_less tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (let ((_let_6 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 (tptp.ord_less_eq tptp.int) _let_6) K_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 _let_6) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int _let_3 M)) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 M) (tptp.one_one tptp.int))) K_4))))))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) N) (tptp.one_one tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) N)) (= (tptp.hAPP tptp.int tptp.int _let_1 _let_3) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) _let_3) (tptp.hAPP tptp.int tptp.int _let_1 N)))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fact_fact tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N)) (= (tptp.hAPP tptp.int tptp.int _let_2 N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) N) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) N) (tptp.one_one tptp.int))))))))) (forall ((I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.list tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) I_1)) (= (tptp.hAPP _let_2 tptp.nat (tptp.size_size _let_2) (tptp.hAPP tptp.int _let_2 tptp.quickc666637781d_zero I_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 I_1))) (tptp.one_one tptp.nat))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_2) P_4)) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset A_2) P_4)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 A_2)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.real tptp.real))) (let ((_let_2 (tptp.product_prod tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 _let_1 A_4))) (let ((_let_5 (tptp.ord_less_eq tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 _let_4 B_4))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 _let_1 B_4) C_4))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 A_4) B_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 B_4) C_4))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 _let_4 C_4))))))))))) (=> (forall ((X_2 $$unsorted)) (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 A_4) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 X_2) B_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) B_4) A_4)) D_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.product_Pair tptp.real tptp.real) A_4) B_4))))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.product_Pair tptp.real tptp.real) A_2) B_1)))))))) (forall ((Ma $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_2) B_1)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset A_2) Ma))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset A_2) Ma))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_1) A_2))))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset A_2) Ma))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset A_2) Ma))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B_1))))) (forall ((P_1 $$unsorted)) (=> (and (forall ((A_4 $$unsorted) (B_4 $$unsorted) (C_4 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.real tptp.real))) (let ((_let_2 (tptp.product_prod tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 _let_1 A_4))) (let ((_let_5 (tptp.ord_less_eq tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 A_4) B_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 _let_5 B_4) C_4)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 _let_4 B_4))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 _let_1 B_4) C_4)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool P_1 (tptp.hAPP tptp.real _let_2 _let_4 C_4))))))))))) (forall ((X_2 $$unsorted)) (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 A_4) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 X_2) B_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) B_4) A_4)) D_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.product_Pair tptp.real tptp.real) A_4) B_4)))))))))))) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_4) B_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool P_1 (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.product_Pair tptp.real tptp.real) A_4) B_4)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) tptp.bezw X) Y))) (let ((_let_4 (tptp.times_times tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP _let_2 tptp.int (tptp.product_fst tptp.int tptp.int) _let_3)) (tptp.hAPP tptp.nat tptp.int _let_1 X))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP _let_2 tptp.int (tptp.product_snd tptp.int tptp.int) _let_3)) (tptp.hAPP tptp.nat tptp.int _let_1 Y))) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((V_1 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_1)) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V_1)) (tptp.one_one X_a))) X_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) M) N)) N))) (forall ((M $$unsorted) (N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) M) N)) M))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.gcd_gcd tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K_4) N))))) (forall ((N $$unsorted) (M $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.power_power tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.gcd_gcd tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_4 A_1) B) _let_1) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 A_1) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 B) M)) _let_1))))))) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.power_power tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 A_1) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 B) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B)) N)))))) (forall ((A_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) A_1) A_1)) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X) X) X)) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) A_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 X) Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Y) X))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 B))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 _let_2) _let_2)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 Y))) (= (tptp.hAPP tptp.nat tptp.nat _let_1 _let_2) _let_2)))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 B))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 A_1))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat _let_4 C)) (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 C)))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 _let_1 Y))) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat _let_4 Z_1)) (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 Z_1)))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 A_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 B)) C) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B) C))))))) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 _let_1 X))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat _let_3 Y)) Z_1) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Y) Z_1))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 X))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 B) X)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 B)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) X)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 _let_1)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 X))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 A_1) X)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 A_1)))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 _let_1) X)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_4 _let_1)))))))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B)))))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) M) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) M) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M))))) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.dvd_dvd tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 B) D)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 C) D)))))))))) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) Y) Z_1))))))) (forall ((B $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B))))))) (forall ((N $$unsorted) (K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) M) N))))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) Y) X)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X) Y) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X) Y)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X) Y) X))) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 B) X)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B)) X)))))) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 A_1) X)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B)) X)))))) (forall ((B_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) D_1))) (= (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) E))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 D_1)))))) (= D_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_2) B_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X_1))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) Y_1) Z))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Z)))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 N_1)))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X_1) Y_1)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X_1) Y_1) X_1))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X) Y)) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X) Y)) X))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.gcd_gcd tptp.nat) M))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) M) N)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) M) N)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K_4))) (let ((_let_3 (tptp.gcd_gcd tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 M) N)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat _let_2 M)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) _let_1) X) _let_1))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) M) _let_1) _let_1))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X) _let_1) _let_1))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) (tptp.zero_zero tptp.nat)) X) X)) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X) (tptp.zero_zero tptp.nat)) X)) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) Ma) N_1) _let_1) (and (= Ma _let_1) (= N_1 _let_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X_1) Y_1) _let_1) (and (= X_1 _let_1) (= Y_1 _let_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.gcd_gcd tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 X) Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) X) Y)))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) M) _let_1) _let_1))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) Ma) N_1))) (or (not (= Ma _let_1)) (not (= N_1 _let_1)))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (not (= A_1 (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B)) A_1)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (not (= B (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B)) B)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) N) (tptp.one_one tptp.nat))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.gcd_gcd tptp.nat) M))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) K_4) M)) N)) (tptp.hAPP tptp.nat tptp.nat _let_2 N))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B) _let_1) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_2 B)) (= X _let_1))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_2) B_1) (tptp.one_one tptp.nat)) (forall ((D_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) D_3))) (= (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1))) (= D_3 (tptp.one_one tptp.nat))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.plus_plus tptp.nat) N) _let_1)) N) _let_1)))) (forall ((D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) D_1))) (= (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) A_2) B_1)) _let_1) (and (= (tptp.hAPP tptp.nat tptp.nat _let_3 A_2) _let_1) (= (tptp.hAPP tptp.nat tptp.nat _let_3 B_1) _let_1))))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 K_4) N) (tptp.one_one tptp.nat)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) K_4) M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) D))) (=> (= (tptp.hAPP tptp.nat tptp.nat _let_3 A_1) _let_1) (=> (= (tptp.hAPP tptp.nat tptp.nat _let_3 B) _let_1) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) A_1) B)) _let_1))))))) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.one_one tptp.nat))) (let ((_let_4 (tptp.gcd_gcd tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 A_2) D_1) _let_3) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 B_1) C_1) _let_3) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_2) C_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 B_1) D_1)) (and (= A_2 B_1) (= C_1 D_1)))))))))) (forall ((D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) D))) (=> (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) A_1) B)) _let_1) (= (tptp.hAPP tptp.nat tptp.nat _let_3 A_1) _let_1)))))) (forall ((D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) D))) (=> (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) A_1) B)) _let_1) (= (tptp.hAPP tptp.nat tptp.nat _let_3 B) _let_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M) N)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) N) M)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N) M)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) M) N)) N) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.gcd_gcd tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 X) Y))) (let ((_let_4 (= Y (tptp.zero_zero tptp.nat)))) (and (=> _let_4 (= _let_3 X)) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) X) Y)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.gcd_gcd tptp.nat))) (=> (not (= Y (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 X) Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) X) Y))))))) (forall ((N $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) D))) (=> (= (tptp.hAPP tptp.nat tptp.nat _let_3 A_1) _let_1) (= (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.power_power tptp.nat) A_1) N)) _let_1)))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (= (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) (tptp.zero_zero X_a)) (tptp.zero_zero tptp.int)))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.hAPP X_a tptp.int _let_1 Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int _let_1 Y)) (tptp.hAPP X_a tptp.int _let_1 X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (= (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) (tptp.one_one X_a)) (tptp.one_one tptp.int)))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((V $$unsorted)) (= (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.nat tptp.natceiling X) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X)))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((N $$unsorted)) (= (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))))) (forall ((B_5 $$unsorted) (A_6 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B))) (let ((_let_4 (tptp.times_times tptp.nat))) (=> (not (= _let_3 (tptp.zero_zero tptp.nat))) (=> (= A_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 A_6) _let_3)) (=> (= B (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 B_5) _let_3)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_6) B_5) (tptp.one_one tptp.nat)))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (not (= N (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) N) _let_1)) N) _let_1))))) (forall ((N $$unsorted) (M $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.dvd_dvd tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 M) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 N) R_4)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.gcd_gcd tptp.nat) M) N) (tptp.one_one tptp.nat)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) M) N)) R_4))))))))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) K) N_1) (tptp.one_one tptp.nat)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) Ma) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 Ma))))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) K_4))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) K_4) N) (tptp.one_one tptp.nat)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) M) N))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 M))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B))) (let ((_let_4 (tptp.div_div tptp.nat))) (let ((_let_5 (tptp.zero_zero tptp.nat))) (=> (or (not (= A_1 _let_5)) (not (= B _let_5))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 A_1) _let_3)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 B) _let_3)) (tptp.one_one tptp.nat))))))))) (forall ((X $$unsorted) (Y $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.div_mod tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.times_times tptp.nat) X) Y)) M) _let_1) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.gcd_gcd tptp.nat) X) M) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X)) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X)) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_2) B_1) (tptp.one_one tptp.nat)) (forall ((D_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) D_3))) (= (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool _let_1 B_1))) (= D_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1)) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1)) (tptp.one_one tptp.int))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) (tptp.zero_zero X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.one_one tptp.int)) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.one_one X_a)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1)) (tptp.one_one tptp.int))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((V_1 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_1)) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V_1)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted) (V_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X) (tptp.one_one X_a))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.one_one tptp.int))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X) (tptp.one_one X_a))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.one_one tptp.int))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1)) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted) (V_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V_1)) (tptp.one_one X_a)))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (not (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) A_1) B) (tptp.zero_zero tptp.nat))) (exists ((A_5 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_1) B))) (let ((_let_4 (tptp.times_times tptp.nat))) (and (= A_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 A_5) _let_3)) (= B (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_4 B_3) _let_3)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 A_5) B_3) (tptp.one_one tptp.nat)))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (=> (not (= A_1 (tptp.zero_zero tptp.nat))) (exists ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 A_1) X_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 B) Y_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.gcd_gcd tptp.nat) A_1) B)))))))) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.real) tptp.bool (tptp.cauchy tptp.real) X_3)) (forall ((J_1 $$unsorted)) (exists ((M_3 $$unsorted)) (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) M_2)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.nat tptp.real X_3 M_2)) (tptp.hAPP tptp.nat tptp.real X_3 N_2)))) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc J_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((E_2 $$unsorted) (X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.cauchy X_a) X_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) E_2)) (exists ((M_3 $$unsorted)) (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) M_2)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.nat X_a X_3 M_2)) (tptp.hAPP tptp.nat X_a X_3 N_2)))) E_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.cauchy X_a) X_3)) (forall ((E $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) E)) (exists ((M_3 $$unsorted)) (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) M_2)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.nat X_a X_3 M_2)) (tptp.hAPP tptp.nat X_a X_3 N_2)))) E))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (=> (forall ((E $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) E)) (exists ((M_3 $$unsorted)) (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) M_2)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.nat X_a X_3 M_2)) (tptp.hAPP tptp.nat X_a X_3 N_2)))) E))))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.cauchy X_a) X_3)))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) _let_1) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) N) (tptp.one_one tptp.int)))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Y_1)) (tptp.hAPP (tptp.fun X_a tptp.nat) _let_2 (tptp.measure X_a) F))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP X_a tptp.nat F X_1)) (tptp.hAPP X_a tptp.nat F Y_1))))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.one_one tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) A_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real tptp.ln X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr X) A_1)) A_1))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X_1)) (tptp.hAPP tptp.int tptp.real _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X_1) Y_1))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (not (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X) A_1) (tptp.zero_zero tptp.real)))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr _let_1) A_1) _let_1))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N)) (tptp.ti tptp.int N))) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X_1)) X_1) (exists ((N_2 $$unsorted)) (= X_1 (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N_2))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.powr X))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr (tptp.hAPP tptp.real tptp.real _let_2 A_1)) B) (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) A_1) B)))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.powr X))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr (tptp.hAPP tptp.real tptp.real _let_2 A_1)) B) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr (tptp.hAPP tptp.real tptp.real _let_2 B)) A_1))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (= (tptp.hAPP tptp.int tptp.real _let_1 X_1) (tptp.hAPP tptp.int tptp.real _let_1 Y_1)) (= (tptp.ti tptp.int X_1) (tptp.ti tptp.int Y_1))))) (= (tptp.hAPP tptp.int tptp.real _let_44 _let_1) _let_37) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) X_1) (tptp.zero_zero tptp.real)) (= (tptp.ti tptp.int X_1) (tptp.zero_zero tptp.int)))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X_1)) (tptp.hAPP tptp.int tptp.real _let_1 Y_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) X_1) Y_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X)) (tptp.hAPP tptp.int tptp.real _let_1 Y))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X)) N) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) N))))) (forall ((X $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) N)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X)) N)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X)) (tptp.hAPP tptp.int tptp.real _let_1 Y))))) (forall ((V $$unsorted)) (= (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) V))) (= (tptp.hAPP tptp.int tptp.real _let_44 _let_2) _let_136) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X)) (tptp.hAPP tptp.int tptp.real _let_1 Y))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N)) (tptp.ti tptp.int N))) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X_1)) X_1) (exists ((N_2 $$unsorted)) (= X_1 (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N_2))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) X)) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X))))) (forall ((X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X)) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X))))) (forall ((R_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) R_4))) R_4))) (forall ((R_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) R_4) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) R_4))))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X) Y)))) (forall ((X $$unsorted) (A_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X) A_1)))) (forall ((Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_4 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_4 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr X) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr Y) A_1))))))))))) (forall ((Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 A_1) _let_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_4) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr Y) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr X) A_1))))))))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.one_one tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 A_1)) (tptp.hAPP tptp.real tptp.real _let_1 B))))))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X) (tptp.zero_zero tptp.real)) (tptp.one_one tptp.real))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 A_2)) (tptp.hAPP tptp.real tptp.real _let_3 B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) B_1)))))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 A_1) B)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.one_one tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 A_1)) (tptp.hAPP tptp.real tptp.real _let_1 B))))))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 A_1)) (tptp.hAPP tptp.real tptp.real _let_3 B))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)) X)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((R_4 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) R_4))) (= (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) _let_1)) _let_1))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.powr X))) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) A_1) B)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real _let_2 A_1)) (tptp.hAPP tptp.real tptp.real _let_2 B)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((R_4 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) R_4))) (= (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) _let_1)) _let_1))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.powr X))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real _let_2 A_1)) (tptp.hAPP tptp.real tptp.real _let_2 B)) (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) A_1) B)))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X))) (= (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.real tptp.real _let_1 A_1))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) N) X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N)) (tptp.hAPP tptp.int tptp.real _let_1 X)))))) (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X_1)) A_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) X_1) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_2))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_1)) X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) A_1) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) A_1) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_1)) X)))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) A_2) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_2)) X_1)))) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor tptp.real))) (= (tptp.hAPP tptp.real tptp.int _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_1))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.real tptp.int _let_1 X)) A_1)))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) A_2) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_2)) X_1)))) (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X_1)) A_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X_1) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_2))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X)) A_1)))) (forall ((X $$unsorted) (A_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X)) A_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_1))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real tptp.int _let_1 X))) (=> (= X (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) _let_2)) (= (tptp.hAPP tptp.real tptp.int _let_1 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) N)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) _let_2) N)))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor tptp.real))) (= (tptp.hAPP tptp.real tptp.int _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_1))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.real tptp.int _let_1 X)) A_1)))) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling tptp.real))) (= (tptp.hAPP tptp.real tptp.int _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_1))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.real tptp.int _let_1 X)) A_1)))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N))) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) N))) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling tptp.real))) (= (tptp.hAPP tptp.real tptp.int _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_1))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.real tptp.int _let_1 X)) A_1)))) (forall ((Y $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_4) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.ord_less tptp.real) _let_4) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) Y)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr X) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr Y) A_1))))))))))) (forall ((A_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 Y)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_2 X) Y)) A_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr X) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr Y) A_1))))))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.one_one tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) A_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X) A_1))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.one_one tptp.real)) X_1)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real _let_3 A_2)) (tptp.hAPP tptp.real tptp.real _let_3 B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) B_1)))))))) (forall ((X_1 $$unsorted)) (= (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X_1) (tptp.one_one tptp.real)) X_1) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_1)))) (forall ((A_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.inverse_divide tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_3 Y)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_2 X) Y)) A_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr X) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr Y) A_1))))))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.powr X))) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.real tptp.real _let_2 A_1)))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr X) A_1) (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) A_1) (tptp.hAPP tptp.real tptp.real tptp.ln X)))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N_1)) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) N_1) (tptp.zero_zero tptp.int))))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N_1)))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) N_1)))) (forall ((N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N_1)) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) N_1) (tptp.zero_zero tptp.int))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) Ma)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Ma) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) N_1))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N_1)) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) Ma))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) N_1)) Ma)))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) Ma)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Ma) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) N_1))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) N_1)) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) Ma))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) N_1)) Ma)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) N_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N_1)) (tptp.one_one tptp.real))) (tptp.hAPP tptp.int tptp.real _let_1 Ma)))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 X)) (tptp.one_one tptp.real)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) N) X))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) N_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 Ma)) (tptp.one_one tptp.real))))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X)) (= (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) X)))) (forall ((N $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (=> (not (= (tptp.ti tptp.int D) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D) N)) (= (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) N) D)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N)) (tptp.hAPP tptp.int tptp.real _let_1 D))))))) (forall ((R_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) R_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) R_4))) (tptp.one_one tptp.real))))) (forall ((R_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) R_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) R_4))) (tptp.one_one tptp.real))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) _let_1) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X) (tptp.ti tptp.int N)))))))) (forall ((X $$unsorted) (I_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.tan (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) I_1)) tptp.pi))) (tptp.hAPP tptp.real tptp.real tptp.tan X)))) (forall ((R_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) R_4) (tptp.one_one tptp.real))) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) R_4))))) (forall ((R_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) R_4) (tptp.one_one tptp.real))) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) R_4))))) (forall ((R_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) R_4))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) R_4) (tptp.one_one tptp.real))))) (forall ((R_4 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) R_4))) (tptp.one_one tptp.real))) R_4))) (forall ((N $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) N)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 Y)) (= (tptp.hAPP tptp.real tptp.real tptp.ln (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) Y) (tptp.hAPP tptp.real tptp.real tptp.ln X)))))))) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 A_1)) (=> (not (= A_1 (tptp.one_one tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 X)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr A_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.log A_1) X)) X))))))) (forall ((Y $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) A_1)) (=> (not (= A_1 (tptp.one_one tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.log A_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr A_1) Y)) Y))))) (forall ((N $$unsorted) (M $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 M)) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) R_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N)) (tptp.one_one tptp.real)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) M) N))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N)) (tptp.hAPP tptp.int tptp.real _let_1 X))) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) N) X)))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N)) (tptp.hAPP tptp.int tptp.real _let_1 X))) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) N) X)))) (tptp.one_one tptp.real)))))) (forall ((X $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.real _let_1 D))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.inverse_divide tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (=> (not (= (tptp.ti tptp.int D) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.int tptp.real _let_1 X)) _let_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.div_div tptp.int) X) D))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.div_mod tptp.int) X) D))) _let_2)))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) _let_1) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X) (tptp.ti tptp.int N))))))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) A_2) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_2)) (tptp.one_one tptp.real))) X_1)))) (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X_1)) A_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_2)) (tptp.one_one tptp.real)))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) _let_1) (tptp.one_one tptp.real))) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) X) _let_1)) (= (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X) (tptp.ti tptp.int N))))))) (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X_1)) A_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_2)) (tptp.one_one tptp.real)))))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) A_2) (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) A_2)) (tptp.one_one tptp.real))) X_1)))) (forall ((B $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 tptp.log B))) (let ((_let_3 (tptp.zero_zero tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.ord_less tptp.real) _let_3) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.ord_less_eq tptp.real) _let_3) Y)) (= (tptp.hAPP tptp.real tptp.real _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) Y) (tptp.hAPP tptp.real tptp.real _let_2 X)))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) N))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) _let_1) (tptp.one_one tptp.real)))) (= (tptp.hAPP tptp.real tptp.int (tptp.archimedean_ceiling tptp.real) X) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) N) (tptp.one_one tptp.int))))))))) (forall ((N $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) X) N))) (let ((_let_2 (tptp.zero_zero tptp.real))) (let ((_let_3 (= X _let_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) _let_2) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N)) (and (=> _let_3 (= _let_1 _let_2)) (=> (not _let_3) (= _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) tptp.powr X) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N))))))))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 (tptp.one_one tptp.real)) X)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 (tptp.zero_zero tptp.real)) A_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr (tptp.hAPP tptp.real tptp.real tptp.ln X)) A_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 tptp.powr A_1) A_1)) X))))))))) (forall ((R_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) R_4)) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N_2)) R_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) R_4) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) N_2) (tptp.one_one tptp.int))))))))))) (forall ((R_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) R_4) (tptp.zero_zero tptp.real))) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N_2)) R_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) R_4) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) N_2) (tptp.one_one tptp.int))))))))))) (forall ((R_4 $$unsorted)) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 N_2)) R_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) R_4) (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) N_2) (tptp.one_one tptp.int)))))))))) (forall ((C $$unsorted) (N $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) tptp.coprime A_1) B)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) A_1) B) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.power_power tptp.nat) C) N)) (exists ((R_2 $$unsorted) (S_1 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (and (= A_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 R_2) N)) (= B (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 S_1) N)))))))))) (forall ((X $$unsorted) (Y $$unsorted) (K_4 $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_5)) (=> (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) X) Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.power_power tptp.nat) P_5) K_4)) (exists ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.power_power tptp.nat) P_5))) (and (= X (tptp.hAPP tptp.nat tptp.nat _let_1 I_2)) (= Y (tptp.hAPP tptp.nat tptp.nat _let_1 J_1))))))))) (forall ((X $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) M)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd X) M) _let_1) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) (tptp.hAPP tptp.int tptp.nat tptp.phi M))) _let_1) M))))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd I_1) J_2)) I_1))) (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd I_1) J_2)) J_2))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd K_4) N) (tptp.one_one tptp.int)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_4) M)) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N))))) (forall ((N $$unsorted) (K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd K_4) M) _let_1) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd N) M) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) K_4) N)) M) _let_1)))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) M) N))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd M) _let_1) _let_1))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd _let_1) M) _let_1))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd I) J) _let_1) (and (= (tptp.ti tptp.int I) _let_1) (= (tptp.ti tptp.int J) _let_1))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N_1)))))) (forall ((N $$unsorted) (K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd M) N))))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd K_4))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int _let_2 M)) N) (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N)))))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd K_4))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int _let_3 N)) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_2 N))))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd I_1) J_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd J_2) I_1)))) (forall ((A_1 $$unsorted) (B $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int))) (let ((_let_2 (tptp.fun tptp.nat tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.legacy_zgcd A_1) B)) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.legacy_zgcd (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) N)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) N))))))) (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) I_1)) J_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd I_1) J_2)))) (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd I_1))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) J_2)) (tptp.hAPP tptp.int tptp.int _let_1 J_2)))) (forall ((M $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) M)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd M) M) (tptp.ti tptp.int M)))) (forall ((I_1 $$unsorted) (J_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd I_1) J_2)))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd X) Y)))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) M) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) N) K_4))) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N)))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.times_times tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 _let_2 K_4))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int _let_3 M)) (tptp.hAPP tptp.int tptp.int _let_3 N)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) K_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N))))))) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd A_1) B) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1) N)) B) _let_1))))) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.power_power tptp.int))) (let ((_let_3 (tptp.fun tptp.nat tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 tptp.legacy_zgcd A_1) B) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 tptp.legacy_zgcd (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 A_1) N)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 B) N)) _let_1))))))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd (tptp.zero_zero tptp.int)) M) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) M))) (forall ((M $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd M) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) M))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_4) M)) N))))) (forall ((N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) K_4)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd K_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_4) N)) (tptp.ti tptp.int K_4))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) K_4)) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int _let_2 M)) (tptp.hAPP tptp.int tptp.int _let_2 N))))))) (forall ((N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) K_4)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_4) N)) K_4) (tptp.ti tptp.int K_4))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) Ma) N_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd N_1) Ma) (tptp.ti tptp.int Ma)))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd A_1) B))) (let ((_let_3 (tptp.div_div tptp.int))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (or (not (= (tptp.ti tptp.int A_1) _let_4)) (not (= (tptp.ti tptp.int B) _let_4))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 A_1) _let_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 B) _let_2)) (tptp.one_one tptp.int)))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) M) N)))))) (forall ((N $$unsorted) (A_1 $$unsorted) (B $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong A_1) B))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 N)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N) (tptp.one_one tptp.int)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) M) N)))))))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd K_4) N) (tptp.one_one tptp.int)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_4) M)) N)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd M) N)))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K_4))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd N) K_4) (tptp.one_one tptp.int)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) M) N))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M))))))) (forall ((K_4 $$unsorted) (I_1 $$unsorted) (J_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) I_1))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd I_1) J_2) (tptp.one_one tptp.int)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) K_4) J_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 K_4))))))) (forall ((Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd (tptp.zero_zero tptp.int)) Ma) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) Ma) _let_1)))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd K) L) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.bool (tptp.fun tptp.int _let_2) (tptp.if tptp.int) (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.fequal tptp.int) L) (tptp.zero_zero tptp.int))) K) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd L) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_mod tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 K)) (tptp.hAPP tptp.int tptp.int _let_1 L))))))))) (forall ((N $$unsorted) (P_5 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_5) N))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd N) P_5) (tptp.one_one tptp.int))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd A_2) B_1) (tptp.one_one tptp.int)) (not (exists ((P_6 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) P_6))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_6)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 B_1)))))))) (forall ((B $$unsorted) (A_1 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) M)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd A_1) M) _let_1) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.zcong A_1) B) M)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd B) M) _let_1)))))))) (forall ((N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 N) P_5)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd N) P_5) (tptp.one_one tptp.int)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (K $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.times_times tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Ma)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 tptp.legacy_zgcd K) Ma) (tptp.one_one tptp.int)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_3 A_2) K)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 _let_3 B_1) K)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong A_2) B_1) Ma)))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (K $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) K))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Ma)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.legacy_zgcd K) Ma) (tptp.one_one tptp.int)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong (tptp.hAPP tptp.int tptp.int _let_4 A_2)) (tptp.hAPP tptp.int tptp.int _let_4 B_1)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong A_2) B_1) Ma)))))))))) (forall ((M $$unsorted) (N $$unsorted) (K_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) K_4))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 tptp.legacy_zgcd N) K_4) (tptp.one_one tptp.int)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 (tptp.times_times tptp.int) M) N))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) M)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 M))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd B_1) Ma) (tptp.one_one tptp.int)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_1) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) B_1) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset A_2) Ma)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) A_2) B_1) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) C_1) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.one_one tptp.nat)) _let_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_2 tptp.bool) (tptp.member tptp.int) X_1) tptp.zOdd)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd A_2) B_1) (tptp.one_one tptp.int)) (exists ((K_1 $$unsorted)) (= (tptp.ti tptp.int A_2) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) K_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1)))))))))))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N_1)) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd Ma) N_1) (tptp.ti tptp.int K)) (exists ((S_1 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int _let_1))) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.xzgcd Ma) N_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP tptp.int (tptp.fun _let_1 _let_2) (tptp.product_Pair tptp.int _let_1) K) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) S_1) T_4))))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) A_1) B) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) C) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.one_one tptp.nat)) N)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd A_1) B) (tptp.one_one tptp.int)) (exists ((K_1 $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) A_1) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) K_1) N)))))))) (forall ((M $$unsorted) (N $$unsorted) (R_5 $$unsorted) (R_4 $$unsorted) (S_4 $$unsorted) (S_3 $$unsorted) (T_6 $$unsorted) (T_5 $$unsorted) (K_4 $$unsorted)) (=> (exists ((Sn $$unsorted) (Tn $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int _let_1))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_8) tptp.xzgcda M) N) R_5) R_4) S_4) S_3) T_6) T_5) (tptp.hAPP _let_1 _let_2 (tptp.hAPP tptp.int (tptp.fun _let_1 _let_2) (tptp.product_Pair tptp.int _let_1) K_4) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) Sn) Tn)))))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) R_4)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd R_5) R_4) (tptp.ti tptp.int K_4))))) (forall ((B $$unsorted) (A_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd A_1) N) (tptp.one_one tptp.int)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) X_2) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) X_2)) B) N)) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) Y_2) N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) Y_2)) B) N))) (= (tptp.ti tptp.int Y_2) (tptp.ti tptp.int X_2))))))))))) (forall ((A_1 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd A_1) N) (tptp.one_one tptp.int)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) A_1) X_2)) (tptp.one_one tptp.int)) N))))))) (forall ((M $$unsorted) (N $$unsorted) (S_4 $$unsorted) (S_3 $$unsorted) (T_6 $$unsorted) (T_5 $$unsorted) (R_5 $$unsorted) (R_4 $$unsorted) (K_4 $$unsorted)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd R_5) R_4) (tptp.ti tptp.int K_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) R_4)) (exists ((Sn $$unsorted) (Tn $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int _let_1))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun tptp.int _let_6))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 (tptp.hAPP tptp.int _let_7 (tptp.hAPP tptp.int _let_8 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_8) tptp.xzgcda M) N) R_5) R_4) S_4) S_3) T_6) T_5) (tptp.hAPP _let_1 _let_2 (tptp.hAPP tptp.int (tptp.fun _let_1 _let_2) (tptp.product_Pair tptp.int _let_1) K_4) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) Sn) Tn))))))))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1))) (let ((_let_5 (tptp.times_times tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_5 A_2) B_1)) C_1) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) D_1) _let_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.one_one tptp.nat)) _let_4)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_3 tptp.bool) (tptp.member tptp.int) X_1) tptp.zOdd)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd A_2) B_1) _let_1) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd B_1) C_1) _let_1) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd C_1) A_2) _let_1) (exists ((K_1 $$unsorted) (L_3 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1))) (let ((_let_2 (tptp.power_power tptp.int))) (let ((_let_3 (tptp.fun tptp.nat tptp.int))) (and (= (tptp.ti tptp.int A_2) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 K_1) _let_1)) (= (tptp.ti tptp.int B_1) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 L_3) _let_1)) (= (tptp.ti tptp.int C_1) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 M_2) _let_1))))))))))))))))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) N)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd M) N) (tptp.ti tptp.int K_4)) (exists ((S_1 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.ti tptp.int K_4) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 S_1) M)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 T_4) N))))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.times_times tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 A_1) B)) C) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) D) N)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.one_one tptp.nat)) N)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd A_1) B) _let_1) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd B) C) _let_1) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd C) A_1) _let_1) (exists ((K_1 $$unsorted) (L_3 $$unsorted) (M_2 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.int))) (let ((_let_2 (tptp.fun tptp.nat tptp.int))) (let ((_let_3 (tptp.abs_abs tptp.int))) (and (= (tptp.hAPP tptp.int tptp.int _let_3 A_1) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_1) N)) (= (tptp.hAPP tptp.int tptp.int _let_3 B) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 L_3) N)) (= (tptp.hAPP tptp.int tptp.int _let_3 C) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_2 _let_1 M_2) N)))))))))))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (or (not (= (tptp.ti tptp.int A_1) _let_1)) (not (= (tptp.ti tptp.int B) _let_1))) (exists ((C_4 $$unsorted) (D_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd A_1) B)))) (and (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int _let_2 C_4)) (= (tptp.ti tptp.int B) (tptp.hAPP tptp.int tptp.int _let_2 D_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.legacy_zgcd C_4) D_3) (tptp.one_one tptp.int))))))))) (forall ((Sa $$unsorted) (Ta $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.nat tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.product_prod _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_6 (tptp.ord_less_eq tptp.nat) A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_6 (tptp.ord_less tptp.nat) Sa) Ta)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_4) (tptp.product_Pair _let_2 _let_2) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 A_2) Sa)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 B_1) Ta))) tptp.pair_less))))))))))) (forall ((Sa $$unsorted) (Ta $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.nat tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.product_prod _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) A_2) B_1)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_4) (tptp.product_Pair _let_2 _let_2) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 A_2) Sa)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 B_1) Ta))) tptp.pair_less))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_8 $$unsorted) (B_7 $$unsorted) (R_1 $$unsorted) (Sa $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.product_prod X_a X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.product_prod X_a X_b))) (let ((_let_6 (tptp.product_prod _let_5 _let_5))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.product_Pair X_a X_b))) (let ((_let_9 (tptp.fun X_b _let_5))) (= (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP _let_6 (tptp.fun _let_7 tptp.bool) (tptp.member _let_6) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_5 _let_6) (tptp.product_Pair _let_5 _let_5) (tptp.hAPP X_b _let_5 (tptp.hAPP X_a _let_9 _let_8 A_2) B_1)) (tptp.hAPP X_b _let_5 (tptp.hAPP X_a _let_9 _let_8 A_8) B_7))) (tptp.hAPP _let_2 _let_7 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_7) (tptp.lex_prod X_a X_b) R_1) Sa))) (or (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP X_a _let_3 (tptp.hAPP X_a (tptp.fun X_a _let_3) (tptp.product_Pair X_a X_a) A_2) A_8)) R_1)) (and (= (tptp.ti X_a A_2) (tptp.ti X_a A_8)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_b (tptp.fun X_b _let_1) (tptp.product_Pair X_b X_b) B_1) B_7)) Sa))))))))))))))) (forall ((Sa $$unsorted) (Ta $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.nat tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.product_prod _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.ord_less_eq tptp.nat))) (let ((_let_7 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_7 _let_6 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_7 _let_6 Sa) Ta)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_4) (tptp.product_Pair _let_2 _let_2) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 A_2) Sa)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 B_1) Ta))) tptp.pair_leq)))))))))))) (forall ((Sa $$unsorted) (Ta $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_Pair tptp.nat tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.product_prod _let_2 _let_2))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) A_2) B_1)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_4) (tptp.product_Pair _let_2 _let_2) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 A_2) Sa)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 B_1) Ta))) tptp.pair_leq))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3)) (exists ((K_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_1)) (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.nat X_a X_3 N_3))))) K_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3)) (exists ((K_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_1)) (exists ((X_2 $$unsorted)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X_2)))) K_1)))))))))) (forall ((Y $$unsorted) (X $$unsorted)) (exists ((R_2 $$unsorted) (A_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_2))) (and (= X (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos A_4))) (= Y (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real tptp.sin A_4))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.cauchy X_a) X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.bseq X_a) X_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a X_3 N_2))) K_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3)) (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a X_3 N_2))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3)) (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a X_3 N_2))) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted) (K_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_3)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a X_3 N_2))) K_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a X_3 N_2))) K_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted) (K_3 $$unsorted) (N_4 $$unsorted)) (=> (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_4) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a X_3 N_2))) K_3)))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted) (K_3 $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a X_3 N_2))) K_3))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.bseq X_a) X_3)) (not (forall ((K_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (not (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a X_3 N_2))) K_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X2_1 $$unsorted) (Y $$unsorted) (X1_1 $$unsorted) (E_1 $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.ord_less tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) E_1) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_6 (tptp.hAPP X_a _let_2 _let_1 Y))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP X_a tptp.real _let_6 X1_1)) _let_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP X_a tptp.real _let_6 X2_1)) _let_5)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 X1_1) X2_1)) E_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dist_norm X_a) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X) Y) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted) (Y $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 X) Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP X_a tptp.real _let_3 X)) (tptp.hAPP X_a tptp.real _let_3 Y)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_3 Y)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP X_a tptp.real _let_3 Z_1)) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted) (Z_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_3 Z_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP X_a tptp.real _let_3 Y)) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((Y $$unsorted) (Z_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP X_a tptp.real _let_3 Y)) (tptp.hAPP X_a tptp.real _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted) (Z_1 $$unsorted) (Y $$unsorted) (E_1 $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (let ((_let_4 (tptp.ord_less_eq tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP X_a tptp.real _let_3 Z_1)) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))) E_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP X_a tptp.real _let_3 Y)) E_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted) (Z_1 $$unsorted) (Y $$unsorted) (E_1 $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (let ((_let_4 (tptp.ord_less tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP X_a tptp.real _let_3 Z_1)) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))) E_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP X_a tptp.real _let_3 Y)) E_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_1) Y_1)) (tptp.zero_zero tptp.real))) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X) Y))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_1) Y_1))) (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (not (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_1) Y_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted) (Y $$unsorted)) (not (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X) Y)) (tptp.zero_zero tptp.real))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X) X) (tptp.zero_zero tptp.real))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (= (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_1) Y_1) (tptp.zero_zero tptp.real)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (let ((_let_2 (tptp.fun X_a tptp.real))) (= (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 X) Y) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 Y) X))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.dist_dist tptp.real) X) Y) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.minus_minus tptp.real) X) Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.real) (tptp.dist_dist tptp.complex) X) Y) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.complex (tptp.fun tptp.complex tptp.complex) (tptp.minus_minus tptp.complex) X) Y)))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X2_1 $$unsorted) (X1_1 $$unsorted) (Y $$unsorted) (E_1 $$unsorted)) (let ((_let_1 (tptp.dist_dist X_a))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X1_1))) (let ((_let_4 (tptp.ord_less tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) E_1) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP X_a tptp.real _let_3 Y)) _let_6)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP X_a tptp.real (tptp.hAPP X_a _let_2 _let_1 X2_1) Y)) _let_6)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP X_a tptp.real _let_3 X2_1)) E_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.cauchy X_a) X_3)) (forall ((E $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) E)) (exists ((M_3 $$unsorted)) (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) M_2)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) (tptp.hAPP tptp.nat X_a X_3 M_2)) (tptp.hAPP tptp.nat X_a X_3 N_2))) E))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((E_2 $$unsorted) (X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.cauchy X_a) X_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) E_2)) (exists ((M_3 $$unsorted)) (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) M_2)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) (tptp.hAPP tptp.nat X_a X_3 M_2)) (tptp.hAPP tptp.nat X_a X_3 N_2))) E_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X) (tptp.zero_zero X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted)) (=> (forall ((E $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) E)) (exists ((M_3 $$unsorted)) (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) M_2)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) (tptp.hAPP tptp.nat X_a X_3 M_2)) (tptp.hAPP tptp.nat X_a X_3 N_2))) E))))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.cauchy X_a) X_3)))))) (forall ((Z_1 $$unsorted)) (=> (forall ((N_2 $$unsorted)) (not (= (tptp.ti tptp.int Z_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_2)))) (not (forall ((N_2 $$unsorted)) (not (= (tptp.ti tptp.int Z_1) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))))))) (forall ((Z $$unsorted) (P_1 $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_2)))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 Z))))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) B_1))) (exists ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) Y_2) (tptp.zero_zero tptp.real)))))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F B_1)) (tptp.hAPP tptp.real tptp.real F A_2)))))))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) B_1))) (exists ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) Y_2))))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F A_2)) (tptp.hAPP tptp.real tptp.real F B_1)))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted) (P_1 $$unsorted)) (=> (forall ((M_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) P_1 M_2) (tptp.zero_zero tptp.nat)))) (=> (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 P_1 N_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) M_2) N_2))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 P_1 M_2) N_2)))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) P_1 Ma) N_1))))) (forall ((X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Code_numeral $$unsorted)) (let ((_let_1 (tptp.fun tptp.code_code_numeral X_a))) (= (tptp.hAPP tptp.code_code_numeral X_a (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.code_c600343653l_case X_a) F1) F2) (tptp.hAPP tptp.code_code_numeral tptp.code_code_numeral tptp.code_S1047413653umeral Code_numeral)) (tptp.hAPP tptp.code_code_numeral X_a F2 Code_numeral)))) (forall ((N $$unsorted) (P_5 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.one_one tptp.nat)) P_5)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 _let_2 P_5) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.dvd_dvd tptp.nat) P_5) (tptp.hAPP tptp.nat tptp.nat tptp.fact N)))))))) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.quickcheck_code_int tptp.quickcheck_code_int (tptp.hAPP tptp.quickcheck_code_int (tptp.fun tptp.quickcheck_code_int tptp.quickcheck_code_int) (tptp.div_mod tptp.quickcheck_code_int) N) M) (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of N)) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of M))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int N_1) (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int Ma)) (= (tptp.ti tptp.int N_1) (tptp.ti tptp.int Ma)))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of X)) X)) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of K_4)) K_4)) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int N)) (tptp.ti tptp.int N))) _let_204 (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.fact M)) (tptp.hAPP tptp.nat tptp.nat tptp.fact N))))))) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.quickcheck_code_int tptp.quickcheck_code_int (tptp.hAPP tptp.quickcheck_code_int (tptp.fun tptp.quickcheck_code_int tptp.quickcheck_code_int) (tptp.times_times tptp.quickcheck_code_int) N) M) (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of N)) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of M))))) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.quickcheck_code_int tptp.quickcheck_code_int (tptp.hAPP tptp.quickcheck_code_int (tptp.fun tptp.quickcheck_code_int tptp.quickcheck_code_int) (tptp.plus_plus tptp.quickcheck_code_int) N) M) (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of N)) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of M))))) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.quickcheck_code_int tptp.quickcheck_code_int (tptp.hAPP tptp.quickcheck_code_int (tptp.fun tptp.quickcheck_code_int tptp.quickcheck_code_int) (tptp.minus_minus tptp.quickcheck_code_int) N) M) (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of N)) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of M))))) (= _let_202 (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int _let_1)) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.fact N)))) (= (tptp.hAPP tptp.nat tptp.nat tptp.fact _let_40) _let_179) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N))) (= (tptp.hAPP tptp.nat tptp.nat tptp.fact _let_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) _let_1) (tptp.hAPP tptp.nat tptp.nat tptp.fact N))))) (forall ((N $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.one_one tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.fact N)))) (= _let_201 (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int _let_2)) (forall ((X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.code_code_numeral X_a))) (= (tptp.hAPP tptp.code_code_numeral X_a (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.code_c600343653l_case X_a) F1) F2) (tptp.zero_zero tptp.code_code_numeral)) (tptp.ti X_a F1)))) (forall ((N $$unsorted) (M $$unsorted)) (= (tptp.hAPP tptp.quickcheck_code_int tptp.quickcheck_code_int (tptp.hAPP tptp.quickcheck_code_int (tptp.fun tptp.quickcheck_code_int tptp.quickcheck_code_int) (tptp.div_div tptp.quickcheck_code_int) N) M) (tptp.hAPP tptp.int tptp.quickcheck_code_int tptp.quickcheck_of_int (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of N)) (tptp.hAPP tptp.quickcheck_code_int tptp.int tptp.quickcheck_int_of M))))) (forall ((N $$unsorted)) (exists ((P_6 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool tptp.prime P_6)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) N) P_6)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) P_6) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.fact N)))))))) (forall ((F $$unsorted)) (=> (forall ((I_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat tptp.suc I_2))) (tptp.hAPP tptp.nat tptp.nat F I_2)))) (exists ((I_2 $$unsorted)) (forall ((K_1 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) I_2) K_1)) (tptp.hAPP tptp.nat tptp.nat F I_2)))))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun _let_1 _let_2) _let_2 (tptp.accp _let_1) tptp.norm_frac_rel) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) A0) A1))) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.uminus_uminus tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun _let_3 _let_4) _let_4 (tptp.accp _let_3) tptp.norm_frac_rel) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) (tptp.product_Pair tptp.int tptp.int) A_4) B_4))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) B_4) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 P_1 (tptp.hAPP tptp.int tptp.int _let_2 A_4)) (tptp.hAPP tptp.int tptp.int _let_2 B_4)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 P_1 A_4) B_4))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) P_1 A0) A1))))))) (forall ((X_a $$unsorted) (R_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun (tptp.product_prod X_a X_a) tptp.bool) tptp.bool (tptp.refl X_a) R_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_2) X_2)) R_1))))))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun _let_1 _let_2) _let_2 (tptp.accp _let_1) tptp.upto_rel) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) A0) A1))) (=> (forall ((I_2 $$unsorted) (J_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun _let_2 _let_3) _let_3 (tptp.accp _let_2) tptp.upto_rel) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.product_Pair tptp.int tptp.int) I_2) J_1))) (=> (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) I_2) J_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I_2) (tptp.one_one tptp.int))) J_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 P_1 I_2) J_1)))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) P_1 A0) A1))))))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun _let_1 _let_2) _let_2 (tptp.accp _let_1) tptp.lazy_small_lazy_rel) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) A0) A1))) (=> (forall ((D_3 $$unsorted) (I_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 P_1 D_3))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun _let_3 _let_4) _let_4 (tptp.accp _let_3) tptp.lazy_small_lazy_rel) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) (tptp.product_Pair tptp.int tptp.int) D_3) I_2))) (=> (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) D_3) I_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) I_2) (tptp.one_one tptp.int))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 I_2))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) P_1 A0) A1))))))) (forall ((X_a $$unsorted) (Xs $$unsorted) (Ys $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.size_size _let_1))) (=> (not (= (tptp.hAPP _let_1 tptp.nat _let_2 Xs) (tptp.hAPP _let_1 tptp.nat _let_2 Ys))) (not (= Xs Ys)))))) (forall ((X_a $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun _let_1 tptp.bool) tptp.bool (tptp.finite_finite_1 _let_1) M_1)) (exists ((N_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.list X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) M_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP _let_1 tptp.nat (tptp.size_size _let_1) X_2)) N_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (let ((_let_2 (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) K_4))) (let ((_let_3 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) K_4) (tptp.zero_zero tptp.int))))) (and (=> _let_3 (= _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) K_4)))))) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 K_4))))))))))) (forall ((Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Ma) (tptp.one_one tptp.int))) Ma)))) _let_200 _let_200 (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.int tptp.complex (tptp.ring_1_of_int tptp.complex) Z_1)) (tptp.zero_zero tptp.real))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1)) (tptp.ti tptp.int Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((V $$unsorted)) (= (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) V)) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) V))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((Z_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) Z_1) N)) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP tptp.int X_a _let_1 Z_1)) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X))) X))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) Z_1)) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.int X_a _let_1 Z_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.int X_a _let_1 W_1)) (tptp.hAPP tptp.int X_a _let_1 Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) W_1) Z))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a _let_1 W_1)) (tptp.hAPP tptp.int X_a _let_1 Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) W_1) Z))))))) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.int tptp.complex (tptp.ring_1_of_int tptp.complex) Z_1)) (tptp.hAPP tptp.int tptp.real (tptp.ring_1_of_int tptp.real) Z_1))) (forall ((Z_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.complex (tptp.ring_1_of_int tptp.complex) Z_1))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj _let_1) _let_1))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP tptp.real X_a (tptp.of_real X_a) (tptp.hAPP tptp.int tptp.real (tptp.ring_1_of_int tptp.real) Z_1)) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_char_0 X_a) (forall ((W_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (= (= (tptp.hAPP tptp.int X_a _let_1 W_1) (tptp.hAPP tptp.int X_a _let_1 Z)) (= (tptp.ti tptp.int W_1) (tptp.ti tptp.int Z))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n2089651433ebra_1 X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1)) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.ring_1_of_int tptp.real) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((Z_1 $$unsorted)) (= (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1)) (tptp.ti tptp.int Z_1))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N))) (= (tptp.hAPP tptp.int tptp.int (tptp.ring_1_of_int tptp.int) _let_1) _let_1))) (forall ((X_a $$unsorted)) (=> (tptp.ring_char_0 X_a) (forall ((Z $$unsorted)) (= (= (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z) (tptp.zero_zero X_a)) (= (tptp.ti tptp.int Z) (tptp.zero_zero tptp.int)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_char_0 X_a) (forall ((Z $$unsorted)) (= (= (tptp.zero_zero X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) (= (tptp.ti tptp.int Z) (tptp.zero_zero tptp.int)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (= (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) (tptp.zero_zero tptp.int)) (tptp.zero_zero X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) K_4) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) K_4))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) X) (tptp.hAPP tptp.int tptp.real (tptp.ring_1_of_int tptp.real) X))) (forall ((W $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W) (tptp.hAPP tptp.int tptp.int (tptp.ring_1_of_int tptp.int) W))) (forall ((W $$unsorted)) (= (tptp.hAPP tptp.int tptp.complex (tptp.number_number_of tptp.complex) W) (tptp.hAPP tptp.int tptp.complex (tptp.ring_1_of_int tptp.complex) W))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (= (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) (tptp.one_one tptp.int)) (tptp.one_one X_a)))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) W) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 Z_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) W) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 Z_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((W $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) W) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a _let_1 W)) (tptp.hAPP tptp.int X_a _let_1 Z_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (= (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) tptp.min_1)) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) tptp.min_1)))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1)) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_1) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Z) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Z) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1)) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) X) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.archim2085082626_floor X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.archimedean_ceiling X_a))) (= (tptp.hAPP X_a tptp.int _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) (tptp.hAPP X_a tptp.int _let_1 X)) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Z)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Z) (tptp.zero_zero tptp.int))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z)))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Z) (tptp.zero_zero tptp.int))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((Z_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) Z_1)) (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_1)) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((Z_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) _let_1) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) _let_1) (tptp.one_one X_a)))) (= (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X) (tptp.ti tptp.int Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((Z_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_1))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) _let_1) (tptp.one_one X_a))) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) X) _let_1)) (= (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X) (tptp.ti tptp.int Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X)))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) _let_1) (tptp.one_one X_a))) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) X) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Z) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) (tptp.one_one X_a))) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X_1)) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) (tptp.one_one X_a)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X_1 $$unsorted) (Z $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1)) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) (tptp.one_one X_a)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((Z $$unsorted) (X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Z) (tptp.hAPP X_a tptp.int (tptp.archimedean_ceiling X_a) X_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) (tptp.one_one X_a))) X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1727834104eiling X_a) (forall ((X $$unsorted)) (let ((_let_1 (tptp.hAPP X_a tptp.int (tptp.archim2085082626_floor X_a) X))) (let ((_let_2 (tptp.ring_1_of_int X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a _let_2 _let_1)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.ord_less X_a) X) (tptp.hAPP tptp.int X_a _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) _let_1) (tptp.one_one tptp.int)))))))))))) (forall ((Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hAPP tptp.int tptp.nat tptp.phi Ma) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma))))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) Ma)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd A_2) Ma) _let_1) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) X_2) Ma)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_2) (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) Y_2) Ma)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Y_2) (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma)))) (= (tptp.ti tptp.int Y_2) (tptp.ti tptp.int X_2)))))))))))) (forall ((X_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.finite_card tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd X_1) Ma) (tptp.one_one tptp.int)) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.noXRRset Ma) X_1)) (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((X $$unsorted)) (exists ((Z_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a _let_1 Z_2)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) X) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Z_2) (tptp.one_one tptp.int)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((X $$unsorted)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a _let_1 X_2)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) X) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) (tptp.one_one tptp.int))))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) (tptp.hAPP tptp.int X_a _let_1 Y_2)) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) X) (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Y_2) (tptp.one_one tptp.int)))))) (= (tptp.ti tptp.int Y_2) (tptp.ti tptp.int X_2))))))))))))) (forall ((X_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd X_1) Ma) (tptp.one_one tptp.int)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_1 _let_1 tptp.is_RRset (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.noXRRset Ma) X_1)) Ma)))))) (forall ((A_2 $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_1 _let_1 tptp.is_RRset A_3) Ma)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) A_2) A_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.legacy_zgcd A_2) Ma) (tptp.one_one tptp.int)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.member tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_2 _let_2 tptp.is_RRset A_3) Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong A_2) B_1) Ma)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 A_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_3 _let_1 B_1) A_3)) (= (tptp.ti tptp.int A_2) (tptp.ti tptp.int B_1))))))))))) (forall ((A_2 $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.int _let_2) tptp.rRset2norRR A_3) Ma) A_2))) (let ((_let_4 (tptp.member tptp.int))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_1 _let_1 tptp.is_RRset A_3) Ma)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 A_2) A_3)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong A_2) _let_3) Ma)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 _let_3) (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma))))))))))))) (forall ((A_2 $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.member tptp.int))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_1 _let_1 tptp.is_RRset A_3) Ma)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 A_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.int _let_2) tptp.rRset2norRR A_3) Ma) A_2)) (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma))))))))))) (forall ((A_2 $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_2 _let_2 tptp.is_RRset A_3) Ma)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_2 tptp.bool) (tptp.member tptp.int) A_2) A_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong A_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_2 (tptp.fun tptp.int _let_1) tptp.rRset2norRR A_3) Ma) A_2)) Ma)))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((X $$unsorted)) (exists ((Z_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_2)) X)))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((X $$unsorted)) (exists ((Z_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.archim1804426504_field X_a) (forall ((X $$unsorted)) (exists ((Z_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_2))))))) (forall ((A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_1 _let_1 tptp.is_RRset A_3) Ma)) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) A_3) (tptp.hAPP tptp.int _let_2 tptp.rsetR Ma))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) A_3) (tptp.hAPP tptp.int tptp.nat tptp.phi Ma))))))) (forall ((A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) A_3) (tptp.hAPP tptp.int _let_2 tptp.rsetR Ma))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) A_3)))))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_2) Ma)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset A_2) Ma)) (tptp.hAPP tptp.int _let_2 tptp.rsetR Ma))))))) (forall ((A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_1 _let_1 tptp.is_RRset A_3) Ma)) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image tptp.int tptp.int) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.int _let_2) tptp.rRset2norRR A_3) Ma)) A_3) (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.int_lcm X) Y) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) tptp.nat_lcm (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 X))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 Y))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti X_a B_1) (tptp.hAPP X_b X_a F X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_3)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (H $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) F_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) H) F_1))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_3))) (exists ((AA $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) AA) A_3)) (= (tptp.ti _let_1 B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) AA)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_2)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (let ((_let_6 (tptp.hAPP (tptp.fun X_b X_a) _let_5 (tptp.image X_b X_a) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) (tptp.hAPP _let_3 _let_1 _let_6 A_3)) B_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_4 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_2) (tptp.image _let_3 _let_1) _let_6) (tptp.hAPP _let_3 _let_4 (tptp.pow X_b) A_3))) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) B_2))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (Z $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Z) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_3))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3)) (= (tptp.ti X_a Z) (tptp.hAPP X_b X_a F X_2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_3))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_1) A_3)) (=> (= (tptp.ti X_b B_1) (tptp.hAPP X_a X_b F X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_3)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun _let_3 _let_1))) (let ((_let_6 (tptp.hAPP (tptp.fun X_b X_a) _let_5 (tptp.image X_b X_a) F))) (=> (= (tptp.hAPP _let_3 _let_1 _let_6 A_3) (tptp.ti _let_1 B_2)) (= (tptp.hAPP _let_4 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_2) (tptp.image _let_3 _let_1) _let_6) (tptp.hAPP _let_3 _let_4 (tptp.pow X_b) A_3)) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) B_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_1 _let_2) (tptp.image X_b X_a) F))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) (tptp.hAPP _let_1 _let_2 _let_3 A_3)) (tptp.hAPP _let_1 _let_2 _let_3 B_2))) (tptp.hAPP _let_1 _let_2 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (B_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_2))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_b) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 _let_2) (tptp.image X_a X_b) F) A_3))) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_3))))))) (forall ((F $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) tptp.resSet Ma))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_2) A_3)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) A_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong (tptp.hAPP tptp.int tptp.int F X_2)) (tptp.hAPP tptp.int tptp.int F Xa)) Ma)) (= (tptp.ti tptp.int X_2) (tptp.ti tptp.int Xa))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.int tptp.int) (tptp.fun _let_1 _let_1) (tptp.image tptp.int tptp.int) F) A_3))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_3))) (exists ((C_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) C_3) A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) C_3)) (= (tptp.ti _let_1 B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) C_3))))))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_2)))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_2)))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)))) (= (= A_3 B_2) (= (tptp.hAPP _let_2 _let_1 _let_3 A_3) (tptp.hAPP _let_2 _let_1 _let_3 B_2))))))) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_3 tptp.bool) (tptp.member tptp.nat) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_2 tptp.bool) (tptp.member tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X_1)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_3 _let_2) (tptp.image tptp.nat tptp.int) _let_1) A_3)))))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_1 _let_2) (tptp.image tptp.int tptp.nat) tptp.nat_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) A_3)) A_3)))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.nat) A_3) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) A_3)))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 tptp.nat) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) A_3))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.setS A_2) P_4) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.image tptp.int _let_1) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.multInvPair A_2) P_4)) (tptp.hAPP tptp.int _let_1 tptp.sRStar P_4))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (B_2 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) (tptp.hAPP X_a X_b F X_2)) B_2)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_3)) B_2)))))) (forall ((S $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) S))) (forall ((M_2 $$unsorted)) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) N_2) S)))))))) (forall ((S $$unsorted)) (= (not (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) S))) (forall ((M_2 $$unsorted)) (exists ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) N_2) S)))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 tptp.nat_lcm X) Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) X) Y)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 tptp.nat_gcd X) Y))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.image tptp.int tptp.nat) tptp.nat_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set B_2)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_2)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.gcd_gcd tptp.nat) X) Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 tptp.nat_gcd X) Y)))) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.nat_nat_set A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) A_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)))))) (forall ((S $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.int tptp.bool) tptp.bool tptp.nat_nat_set S)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_2) S)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2))))))) (forall ((C_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.nat_nat_set (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) C_2)))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.image tptp.int tptp.nat) tptp.nat_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set B_2)) (= (= A_3 B_2) (= (tptp.hAPP _let_2 _let_1 _let_3 A_3) (tptp.hAPP _let_2 _let_1 _let_3 B_2))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 tptp.nat_gcd X) Y))) (let ((_let_3 (= Y (tptp.zero_zero tptp.nat)))) (and (=> _let_3 (= _let_2 X)) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 tptp.nat_gcd Y) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) X) Y))))))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set A_3)) (= (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_1 _let_2) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.image tptp.int tptp.nat) tptp.nat_1) A_3)) A_3))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set A_3)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 tptp.int) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.image tptp.int tptp.nat) tptp.nat_1) A_3)))))))) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set A_3)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.int) A_3) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.image tptp.int tptp.nat) tptp.nat_1) A_3))))))) (forall ((B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.image tptp.int tptp.nat) tptp.nat_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set B_2)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP _let_2 _let_1 _let_3 A_3)) (tptp.hAPP _let_2 _let_1 _let_3 B_2)))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 tptp.nat_gcd X_1) Y_1))) (let ((_let_3 (= Y_1 (tptp.zero_zero tptp.nat)))) (let ((_let_4 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP (tptp.fun _let_4 _let_5) _let_5 (tptp.accp _let_4) tptp.nat_gcd_rel) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_4) (tptp.product_Pair tptp.nat tptp.nat) X_1) Y_1))) (and (=> _let_3 (= _let_2 X_1)) (=> (not _let_3) (= _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 tptp.nat_gcd Y_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_mod tptp.nat) X_1) Y_1)))))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.int_gcd X) Y) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) tptp.nat_gcd (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 X))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 Y))))))) (forall ((P_1 $$unsorted) (A0 $$unsorted) (A1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun _let_1 _let_2) _let_2 (tptp.accp _let_1) tptp.nat_gcd_rel) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.product_Pair tptp.nat tptp.nat) A0) A1))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun _let_2 _let_3) _let_3 (tptp.accp _let_2) tptp.nat_gcd_rel) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.product_Pair tptp.nat tptp.nat) X_2) Y_2))) (=> (=> (not (= Y_2 (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 P_1 Y_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.div_mod tptp.nat) X_2) Y_2)))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 P_1 X_2) Y_2)))))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) P_1 A0) A1))))))) (forall ((N_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N_4)) (exists ((M_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) X_2) M_2)))))))) (forall ((N_4 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N_4)) (exists ((M_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) M_2)))))))) (forall ((N_1 $$unsorted) (N_4 $$unsorted)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) N_4)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) N_1))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) N_4)))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.ord_gr676655987ssThan tptp.int) L) U_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) U_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) L) (tptp.one_one tptp.int)))))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_gr676655987ssThan tptp.int) L) U_1))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_gr676655987ssThan X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (= (tptp.hAPP _let_3 _let_3 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_3 _let_3) (tptp.image X_a X_a) _let_1) (tptp.hAPP X_a _let_3 (tptp.hAPP X_a _let_4 _let_2 X_1) Y_1)) (tptp.hAPP X_a _let_3 (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a _let_1 Y_1)) (tptp.hAPP X_a X_a _let_1 X_1)))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_1) (tptp.field_char_0_Rats tptp.real))) (not (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (=> (not (= N_2 (tptp.zero_zero tptp.nat))) (=> (= (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.nat tptp.real _let_1 M_2)) (tptp.hAPP tptp.nat tptp.real _let_1 N_2))) (not (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) M_2) N_2) (tptp.one_one tptp.nat))))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.zero_frac X_a) (tptp.hAPP _let_1 X_a (tptp.abs_Frac X_a) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) (tptp.zero_zero tptp.int)) (tptp.one_one tptp.int)))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_gr676655987ssThan tptp.nat) L) U_1))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) (tptp.field_char_0_Rats tptp.real))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_gr676655987ssThan tptp.nat) L) U_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) U_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc L))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (= (tptp.one_frac X_a) (tptp.hAPP _let_2 X_a (tptp.abs_Frac X_a) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.product_Pair tptp.int tptp.int) _let_1) _let_1)))))) (forall ((X_a $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP tptp.int X_a (tptp.number_of_frac X_a) N) (tptp.hAPP _let_1 X_a (tptp.abs_Frac X_a) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) N) (tptp.one_one tptp.int)))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) X_1) Y_1)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_2 tptp.bool) (tptp.member tptp.real) X_2) (tptp.field_char_0_Rats tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) Y_1)))))))))) (forall ((F $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.ord_gr676655987ssThan tptp.real) A_2) B_1))) (let ((_let_3 (tptp.member tptp.real))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 X_1) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_4 _let_3 Y_1) _let_2)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_2) (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real _let_2 (tptp.ord_gr676655987ssThan tptp.real) A_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) _let_2 (tptp.deriv tptp.real) F) X_2) (tptp.zero_zero tptp.real))))))) (= (tptp.hAPP tptp.real tptp.real F X_1) (tptp.hAPP tptp.real tptp.real F Y_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_char_0 X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (=> (not (= (tptp.ti X_a A_2) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_2)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_char_0 X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 B_1) _let_1)) (=> (not (= (tptp.ti X_a B_1) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_2) B_1)) _let_1)))))))))))) (forall ((K $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.iszero tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) K))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.iszero tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.field_char_0 X_a) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.zero_zero X_a)) (tptp.field_char_0_Rats X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.field_char_0 X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_2) B_1)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_char_0 X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.number_ring X_a) (tptp.field_char_0 X_a)) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1)) (tptp.field_char_0_Rats X_a))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.field_char_0 X_a) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.one_one X_a)) (tptp.field_char_0_Rats X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.field_char_0 X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_2) B_1)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_char_0 X_a) (forall ((N_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_2) N_1)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_char_0 X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.field_char_0 X_a)) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.inverse_divide X_a) A_2) B_1)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_char_0 X_a) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_1)) (tptp.field_char_0_Rats X_a))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.field_inverse_zero X_a) (tptp.field_char_0 X_a)) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.field_char_0_Rats X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.inverse_inverse X_a) A_2)) _let_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field_char_0 X_a) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) (tptp.field_char_0_Rats X_a))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) X_1) Y_1)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_2 tptp.bool) (tptp.member tptp.real) X_2) (tptp.field_char_0_Rats tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) Y_1)))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) Y_1) X_1)) (= (tptp.hAPP _let_1 tptp.real (tptp.complete_Sup_Sup tptp.real) (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.ord_gr676655987ssThan tptp.real) Y_1) X_1)) X_1)))) (forall ((X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_1) X_3)) (=> (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_2) X_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) X_2) Z_2)))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) X_1) (tptp.hAPP _let_1 tptp.real (tptp.complete_Sup_Sup tptp.real) X_3))))))) (forall ((Z $$unsorted) (X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_1) X_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_2) X_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) X_2) Z))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) X_1) (tptp.hAPP _let_1 tptp.real (tptp.complete_Sup_Sup tptp.real) X_3))))))) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP _let_1 tptp.rat tptp.frct (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K_4)) (tptp.one_one tptp.int))) (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) K_4)))) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP _let_1 tptp.rat tptp.frct (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) K_4) (tptp.zero_zero tptp.int))) (tptp.zero_zero tptp.rat)))) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP _let_1 tptp.rat tptp.frct (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) (tptp.zero_zero tptp.int)) K_4)) (tptp.zero_zero tptp.rat)))) (= (tptp.hAPP _let_141 tptp.rat tptp.frct _let_199) _let_193) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.rat))) (let ((_let_2 (tptp.number_number_of tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP _let_3 tptp.rat tptp.frct (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int _let_2 K_4)) (tptp.hAPP tptp.int tptp.int _let_2 L_4))) (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.inverse_divide tptp.rat) (tptp.hAPP tptp.int tptp.rat _let_1 K_4)) (tptp.hAPP tptp.int tptp.rat _let_1 L_4))))))) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP _let_1 tptp.rat tptp.frct (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) (tptp.one_one tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K_4))) (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.inverse_divide tptp.rat) (tptp.one_one tptp.rat)) (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) K_4))))) (forall ((Z $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) Z) X_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_2) X_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) X_2) Z))))) (= (tptp.hAPP _let_1 tptp.real (tptp.complete_Sup_Sup tptp.real) X_3) Z))))) (forall ((Z $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) Y_1))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_1) X_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 X_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_2) X_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) X_2) Z))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_2 (tptp.hAPP _let_1 tptp.real (tptp.complete_Sup_Sup tptp.real) X_3))))))))) (forall ((Q_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.rat tptp.rat (tptp.abs_abs tptp.rat) Q_3))) (let ((_let_2 (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) Q_3) (tptp.zero_zero tptp.rat))))) (and (=> _let_2 (= _let_1 (tptp.hAPP tptp.rat tptp.rat (tptp.uminus_uminus tptp.rat) Q_3))) (=> (not _let_2) (= _let_1 Q_3)))))) (forall ((Q_3 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.rat))) (let ((_let_2 (tptp.hAPP tptp.rat tptp.rat (tptp.sgn_sgn tptp.rat) Q_3))) (let ((_let_3 (tptp.zero_zero tptp.rat))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) _let_3) Q_3)))) (let ((_let_5 (= Q_3 _let_3))) (and (=> _let_5 (= _let_2 _let_3)) (=> (not _let_5) (and (=> _let_4 (= _let_2 _let_1)) (=> (not _let_4) (= _let_2 (tptp.hAPP tptp.rat tptp.rat (tptp.uminus_uminus tptp.rat) _let_1)))))))))))) (forall ((Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.rat tptp.rat))) (= (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat _let_1 (tptp.inverse_divide tptp.rat) Q_3) R_4) (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat _let_1 (tptp.times_times tptp.rat) Q_3) (tptp.hAPP tptp.rat tptp.rat (tptp.inverse_inverse tptp.rat) R_4))))) (forall ((P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus tptp.int))) (let ((_let_2 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Q_3) (tptp.zero_zero tptp.int))) (= (tptp.hAPP _let_3 _let_3 tptp.normalize (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 _let_2 P_5) Q_3)) (tptp.hAPP _let_3 _let_3 tptp.normalize (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 P_5)) (tptp.hAPP tptp.int tptp.int _let_1 Q_3)))))))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of (tptp.hAPP tptp.rat tptp.rat (tptp.sgn_sgn tptp.rat) P_5)) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.sgn_sgn tptp.int) (tptp.hAPP _let_1 tptp.int (tptp.product_fst tptp.int tptp.int) (tptp.hAPP tptp.rat _let_1 tptp.quotient_of P_5)))) (tptp.one_one tptp.int))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of A_1) (tptp.hAPP tptp.rat _let_1 tptp.quotient_of B)) (= A_1 B)))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of A_2) (tptp.hAPP tptp.rat _let_1 tptp.quotient_of B_1)) (= A_2 B_1)))) (forall ((Q_3 $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.rat tptp.rat))) (= (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat _let_1 (tptp.minus_minus tptp.rat) Q_3) R_4) (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat _let_1 (tptp.plus_plus tptp.rat) Q_3) (tptp.hAPP tptp.rat tptp.rat (tptp.uminus_uminus tptp.rat) R_4))))) (forall ((Z $$unsorted) (W_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.rat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat _let_1 (tptp.ord_less tptp.rat) Z) W_1)) (and (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat _let_1 (tptp.ord_less_eq tptp.rat) Z) W_1)) (not (= Z W_1)))))) (forall ((R_4 $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of R_4) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) P_5) Q_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Q_3))))) (= (tptp.hAPP tptp.rat _let_141 tptp.quotient_of _let_193) _let_199) (forall ((R_4 $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (=> (= (tptp.hAPP _let_1 _let_1 tptp.normalize R_4) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) P_5) Q_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Q_3))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (= (tptp.hAPP _let_3 _let_3 tptp.normalize (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 _let_2 P_5) _let_1)) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 _let_2 _let_1) (tptp.one_one tptp.int)))))))) (forall ((P_5 $$unsorted) (R_4 $$unsorted) (S_3 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.zero_zero tptp.int))) (=> (not (= (tptp.ti tptp.int Q_3) _let_6)) (=> (not (= (tptp.ti tptp.int S_3) _let_6)) (=> (= (tptp.hAPP _let_4 _let_4 tptp.normalize (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 _let_3 P_5) Q_3)) (tptp.hAPP _let_4 _let_4 tptp.normalize (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 _let_3 R_4) S_3))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 P_5) S_3) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 R_4) Q_3)))))))))))) (= (tptp.hAPP tptp.rat _let_141 tptp.quotient_of _let_192) (tptp.hAPP tptp.int _let_141 (tptp.hAPP tptp.int _let_198 _let_197 _let_1) _let_2)) (forall ((K_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) K_4)) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K_4)) (tptp.one_one tptp.int))))) (forall ((R_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.zero_zero tptp.rat)) R_4)) (not (forall ((S_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.zero_zero tptp.rat)) S_1)) (forall ((T_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.zero_zero tptp.rat)) T_4)) (not (= R_4 (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.plus_plus tptp.rat) S_1) T_4)))))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_snd tptp.int tptp.int))) (let ((_let_2 (tptp.product_prod tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP _let_2 tptp.int _let_1 X_1))) (let ((_let_4 (tptp.product_fst tptp.int tptp.int))) (let ((_let_5 (tptp.times_times tptp.int))) (let ((_let_6 (tptp.fun tptp.int tptp.int))) (let ((_let_7 (tptp.hAPP _let_2 tptp.int _let_1 Y_1))) (let ((_let_8 (tptp.zero_zero tptp.int))) (let ((_let_9 (tptp.product_prod _let_2 _let_2))) (let ((_let_10 (tptp.fun _let_9 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP _let_9 (tptp.fun _let_10 tptp.bool) (tptp.member _let_9) (tptp.hAPP _let_2 _let_9 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_9) (tptp.product_Pair _let_2 _let_2) X_1) Y_1)) tptp.ratrel)) (and (not (= _let_3 _let_8)) (not (= _let_7 _let_8)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 (tptp.hAPP _let_2 tptp.int _let_4 X_1)) _let_7) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_6 _let_5 (tptp.hAPP _let_2 tptp.int _let_4 Y_1)) _let_3))))))))))))))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract (tptp.one_one tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K_4)) (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.inverse_divide tptp.rat) (tptp.one_one tptp.rat)) (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) K_4)))) (forall ((R_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.real))) (let ((_let_2 (tptp.number_number_of tptp.rat))) (= (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.inverse_divide tptp.rat) (tptp.hAPP tptp.int tptp.rat _let_2 R_4)) (tptp.hAPP tptp.int tptp.rat _let_2 S_3))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.int tptp.real _let_1 R_4)) (tptp.hAPP tptp.int tptp.real _let_1 S_3)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.rat))) (let ((_let_2 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract A_1) B))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.rat _let_3 tptp.quotient_of _let_2) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) (tptp.product_Pair tptp.int tptp.int) P_5) Q_3)) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract P_5) Q_3) _let_2)))))) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.rat))) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_2 tptp.fract A_1) _let_1) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_2 tptp.fract _let_1) (tptp.one_one tptp.int)))))) (= _let_193 _let_196) (= _let_196 _let_193) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract (tptp.zero_zero tptp.int)) K_4) (tptp.zero_zero tptp.rat))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract K_4) (tptp.zero_zero tptp.int)) (tptp.zero_zero tptp.rat))) (forall ((A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract (tptp.zero_zero tptp.int)))) (= (tptp.hAPP tptp.int tptp.rat _let_1 A_1) (tptp.hAPP tptp.int tptp.rat _let_1 C)))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.nat tptp.rat (tptp.semiring_1_of_nat tptp.rat) K_4) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) K_4)) (tptp.one_one tptp.int)))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) K_4)) (tptp.one_one tptp.int)) (tptp.hAPP tptp.nat tptp.rat (tptp.semiring_1_of_nat tptp.rat) K_4))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.rat (tptp.ring_1_of_int tptp.rat) K_4) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract K_4) (tptp.one_one tptp.int)))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract K_4) (tptp.one_one tptp.int)) (tptp.hAPP tptp.int tptp.rat (tptp.ring_1_of_int tptp.rat) K_4))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int tptp.rat))) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract K_4) L_4) (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.inverse_divide tptp.rat) (tptp.hAPP tptp.int tptp.rat _let_1 K_4)) (tptp.hAPP tptp.int tptp.rat _let_1 L_4))))) (forall ((W $$unsorted)) (= (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) W) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract W) (tptp.one_one tptp.int)))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) (tptp.hAPP tptp.rat tptp.real tptp.ratreal X)) (tptp.hAPP tptp.rat tptp.int (tptp.archim2085082626_floor tptp.rat) X))) (forall ((A_1 $$unsorted) (B $$unsorted)) (= (tptp.hAPP tptp.rat tptp.int (tptp.archim2085082626_floor tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_1) B)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) A_1) B))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.rat))) (= (tptp.hAPP tptp.rat tptp.rat (tptp.inverse_inverse tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract A_1) B)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract B) A_1)))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.rat))) (let ((_let_2 (tptp.uminus_uminus tptp.int))) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract (tptp.hAPP tptp.int tptp.int _let_2 A_1)) (tptp.hAPP tptp.int tptp.int _let_2 B)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract A_1) B))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.rat))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) C))) (=> (not (= (tptp.ti tptp.int C) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract (tptp.hAPP tptp.int tptp.int _let_2 A_1)) (tptp.hAPP tptp.int tptp.int _let_2 B)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract A_1) B)))))) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.rat))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (not (= (tptp.ti tptp.int B_1) _let_4)) (=> (not (= (tptp.ti tptp.int D_1) _let_4)) (= (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract A_2) B_1) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract C_1) D_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_2) D_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 C_1) B_1)))))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.rat))) (= (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.inverse_divide tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract A_1) B)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract C) D)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) D)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) C))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.rat))) (= (tptp.hAPP tptp.rat tptp.rat (tptp.uminus_uminus tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract A_1) B)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) A_1)) B)))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.rat))) (= (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.times_times tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract A_1) B)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract C) D)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) C)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) D))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.rat))) (= (tptp.hAPP tptp.rat tptp.rat (tptp.abs_abs tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_2 tptp.fract A_1) B)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_2 tptp.fract (tptp.hAPP tptp.int tptp.int _let_1 A_1)) (tptp.hAPP tptp.int tptp.int _let_1 B)))))) (forall ((A_1 $$unsorted) (B $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.rat))) (let ((_let_2 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (=> (= (tptp.hAPP _let_3 _let_3 tptp.normalize (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 _let_2 A_1) B)) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_4 _let_2 P_5) Q_3)) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract P_5) Q_3) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract A_1) B)))))))) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.rat tptp.real tptp.ratreal X_1)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal Y_1))) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) X_1) Y_1)))) (= _let_195 _let_37) (= _let_37 _let_195) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) K_4) (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) K_4)))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) K_4)) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) K_4))) (= _let_194 _let_136) (= _let_136 _let_194) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.rat tptp.real tptp.ratreal X_1)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal Y_1))) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less_eq tptp.rat) X_1) Y_1)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.rat tptp.real tptp.ratreal X)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal Y)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.plus_plus tptp.rat) X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP tptp.rat tptp.real tptp.ratreal X)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal Y)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.minus_minus tptp.rat) X) Y)))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.rat tptp.real tptp.ratreal X)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.rat tptp.rat (tptp.uminus_uminus tptp.rat) X)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.rat tptp.real tptp.ratreal X)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal Y)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.inverse_divide tptp.rat) X) Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.rat tptp.real tptp.ratreal X)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal Y)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.times_times tptp.rat) X) Y)))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.rat tptp.real tptp.ratreal X)) (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.rat tptp.rat (tptp.inverse_inverse tptp.rat) X)))) (= _let_192 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_191 tptp.fract _let_1) _let_2)) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) K_4) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K_4)) (tptp.one_one tptp.int)))) (forall ((K_4 $$unsorted)) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) K_4)) (tptp.one_one tptp.int)) (tptp.hAPP tptp.int tptp.rat (tptp.number_number_of tptp.rat) K_4))) (forall ((K_4 $$unsorted) (L_4 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.rat))) (let ((_let_2 (tptp.number_number_of tptp.int))) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract (tptp.hAPP tptp.int tptp.int _let_2 K_4)) (tptp.hAPP tptp.int tptp.int _let_2 L_4)) (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.inverse_divide tptp.rat) (tptp.hAPP tptp.int tptp.rat _let_1 K_4)) (tptp.hAPP tptp.int tptp.rat _let_1 L_4)))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_1) B)) (tptp.hAPP _let_1 _let_1 tptp.normalize (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) A_1) B))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP _let_1 tptp.rat tptp.frct P_5) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract (tptp.hAPP _let_1 tptp.int (tptp.product_fst tptp.int tptp.int) P_5)) (tptp.hAPP _let_1 tptp.int (tptp.product_snd tptp.int tptp.int) P_5))))) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B_1) D_1))) (let ((_let_4 (tptp.fun tptp.int tptp.rat))) (let ((_let_5 (tptp.zero_zero tptp.int))) (=> (not (= (tptp.ti tptp.int B_1) _let_5)) (=> (not (= (tptp.ti tptp.int D_1) _let_5)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_4 tptp.fract A_2) B_1)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_4 tptp.fract C_1) D_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_2) D_1)) _let_3)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 C_1) B_1)) _let_3)))))))))))) (forall ((R_4 $$unsorted) (S_3 $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.real))) (let ((_let_2 (tptp.inverse_divide tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.number_number_of tptp.rat))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.int tptp.rat _let_4 R_4))) (tptp.hAPP tptp.rat tptp.real tptp.ratreal (tptp.hAPP tptp.int tptp.rat _let_4 S_3))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real _let_1 R_4)) (tptp.hAPP tptp.int tptp.real _let_1 S_3)))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.sgn_sgn tptp.int))) (= (tptp.hAPP tptp.rat tptp.rat (tptp.sgn_sgn tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_1) B)) (tptp.hAPP tptp.int tptp.rat (tptp.ring_1_of_int tptp.rat) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 A_1)) (tptp.hAPP tptp.int tptp.int _let_1 B)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 _let_1) B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_2) B_1)) (tptp.zero_zero tptp.rat))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 A_2) _let_1)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.zero_zero tptp.rat)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 A_2)))))) (forall ((A_2 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B_1) D_1))) (let ((_let_4 (tptp.fun tptp.int tptp.rat))) (let ((_let_5 (tptp.zero_zero tptp.int))) (=> (not (= (tptp.ti tptp.int B_1) _let_5)) (=> (not (= (tptp.ti tptp.int D_1) _let_5)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less_eq tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_4 tptp.fract A_2) B_1)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_4 tptp.fract C_1) D_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_2) D_1)) _let_3)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 C_1) B_1)) _let_3)))))))))))) (forall ((A_1 $$unsorted) (C $$unsorted) (D $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.rat))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (not (= (tptp.ti tptp.int B) _let_4)) (=> (not (= (tptp.ti tptp.int D) _let_4)) (= (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.plus_plus tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract A_1) B)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract C) D)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) D)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 C) B))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) D)))))))))) (forall ((A_1 $$unsorted) (C $$unsorted) (D $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.rat))) (let ((_let_4 (tptp.zero_zero tptp.int))) (=> (not (= (tptp.ti tptp.int B) _let_4)) (=> (not (= (tptp.ti tptp.int D) _let_4)) (= (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.minus_minus tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract A_1) B)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract C) D)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_3 tptp.fract (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) D)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 C) B))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) D)))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_2) B_1)) (tptp.one_one tptp.rat))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 A_2) B_1))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)) B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.one_one tptp.rat)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 B_1) A_2))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.rat))) (=> (not (= (tptp.ti tptp.int N) (tptp.zero_zero tptp.int))) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) M) N)) N) (tptp.hAPP tptp.rat tptp.rat (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.rat) (tptp.plus_plus tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract M) N)) (tptp.one_one tptp.rat)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less_eq tptp.rat) (tptp.zero_zero tptp.rat)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_1) A_2))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_1) B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less_eq tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_2) B_1)) (tptp.zero_zero tptp.rat))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) A_2) _let_1))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_div tptp.int) A_1) B))) (let ((_let_3 (tptp.ring_1_of_int tptp.rat))) (let ((_let_4 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_1) B))) (let ((_let_5 (tptp.fun tptp.rat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat _let_5 (tptp.ord_less_eq tptp.rat) (tptp.hAPP tptp.int tptp.rat _let_3 _let_2)) _let_4)) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat _let_5 (tptp.ord_less tptp.rat) _let_4) (tptp.hAPP tptp.int tptp.rat _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) _let_2) (tptp.one_one tptp.int)))))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less_eq tptp.rat) (tptp.one_one tptp.rat)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) B_1) A_2)))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B_1)) (= (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less_eq tptp.rat) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_2) B_1)) (tptp.one_one tptp.rat))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) A_2) B_1)))))) (forall ((Q_2 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B_4)) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool P_1 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_4) B_4))))) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool P_1 Q_2)))) (forall ((X_a $$unsorted) (R_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Y_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP X_a tptp.nat F X_1)) (tptp.hAPP X_a tptp.nat F Y_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 R_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_2 _let_2) (tptp.mlex_prod X_a) F) R_3))))))))) (forall ((X_a $$unsorted) (R_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.hAPP X_a tptp.nat F X_1)) (tptp.hAPP X_a tptp.nat F Y_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a (tptp.fun X_a _let_1) (tptp.product_Pair X_a X_a) X_1) Y_1)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_2 _let_2) (tptp.mlex_prod X_a) F) R_3))))))) (forall ((B_1 $$unsorted) (Q_2 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) Q_2))) (let ((_let_3 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_4 (tptp.product_prod tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) R_1) B_1))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (= (tptp.hAPP _let_4 _let_4 (tptp.hAPP tptp.int _let_7 tptp.adjust B_1) (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 _let_3 Q_2) R_1)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_4 _let_7 (tptp.hAPP tptp.bool (tptp.fun _let_4 _let_7) (tptp.if _let_4) (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) _let_6)) (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) _let_2) (tptp.one_one tptp.int))) _let_6)) (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int _let_5 _let_3 _let_2) R_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_idom X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.ord_less X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.plus_plus X_a))) (let ((_let_5 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) A_2) (tptp.ring_1_Ints X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 (tptp.one_one X_a)) A_2)) A_2)) _let_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 A_2) _let_1)))))))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.collect X_a))) (let ((_let_5 (tptp.finite_finite_1 X_a))) (=> (or (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 P_1))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 Q_1)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_5 (tptp.hAPP _let_3 _let_3 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.bool _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.bool _let_1 X_a) tptp.fconj) P_1)) Q_1))))))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) K))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) K))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 _let_1) (tptp.hAPP _let_2 _let_2 (tptp.collect _let_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc _let_1 _let_1 tptp.bool) (tptp.ord_less_eq _let_1)) A_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z)) (tptp.ring_1_Ints X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_1)) (tptp.ring_1_Ints X_a))))))) (tptp.hBOOL (tptp.hAPP _let_22 tptp.bool (tptp.hAPP _let_8 _let_74 (tptp.nat_tr1645093318rphism tptp.nat tptp.int) _let_190) (tptp.hAPP tptp.bool _let_22 (tptp.combk tptp.bool tptp.nat) tptp.fTrue))) (forall ((P_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (= (tptp.hAPP _let_4 _let_4 (tptp.collect tptp.int) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_6 (tptp.fun _let_4 _let_4) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_4 _let_6) (tptp.combb tptp.bool _let_5 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_4 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) P_1)) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_4) (tptp.image tptp.nat tptp.int) _let_1) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.nat) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.combb tptp.int tptp.bool tptp.nat) P_1) _let_1))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.zero_zero tptp.int))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_4) N_1)) (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_6 (tptp.fun _let_2 _let_2) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_2 _let_6) (tptp.combb tptp.bool _let_5 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_4))) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.bool) _let_1) N_1))))) (tptp.ti tptp.int N_1)))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 N_1)) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 (tptp.fun _let_1 _let_1) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 tptp.int) tptp.fconj) _let_3)) (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.int tptp.int tptp.bool) (tptp.ord_less tptp.int)) N_1)))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 N_1))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.zero_zero tptp.int))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_4) N_1)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_6 (tptp.fun _let_2 _let_2) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_2 _let_6) (tptp.combb tptp.bool _let_5 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) _let_4))) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.bool) _let_1) N_1)))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 N_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((G $$unsorted) (E_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a G X_1))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.inverse_divide X_a))) (let ((_let_5 (tptp.fun X_a _let_3))) (let ((_let_6 (tptp.deriv X_a))) (let ((_let_7 (tptp.fun X_a tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_3 _let_8 _let_6 F) X_1) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_3 _let_8 _let_6 G) X_1) E_3)) (=> (not (= _let_1 (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_3) (tptp.combs X_a X_a X_a) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_5) (tptp.combb X_a _let_3 X_a) _let_4) F)) G)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 D_2) _let_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a F X_1)) E_3))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 _let_1) _let_1)))))))))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_1) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)))) (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.int tptp.int tptp.bool) (tptp.ord_less_eq tptp.int)) N_1)))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_1) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.int tptp.int tptp.bool) (tptp.ord_less tptp.int)) N_1)))))))))) (forall ((K $$unsorted) (Xa_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.deriv tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.combb tptp.real tptp.real tptp.real) tptp.cos) (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.real tptp.real tptp.real) _let_1) K))) Xa_2) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 Xa_2) K)))))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) X_2) (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc X_2))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((G $$unsorted) (E_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun X_a _let_3))) (let ((_let_6 (tptp.deriv X_a))) (let ((_let_7 (tptp.fun X_a tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_3 _let_8 _let_6 F) X_1) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_3 _let_8 _let_6 G) X_1) E_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 _let_4 (tptp.combs X_a X_a X_a) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_5) (tptp.combb X_a _let_3 X_a) _let_2) F)) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_4 (tptp.combb X_a X_a X_a) _let_1) G))) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 D_2) (tptp.hAPP X_a X_a _let_1 E_3))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((G $$unsorted) (Db $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Da $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.deriv X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 F) X_1) Da)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 G) X_1) Db)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.combs X_a X_a X_a) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb X_a _let_2 X_a) _let_1) F)) G)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Da) (tptp.hAPP X_a X_a G X_1))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Db) (tptp.hAPP X_a X_a F X_1)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((G $$unsorted) (E_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.deriv X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 F) X_1) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 G) X_1) E_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.combs X_a X_a X_a) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb X_a _let_2 X_a) _let_1) F)) G)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a F X_1)) E_3)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 D_2) (tptp.hAPP X_a X_a G X_1)))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real tptp.cos X_1)) (tptp.hAPP tptp.real tptp.real tptp.sin X_1)))) (let ((_let_4 (tptp.fun tptp.real _let_2))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_5) (tptp.deriv tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_2) (tptp.combs tptp.real tptp.real tptp.real) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_4) (tptp.combb tptp.real _let_2 tptp.real) _let_1) tptp.sin)) tptp.sin)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) _let_3) _let_3))))))))) (forall ((K $$unsorted) (Xa_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.deriv tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.combb tptp.real tptp.real tptp.real) tptp.sin) (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.real tptp.real tptp.real) _let_1) K))) Xa_2) (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 Xa_2) K))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) A_2) B_1)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((G $$unsorted) (E_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.deriv X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 F) X_1) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 G) X_1) E_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.combs X_a X_a X_a) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb X_a _let_2 X_a) _let_1) F)) G)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 D_2) E_3)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((G $$unsorted) (E_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.deriv X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 F) X_1) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 G) X_1) E_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.combs X_a X_a X_a) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb X_a _let_2 X_a) _let_1) F)) G)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 D_2) E_3)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) B_1)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((K $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.bseq X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 X_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_3) (tptp.combb tptp.nat X_a tptp.nat) X_3) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) K)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.bseq X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat X_a tptp.nat) X_3) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_4 _let_4 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) K)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 X_3)))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) X_1))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) N_1))) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat)) X_1))) (tptp.hAPP tptp.nat tptp.nat tptp.suc X_1))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat _let_1 W))) (= (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) _let_2) _let_2))))) (forall ((P_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.nat_nat_set (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.bool _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.bool _let_2 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) P_1)))))))) (forall ((P_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (= (tptp.hAPP _let_3 _let_3 (tptp.collect tptp.nat) P_1) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.image tptp.int tptp.nat) tptp.nat_1) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 (tptp.fun _let_1 _let_1) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb tptp.nat tptp.bool tptp.int) P_1) tptp.nat_1))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.bseq tptp.real) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.bool) _let_1) N_1))))))))))) (forall ((Z $$unsorted) (Z_3 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Z) Z_3))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) _let_3) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Z_3)))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg Z_3)))) (and (=> _let_5 (= _let_4 _let_3)) (=> (not _let_5) (= _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.bool (tptp.fun tptp.nat _let_2) (tptp.if tptp.nat) (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((C_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.deriv X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 F) X_1) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_4 (tptp.hAPP X_a _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc X_a X_a X_a) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb X_a _let_2 X_a) _let_1) F)) C_1)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 D_2) C_1))))))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.ring_1 X_a) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.one_one X_a)) (tptp.ring_1_Ints X_a)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.ring_1 X_a) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.zero_zero X_a)) (tptp.ring_1_Ints X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun X_a _let_1) (tptp.deriv X_a) (tptp.combi X_a)) X_1) (tptp.one_one X_a))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((K $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP _let_1 (tptp.fun X_a _let_2) (tptp.deriv X_a) (tptp.hAPP X_a _let_1 (tptp.combk X_a X_a) K)) X_1) (tptp.zero_zero X_a)))))))) (forall ((I $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (=> (not (= (tptp.ti tptp.int I) (tptp.zero_zero tptp.int))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.int tptp.int tptp.bool) (tptp.dvd_dvd tptp.int)) I)))))))) (forall ((Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (=> (not (= Ma (tptp.zero_zero tptp.nat))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat)) Ma)))))))) (forall ((X_a $$unsorted)) (=> (tptp.number_ring X_a) (forall ((W_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) (tptp.hAPP tptp.int X_a (tptp.number_number_of X_a) W_1)) (tptp.ring_1_Ints X_a))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_c $$unsorted) (F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.fun X_c X_b))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun X_c tptp.bool))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_6 _let_4) (tptp.image X_b X_a) F) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_6) (tptp.image X_c X_b) G) A_3)) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_5 _let_4) (tptp.image X_c X_a) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb X_b X_a X_c) F) G)) A_3))))))))) (forall ((X_a $$unsorted) (Y_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_1 _let_1) (tptp.image X_a X_a) (tptp.combi X_a)) Y_3) (tptp.ti _let_1 Y_3)))) (not (tptp.hBOOL (tptp.hAPP _let_22 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_22 _let_22 (tptp.collect tptp.nat) tptp.prime)))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.finite_finite_1 X_a))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fdisj) P_1)) Q_1)))) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 P_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 _let_1 Q_1))))))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.complex))) (let ((_let_2 (tptp.cauchy tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun _let_1 _let_1) (tptp.combb tptp.complex tptp.complex tptp.nat) tptp.cnj) X_3))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.cauchy tptp.complex) X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.cauchy tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.im) X_3))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.cauchy tptp.complex) X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.cauchy tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.re) X_3))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((N_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) A_2) N_1)) _let_1)))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) (tptp.ring_1_Ints tptp.real))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.real_1 tptp.int) X_1)) (tptp.ring_1_Ints tptp.real))))) (forall ((G $$unsorted) (X_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.deriv tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_1 _let_4 _let_2 G) X_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb tptp.real tptp.real tptp.real) tptp.cos) G)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real G X_1)))) Ma))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.bseq X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) (tptp.uminus_uminus X_a)) X_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 X_3)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.deriv X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_2 _let_5 _let_3 F) X_1) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_2 _let_5 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a X_a) _let_1) F)) X_1) (tptp.hAPP X_a X_a _let_1 D_2)))))))))))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.collect X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.bool tptp.bool) (tptp.fun _let_2 _let_2) (tptp.combb tptp.bool tptp.bool X_a) tptp.fNot) P_1)) (tptp.hAPP _let_2 _let_2 (tptp.uminus_uminus _let_2) (tptp.hAPP _let_2 _let_2 _let_1 P_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) A_2)) _let_1)))))))))) (forall ((G $$unsorted) (X_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.deriv tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_1 _let_4 _let_2 G) X_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb tptp.real tptp.real tptp.real) tptp.sin) G)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real G X_1))) Ma))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.ring_1_Ints X_a))) (let ((_let_2 (tptp.member X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 A_2) _let_1)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 B_1) _let_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) A_2) B_1)) _let_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Db $$unsorted) (F $$unsorted) (G $$unsorted) (X_1 $$unsorted) (Da $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.deriv X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 _let_4 _let_2 F) (tptp.hAPP X_a X_a G X_1)) Da)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 _let_4 _let_2 G) X_1) Db)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb X_a X_a X_a) F) G)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Da) Db)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((G $$unsorted) (E_3 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.deriv X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 _let_4 _let_2 F) X_1) D_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 _let_4 _let_2 G) (tptp.hAPP X_a X_a F X_1)) E_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb X_a X_a X_a) G) F)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) E_3) D_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((C_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) C_1))) (let ((_let_3 (tptp.deriv X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_1 _let_5 _let_3 F) X_1) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_1 _let_5 _let_3 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb X_a X_a X_a) _let_2) F)) X_1) (tptp.hAPP X_a X_a _let_2 D_2)))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((G $$unsorted) (X_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.exp X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.deriv X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_2 _let_5 _let_3 G) X_1) Ma)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_2 _let_5 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a X_a) _let_1) G)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.times_times X_a) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a G X_1))) Ma)))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) X_1))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) N_1))) N_1)))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) X_1))) X_1)))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (F $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (=> (= (tptp.ti _let_1 A_3) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat X_a) F) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) N_1)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3))))))) (forall ((P_1 $$unsorted) (I $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_4 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 tptp.nat) tptp.fconj) P_1)) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) I)))))))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) Z_1))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 W)))) (= (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) _let_3) _let_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) Z_1))) (let ((_let_3 (tptp.hAPP tptp.nat X_a _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 W)))) (= (tptp.hAPP tptp.nat X_a _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W))) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) _let_3) _let_3)))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.monoid_mult X_b) (tptp.number X_b)) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP X_b (tptp.fun tptp.nat X_b) (tptp.power_power X_b) (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V)))) (let ((_let_3 (tptp.hAPP tptp.nat X_b _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 W)))) (= (tptp.hAPP tptp.nat X_b _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 W))) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) _let_3) _let_3)))))))) (forall ((I $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)))) (let ((_let_4 (tptp.member tptp.nat))) (let ((_let_5 (tptp.combc tptp.nat _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_1 _let_10) (tptp.combb tptp.bool _let_9 tptp.nat) tptp.fconj))) (let ((_let_12 (tptp.combs tptp.nat tptp.bool tptp.bool))) (let ((_let_13 (tptp.collect tptp.nat))) (let ((_let_14 (tptp.finite_card tptp.nat))) (let ((_let_15 (tptp.fun tptp.nat tptp.nat))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_7 _let_4 (tptp.zero_zero tptp.nat)) M_1))) (= (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 (tptp.hAPP _let_15 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_15 _let_8) (tptp.combb tptp.nat _let_7 tptp.nat) _let_4) tptp.suc)) M_1))) (tptp.hAPP tptp.nat _let_1 _let_3 I)))) (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 _let_4) M_1))) (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc I))))))))))))))))))))))) (forall ((I $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.member tptp.nat))) (let ((_let_5 (tptp.fun _let_2 _let_2))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.nat _let_6 _let_4 _let_1) M_1)) (not (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.nat) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_8 _let_5 (tptp.combs tptp.nat tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_8 (tptp.hAPP (tptp.fun tptp.bool _let_7) (tptp.fun _let_2 _let_8) (tptp.combb tptp.bool _let_7 tptp.nat) tptp.fconj) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.nat _let_6) _let_5 (tptp.combc tptp.nat _let_2 tptp.bool) _let_4) M_1))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc I))))) _let_1)))))))))))) (forall ((I $$unsorted) (M_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)))) (let ((_let_4 (tptp.member tptp.nat))) (let ((_let_5 (tptp.combc tptp.nat _let_1 tptp.bool))) (let ((_let_6 (tptp.fun _let_1 _let_1))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_1 _let_10) (tptp.combb tptp.bool _let_9 tptp.nat) tptp.fconj))) (let ((_let_12 (tptp.combs tptp.nat tptp.bool tptp.bool))) (let ((_let_13 (tptp.collect tptp.nat))) (let ((_let_14 (tptp.finite_card tptp.nat))) (let ((_let_15 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat _let_7 _let_4 (tptp.zero_zero tptp.nat)) M_1)) (= (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 (tptp.hAPP _let_15 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_15 _let_8) (tptp.combb tptp.nat _let_7 tptp.nat) _let_4) tptp.suc)) M_1))) (tptp.hAPP tptp.nat _let_1 _let_3 I))))) (tptp.hAPP _let_1 tptp.nat _let_14 (tptp.hAPP _let_1 _let_1 _let_13 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_6 _let_12 (tptp.hAPP _let_1 _let_10 _let_11 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_6 _let_5 _let_4) M_1))) (tptp.hAPP tptp.nat _let_1 _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc I))))))))))))))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.bool) _let_1) N_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a F X_1))) (let ((_let_2 (tptp.inverse_inverse X_a))) (let ((_let_3 (tptp.hAPP X_a X_a _let_2 _let_1))) (let ((_let_4 (tptp.times_times X_a))) (let ((_let_5 (tptp.fun X_a X_a))) (let ((_let_6 (tptp.deriv X_a))) (let ((_let_7 (tptp.fun X_a tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_5 _let_8 _let_6 F) X_1) D_2)) (=> (not (= _let_1 (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_5 _let_8 _let_6 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_5 _let_5) (tptp.combb X_a X_a X_a) _let_2) F)) X_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 _let_3) D_2)) _let_3))))))))))))))))) (forall ((Ma $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (= (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.noXRRset Ma) X_1) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.image tptp.int tptp.int) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.int) (tptp.times_times tptp.int)) X_1)) (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma))))))) (forall ((N_1 $$unsorted) (G $$unsorted) (X_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.power_power tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.times_times tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_2))) (let ((_let_6 (tptp.deriv tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.bool))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_4 _let_8 _let_6 G) X_1) Ma)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_4 _let_8 _let_6 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_5 (tptp.fun tptp.nat _let_4) (tptp.combc tptp.real tptp.nat tptp.real) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_5) (tptp.combb tptp.real _let_2 tptp.real) _let_1) G)) N_1)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real G X_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.one_one tptp.nat))))) Ma))))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 N_1)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_6 (tptp.fun _let_2 _let_2) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_2 _let_6) (tptp.combb tptp.bool _let_5 tptp.int) tptp.fconj) _let_4)) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.bool) _let_1) N_1)))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 N_1)) (tptp.one_one tptp.nat))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 N_1)) (= (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_6 (tptp.fun _let_2 _let_2) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_2 _let_6) (tptp.combb tptp.bool _let_5 tptp.int) tptp.fconj) _let_4)) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.bool) _let_1) N_1))))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) N_1) (tptp.one_one tptp.int))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.zero_zero tptp.int)))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 N_1)) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_6 (tptp.fun _let_2 _let_2) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_2 _let_6) (tptp.combb tptp.bool _let_5 tptp.int) tptp.fconj) _let_4)) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.bool) _let_1) N_1)))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 N_1)) (tptp.one_one tptp.nat))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X_1))) (tptp.hAPP tptp.real tptp.real tptp.cos X_1)))) (let ((_let_4 (tptp.fun tptp.real _let_2))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_5) (tptp.deriv tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_2) (tptp.combs tptp.real tptp.real tptp.real) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_4) (tptp.combb tptp.real _let_2 tptp.real) _let_1) tptp.cos)) tptp.cos)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.plus_plus tptp.real) _let_3) _let_3))))))))) (forall ((N_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1))))) (= (= (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) (and _let_2 (=> _let_2 (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1) N_1))))))) (forall ((V_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1))))) (= (= (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (and _let_2 (=> _let_2 (= (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1) N_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_char_0 X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) A_2) (tptp.ring_1_Ints X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) A_2) A_2) _let_1) (= (tptp.ti X_a A_2) _let_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((N_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun X_a _let_2))) (let ((_let_6 (tptp.deriv X_a))) (let ((_let_7 (tptp.fun X_a tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_6 F) X_1) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_6 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_5 (tptp.fun tptp.nat _let_4) (tptp.combc X_a tptp.nat X_a) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_5) (tptp.combb X_a _let_2 X_a) _let_1) F)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.plus_plus X_a) (tptp.one_one X_a)) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_1))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 D_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a F X_1)) N_1))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (= (tptp.ti X_a X_1) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun X_a _let_2) (tptp.deriv X_a) _let_1) X_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) (tptp.hAPP X_a X_a _let_1 X_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((N_1 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun X_a _let_2))) (let ((_let_6 (tptp.deriv X_a))) (let ((_let_7 (tptp.fun X_a tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_6 F) X_1) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_6 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_5 (tptp.fun tptp.nat _let_4) (tptp.combc X_a tptp.nat X_a) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_5) (tptp.combb X_a _let_2 X_a) _let_1) F)) N_1)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 D_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a F X_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))))))))))))))))) (forall ((W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat _let_1 W))) (let ((_let_3 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 W)))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W))))) (and (=> _let_4 (= _let_3 (tptp.zero_zero tptp.nat))) (=> (not _let_4) (= _let_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) _let_2) _let_2)))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_4) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun tptp.nat _let_3) (tptp.combc tptp.real tptp.nat tptp.real) _let_1) N_1)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_2 _let_1 X_1) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.deriv tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.combs tptp.real tptp.real tptp.real) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.real _let_2 tptp.real) _let_1) tptp.cos)) tptp.cos)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 tptp.min_1))) (tptp.hAPP tptp.real tptp.real tptp.cos X_1))) (tptp.hAPP tptp.real tptp.real tptp.sin X_1))))))))) (forall ((V_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)) N_1)))))))) (forall ((N_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.ord_less tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1))))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1))) (and _let_4 (=> _let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 N_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1))))))))))) (forall ((N_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1))))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1))) (and _let_4 (=> _let_4 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 N_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1))))))))))) (forall ((V_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.ord_less_eq tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)) N_1)))))))) (forall ((X_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.zero_zero tptp.int))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (let ((_let_8 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 _let_4) Ma)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_8 _let_7 (tptp.image tptp.int tptp.int) (tptp.hAPP tptp.int _let_8 tptp.standardRes Ma)) X_3)) (tptp.hAPP _let_2 _let_2 (tptp.collect tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_6 _let_7 (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_2 _let_6) (tptp.combb tptp.bool _let_5 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_4))) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.int tptp.int tptp.bool) _let_1) Ma))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.monoid_mult X_a) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) Z_1))) (let ((_let_3 (tptp.hAPP tptp.nat X_a _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 W))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W))))) (let ((_let_5 (tptp.hAPP tptp.nat X_a _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 W)))) (let ((_let_6 (tptp.times_times X_a))) (let ((_let_7 (tptp.fun X_a X_a))) (and (=> _let_4 (= _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_7 _let_6 Z_1) _let_5)) _let_5))) (=> (not _let_4) (= _let_3 (tptp.one_one X_a)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((G $$unsorted) (E_2 $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a G X_1))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.inverse_divide X_a))) (let ((_let_5 (tptp.fun X_a _let_3))) (let ((_let_6 (tptp.deriv X_a))) (let ((_let_7 (tptp.fun X_a tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_3 _let_8 _let_6 F) X_1) D_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_3 _let_8 _let_6 G) X_1) E_2)) (=> (not (= _let_1 (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_3) (tptp.combs X_a X_a X_a) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_5) (tptp.combb X_a _let_3 X_a) _let_4) F)) G)) X_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 D_1) _let_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 E_2) (tptp.hAPP X_a X_a F X_1)))) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))))))))))))))))))) (forall ((X_1 $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 tptp.rsetR Ma))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.member _let_1))) (let ((_let_7 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 A_3) _let_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Ma)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 tptp.legacy_zgcd X_1) Ma) (tptp.one_one tptp.int)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 _let_7 _let_6 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_1) (tptp.image tptp.int tptp.int) (tptp.hAPP tptp.int _let_4 (tptp.hAPP _let_5 _let_5 (tptp.combc tptp.int tptp.int tptp.int) (tptp.times_times tptp.int)) X_1)) A_3)) _let_3))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((F $$unsorted) (X_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_a F X_1))) (let ((_let_2 (tptp.inverse_inverse X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.deriv X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_3 _let_6 _let_4 F) X_1) D_1)) (=> (not (= _let_1 (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_3 _let_6 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_3 _let_3) (tptp.combb X_a X_a X_a) _let_2) F)) X_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.times_times X_a) D_1) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a (tptp.fun tptp.nat X_a) (tptp.power_power X_a) _let_1) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))))))))))))))))) (forall ((Z_1 $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) Z_1))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 W))))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W))))) (let ((_let_5 (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP tptp.int tptp.nat _let_1 W)))) (let ((_let_6 (tptp.times_times tptp.int))) (let ((_let_7 (tptp.fun tptp.int tptp.int))) (and (=> _let_4 (= _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_6 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_6 Z_1) _let_5)) _let_5))) (=> (not _let_4) (= _let_3 (tptp.one_one tptp.int)))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.deriv tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.combs tptp.real tptp.real tptp.real) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.real _let_2 tptp.real) _let_1) tptp.sin)) tptp.sin)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.real tptp.real tptp.cos X_1))) (tptp.hAPP tptp.real tptp.real tptp.sin X_1))))))))) (forall ((B_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.real _let_1 tptp.log B_1)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.inverse_divide tptp.real) (tptp.one_one tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real tptp.ln B_1)) X_1)))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.monoid_mult X_b) (tptp.number X_b)) (forall ((V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.number_number_of tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.int X_b (tptp.number_number_of X_b) V))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun tptp.nat X_b) (tptp.power_power X_b) _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat X_b _let_3 (tptp.hAPP tptp.int tptp.nat _let_1 (tptp.hAPP tptp.int tptp.int tptp.bit1 W))))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) W))))) (let ((_let_6 (tptp.hAPP tptp.nat X_b _let_3 (tptp.hAPP tptp.int tptp.nat _let_1 W)))) (let ((_let_7 (tptp.times_times X_b))) (let ((_let_8 (tptp.fun X_b X_b))) (and (=> _let_5 (= _let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_8 _let_7 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_8 _let_7 _let_2) _let_6)) _let_6))) (=> (not _let_5) (= _let_4 (tptp.one_one X_b))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.deriv tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.combs tptp.real tptp.real tptp.real) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.real _let_2 tptp.real) _let_1) tptp.cos)) tptp.cos)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP tptp.real tptp.real tptp.cos X_1))) (tptp.hAPP tptp.real tptp.real tptp.sin X_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_char_0 X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a (tptp.fun _let_3 tptp.bool) (tptp.member X_a) A_2) (tptp.ring_1_Ints X_a))) (not (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.one_one X_a)) A_2)) A_2) (tptp.zero_zero X_a)))))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_3) (tptp.combb tptp.real _let_2 tptp.real) (tptp.power_power tptp.real)))) (let ((_let_6 (tptp.combc tptp.real tptp.nat tptp.real))) (let ((_let_7 (tptp.fun tptp.nat _let_4))) (let ((_let_8 (tptp.fun tptp.real _let_4))) (let ((_let_9 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_9 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_9) (tptp.deriv tptp.real) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_8 (tptp.fun _let_4 _let_4) (tptp.combs tptp.real tptp.real tptp.real) (tptp.hAPP _let_4 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_4 _let_8) (tptp.combb tptp.real _let_4 tptp.real) (tptp.plus_plus tptp.real)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_3 _let_7 _let_6 (tptp.hAPP _let_4 _let_3 _let_5 tptp.sin)) _let_1))) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_3 _let_7 _let_6 (tptp.hAPP _let_4 _let_3 _let_5 tptp.cos)) _let_1))) X_2) (tptp.zero_zero tptp.real))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_6) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_5 (tptp.fun tptp.nat _let_3) (tptp.combc tptp.real tptp.nat tptp.real) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_5) (tptp.combb tptp.real _let_4 tptp.real) (tptp.power_power tptp.real)) tptp.sin)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1)) (tptp.hAPP tptp.real tptp.real tptp.cos X_1))) (tptp.hAPP tptp.real tptp.real tptp.sin X_1))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real tptp.cos X_1)) (tptp.hAPP tptp.real tptp.real tptp.sin X_1)))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_5) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_4 (tptp.fun tptp.nat _let_1) (tptp.combc tptp.real tptp.nat tptp.real) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_4) (tptp.combb tptp.real _let_3 tptp.real) (tptp.power_power tptp.real)) tptp.sin)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) _let_2) _let_2))))))))) (forall ((V_1 $$unsorted) (V_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) V_1) (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) V_2))))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.number_number_of tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.int tptp.nat _let_3 V_1))) (let ((_let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) _let_4) (tptp.hAPP tptp.int tptp.nat _let_3 V_2)))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) V_2) tptp.pls)))) (and (=> _let_6 (= _let_5 _let_4)) (=> (not _let_6) (= _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.bool (tptp.fun tptp.nat _let_2) (tptp.if tptp.nat) (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_5) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_4 (tptp.fun tptp.nat _let_2) (tptp.combc tptp.real tptp.nat tptp.real) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_4) (tptp.combb tptp.real _let_3 tptp.real) (tptp.power_power tptp.real)) tptp.cos)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 tptp.min_1))) (tptp.hAPP tptp.real tptp.real tptp.cos X_1))) (tptp.hAPP tptp.real tptp.real tptp.sin X_1)))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_6) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_5 (tptp.fun tptp.nat _let_3) (tptp.combc tptp.real tptp.nat tptp.real) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_5) (tptp.combb tptp.real _let_4 tptp.real) (tptp.power_power tptp.real)) tptp.cos)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) X_1) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1)) (tptp.hAPP tptp.real tptp.real tptp.cos X_1))) (tptp.hAPP tptp.real tptp.real tptp.sin X_1)))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X_1))) (tptp.hAPP tptp.real tptp.real tptp.cos X_1)))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_5) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_4 (tptp.fun tptp.nat _let_1) (tptp.combc tptp.real tptp.nat tptp.real) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_4) (tptp.combb tptp.real _let_3 tptp.real) (tptp.power_power tptp.real)) tptp.cos)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) _let_2) _let_2))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real tptp.cos X_1))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.real tptp.bool))) (=> (not (= _let_1 (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.deriv tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.combs tptp.real tptp.real tptp.real) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.real _let_2 tptp.real) (tptp.inverse_divide tptp.real)) tptp.sin)) tptp.cos)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.nat tptp.real) (tptp.power_power tptp.real) _let_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))))))) (forall ((Y_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.hAPP tptp.real tptp.real tptp.sin Y_1))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.combb tptp.real _let_3 tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_3))) (let ((_let_6 (tptp.fun _let_3 _let_5))) (let ((_let_7 (tptp.hAPP _let_5 _let_6 _let_4 (tptp.times_times tptp.real)))) (let ((_let_8 (tptp.combc tptp.real tptp.real tptp.real))) (let ((_let_9 (tptp.hAPP _let_5 _let_5 _let_8 (tptp.hAPP _let_3 _let_5 _let_7 tptp.sin)))) (let ((_let_10 (tptp.hAPP tptp.real tptp.real tptp.cos Y_1))) (let ((_let_11 (tptp.hAPP _let_5 _let_5 _let_8 (tptp.hAPP _let_3 _let_5 _let_7 tptp.cos)))) (let ((_let_12 (tptp.hAPP _let_5 _let_6 _let_4 (tptp.minus_minus tptp.real)))) (let ((_let_13 (tptp.combs tptp.real tptp.real tptp.real))) (let ((_let_14 (tptp.fun _let_3 _let_3))) (let ((_let_15 (tptp.plus_plus tptp.real))) (let ((_let_16 (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_5 _let_5 _let_8 _let_15) Y_1))) (let ((_let_17 (tptp.combb tptp.real tptp.real tptp.real))) (let ((_let_18 (tptp.fun tptp.nat tptp.real))) (let ((_let_19 (tptp.fun tptp.real _let_18))) (let ((_let_20 (tptp.hAPP _let_19 (tptp.fun _let_3 _let_19) (tptp.combb tptp.real _let_18 tptp.real) (tptp.power_power tptp.real)))) (let ((_let_21 (tptp.combc tptp.real tptp.nat tptp.real))) (let ((_let_22 (tptp.fun tptp.nat _let_3))) (let ((_let_23 (tptp.hAPP _let_5 _let_6 _let_4 _let_15))) (let ((_let_24 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_24 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_24) (tptp.deriv tptp.real) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 _let_14 _let_13 (tptp.hAPP _let_3 _let_5 _let_23 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_19 _let_22 _let_21 (tptp.hAPP _let_3 _let_19 _let_20 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 _let_14 _let_13 (tptp.hAPP _let_3 _let_5 _let_12 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_14 _let_17 tptp.sin) _let_16))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 _let_14 _let_13 (tptp.hAPP _let_3 _let_5 _let_23 (tptp.hAPP tptp.real _let_3 _let_9 _let_10))) (tptp.hAPP tptp.real _let_3 _let_11 _let_2))))) _let_1))) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_19 _let_22 _let_21 (tptp.hAPP _let_3 _let_19 _let_20 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 _let_14 _let_13 (tptp.hAPP _let_3 _let_5 _let_12 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_3 _let_14 _let_17 tptp.cos) _let_16))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 _let_14 _let_13 (tptp.hAPP _let_3 _let_5 _let_12 (tptp.hAPP tptp.real _let_3 _let_11 _let_10))) (tptp.hAPP tptp.real _let_3 _let_9 _let_2))))) _let_1))) X_2) (tptp.zero_zero tptp.real)))))))))))))))))))))))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1)) (tptp.hAPP tptp.real tptp.real tptp.cos X_2))) (tptp.hAPP tptp.real tptp.real tptp.sin X_2)))) (let ((_let_5 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1))) (let ((_let_6 (tptp.fun tptp.nat tptp.real))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.hAPP _let_7 (tptp.fun _let_3 _let_7) (tptp.combb tptp.real _let_6 tptp.real) (tptp.power_power tptp.real)))) (let ((_let_9 (tptp.combc tptp.real tptp.nat tptp.real))) (let ((_let_10 (tptp.fun tptp.nat _let_3))) (let ((_let_11 (tptp.fun tptp.real _let_3))) (let ((_let_12 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_12 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_12) (tptp.deriv tptp.real) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_11 (tptp.fun _let_3 _let_3) (tptp.combs tptp.real tptp.real tptp.real) (tptp.hAPP _let_3 _let_11 (tptp.hAPP _let_11 (tptp.fun _let_3 _let_11) (tptp.combb tptp.real _let_3 tptp.real) (tptp.plus_plus tptp.real)) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_7 _let_10 _let_9 (tptp.hAPP _let_3 _let_7 _let_8 tptp.sin)) _let_5))) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_7 _let_10 _let_9 (tptp.hAPP _let_3 _let_7 _let_8 tptp.cos)) _let_5))) X_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.minus_minus tptp.real) _let_4) _let_4)))))))))))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.uminus_uminus tptp.real))) (let ((_let_3 (tptp.combb tptp.real tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.combb tptp.real _let_4 tptp.real))) (let ((_let_7 (tptp.fun tptp.real _let_4))) (let ((_let_8 (tptp.fun _let_4 _let_7))) (let ((_let_9 (tptp.combs tptp.real tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.nat tptp.real))) (let ((_let_11 (tptp.fun tptp.real _let_10))) (let ((_let_12 (tptp.hAPP _let_11 (tptp.fun _let_4 _let_11) (tptp.combb tptp.real _let_10 tptp.real) (tptp.power_power tptp.real)))) (let ((_let_13 (tptp.combc tptp.real tptp.nat tptp.real))) (let ((_let_14 (tptp.fun tptp.nat _let_4))) (let ((_let_15 (tptp.hAPP _let_7 _let_8 _let_6 (tptp.plus_plus tptp.real)))) (let ((_let_16 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_16 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_16) (tptp.deriv tptp.real) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 _let_5 _let_9 (tptp.hAPP _let_4 _let_7 _let_15 (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_11 _let_14 _let_13 (tptp.hAPP _let_4 _let_11 _let_12 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 _let_5 _let_9 (tptp.hAPP _let_4 _let_7 _let_15 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_4 _let_5 _let_3 tptp.sin) _let_2))) tptp.sin))) _let_1))) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_11 _let_14 _let_13 (tptp.hAPP _let_4 _let_11 _let_12 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 _let_5 _let_9 (tptp.hAPP _let_4 _let_7 (tptp.hAPP _let_7 _let_8 _let_6 (tptp.minus_minus tptp.real)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_4 _let_5 _let_3 tptp.cos) _let_2))) tptp.cos))) _let_1))) X_2) (tptp.zero_zero tptp.real)))))))))))))))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.int_gcd A_2) B_1))) (let ((_let_3 (tptp.div_div tptp.int))) (let ((_let_4 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_5 (tptp.product_prod tptp.int tptp.int))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 tptp.norm_frac A_2) B_1))) (let ((_let_8 (tptp.zero_zero tptp.int))) (let ((_let_9 (or (= (tptp.ti tptp.int A_2) _let_8) (= (tptp.ti tptp.int B_1) _let_8)))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) B_1) _let_8)))) (let ((_let_11 (tptp.uminus_uminus tptp.int))) (let ((_let_12 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP (tptp.fun _let_5 _let_12) _let_12 (tptp.accp _let_5) tptp.norm_frac_rel) (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 A_2) B_1))) (and (=> _let_10 (= _let_7 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 tptp.norm_frac (tptp.hAPP tptp.int tptp.int _let_11 A_2)) (tptp.hAPP tptp.int tptp.int _let_11 B_1)))) (=> (not _let_10) (and (=> _let_9 (= _let_7 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 _let_8) (tptp.one_one tptp.int)))) (=> (not _let_9) (= _let_7 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 A_2) _let_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 B_1) _let_2))))))))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.nat _let_2 tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.times_times tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.one_one tptp.nat)))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (let ((_let_6 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_7 (tptp.fun _let_2 _let_5))) (let ((_let_8 (tptp.one_one tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun tptp.nat _let_9))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X_1)) _let_8)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.monoseq tptp.real) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_11 _let_10 (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_5 _let_11 (tptp.hAPP (tptp.fun tptp.real _let_9) (tptp.fun _let_5 _let_11) (tptp.combb tptp.real _let_9 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_9 _let_10 (tptp.combb tptp.real tptp.real tptp.nat) (tptp.hAPP tptp.real _let_9 (tptp.inverse_divide tptp.real) _let_8)) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_5 _let_7 _let_6 (tptp.real_1 tptp.nat)) _let_4)))) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_5 _let_7 _let_6 (tptp.hAPP tptp.real _let_5 (tptp.power_power tptp.real) X_1)) _let_4))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.monoseq X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_1 _let_1) (tptp.combb X_a X_a tptp.nat) (tptp.uminus_uminus X_a)) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.monoseq X_a) X_3)) (or (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) (tptp.hAPP tptp.nat X_a X_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a X_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hAPP tptp.nat X_a X_3 N_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.monoseq X_a) X_3)) (or (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a X_3 M_2)) (tptp.hAPP tptp.nat X_a X_3 N_2))))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) (tptp.hAPP tptp.nat X_a X_3 M_2)))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 X_1) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.monoseq tptp.real) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 tptp.int_gcd A_1) B))) (let ((_let_3 (tptp.div_div tptp.int))) (let ((_let_4 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_5 (tptp.product_prod tptp.int tptp.int))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 tptp.norm_frac A_1) B))) (let ((_let_8 (tptp.zero_zero tptp.int))) (let ((_let_9 (or (= (tptp.ti tptp.int A_1) _let_8) (= (tptp.ti tptp.int B) _let_8)))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) B) _let_8)))) (let ((_let_11 (tptp.uminus_uminus tptp.int))) (and (=> _let_10 (= _let_7 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 tptp.norm_frac (tptp.hAPP tptp.int tptp.int _let_11 A_1)) (tptp.hAPP tptp.int tptp.int _let_11 B)))) (=> (not _let_10) (and (=> _let_9 (= _let_7 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 _let_8) (tptp.one_one tptp.int)))) (=> (not _let_9) (= _let_7 (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int _let_6 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 A_1) _let_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_3 B) _let_2))))))))))))))))))) (forall ((Z $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (let ((_let_3 (tptp.fun tptp.bool tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.hAPP (tptp.fun tptp.bool _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.bool _let_3 tptp.real) tptp.fconj))) (let ((_let_6 (tptp.combs tptp.real tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.hAPP tptp.complex tptp.complex (tptp.sgn_sgn tptp.complex) Z))) (let ((_let_9 (tptp.fequal tptp.real))) (let ((_let_10 (tptp.combb tptp.real tptp.bool tptp.real))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.fun _let_11 _let_1))) (= (tptp.hAPP tptp.complex tptp.real tptp.arg Z) (tptp.hAPP _let_1 tptp.real (tptp.hilbert_Eps tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_1 _let_4 _let_5 (tptp.hAPP _let_11 _let_1 (tptp.hAPP _let_1 _let_12 _let_10 (tptp.hAPP tptp.real _let_1 _let_9 (tptp.hAPP tptp.complex tptp.real tptp.re _let_8))) tptp.cos))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_1 _let_4 _let_5 (tptp.hAPP _let_11 _let_1 (tptp.hAPP _let_1 _let_12 _let_10 (tptp.hAPP tptp.real _let_1 _let_9 (tptp.hAPP tptp.complex tptp.real tptp.im _let_8))) tptp.sin))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_1 _let_4 _let_5 (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) tptp.pi)))) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.real tptp.real tptp.bool) (tptp.ord_less_eq tptp.real)) tptp.pi))))))))))))))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.ord_less tptp.int) _let_1) P_4)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_5 tptp.zcong A_2) (tptp.zero_zero tptp.int)) P_4))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 tptp.quadRes P_4) A_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int _let_5 tptp.zcong (tptp.hAPP _let_3 tptp.int (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) (tptp.combi tptp.int)) (tptp.hAPP _let_4 _let_3 (tptp.complete_Sup_Sup _let_3) (tptp.hAPP tptp.int _let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_4) tptp.setS A_2) P_4)))) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_2) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_div tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) P_4) (tptp.one_one tptp.int))) _let_1)))) P_4)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.comm_monoid_mult X_a) (tptp.semiring_1 X_a)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.nat))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co302546470etprod X_b tptp.nat) F) A_3)) (tptp.hAPP _let_4 X_a (tptp.hAPP _let_2 (tptp.fun _let_4 X_a) (tptp.big_co302546470etprod X_b X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat X_a X_b) _let_1) F)) A_3))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.comm_monoid_mult X_a) (tptp.ring_1 X_a)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.int))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP _let_4 tptp.int (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.int) (tptp.big_co302546470etprod X_b tptp.int) F) A_3)) (tptp.hAPP _let_4 X_a (tptp.hAPP _let_2 (tptp.fun _let_4 X_a) (tptp.big_co302546470etprod X_b X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.int X_a) (tptp.fun _let_3 _let_2) (tptp.combb tptp.int X_a X_b) _let_1) F)) A_3))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hAPP _let_1 tptp.int (tptp.hAPP (tptp.fun tptp.int tptp.int) (tptp.fun _let_1 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) (tptp.combi tptp.int)) (tptp.hAPP tptp.int _let_1 tptp.d22set A_2)) (tptp.hAPP tptp.int tptp.int tptp.zfact A_2)))) (forall ((A_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_2) Ma)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 tptp.legacy_zgcd (tptp.hAPP _let_1 tptp.int (tptp.hAPP _let_2 (tptp.fun _let_1 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) (tptp.combi tptp.int)) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset A_2) Ma))) Ma) (tptp.one_one tptp.int)))))) (forall ((A_2 $$unsorted) (Ma $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.bnorRset A_2) Ma))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.fun _let_1 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) (tptp.combi tptp.int)))) (let ((_let_5 (tptp.times_times tptp.int))) (let ((_let_6 (tptp.fun tptp.int _let_3))) (=> (not (= (tptp.ti tptp.int X_1) (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) A_2) Ma)) (= (tptp.hAPP _let_1 tptp.int _let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.image tptp.int tptp.int) (tptp.hAPP tptp.int _let_3 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.int tptp.int tptp.int) _let_5) X_1)) _let_2)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_5 (tptp.hAPP _let_1 tptp.int _let_4 _let_2)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X_1) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) _let_2))))))))))))) (forall ((X_1 $$unsorted) (A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong A_2) (tptp.zero_zero tptp.int)) P_4))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 tptp.quadRes P_4) A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_3 tptp.bool) (tptp.member _let_1) X_1) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.setS A_2) P_4))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong (tptp.hAPP _let_1 tptp.int (tptp.hAPP (tptp.fun tptp.int tptp.int) (tptp.fun _let_1 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) (tptp.combi tptp.int)) X_1)) A_2) P_4))))))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) A_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.minus_minus tptp.int) P_4) _let_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP _let_2 tptp.int (tptp.hAPP _let_4 (tptp.fun _let_2 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) (tptp.combi tptp.int)) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 tptp.wset A_2) P_4))) _let_1) P_4)))))))))) (forall ((A_2 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.zprime P_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) P_4)) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) tptp.zcong A_2) (tptp.zero_zero tptp.int)) P_4))) (= (tptp.hAPP _let_2 tptp.int (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) (tptp.combi tptp.int)) (tptp.hAPP _let_3 _let_2 (tptp.complete_Sup_Sup _let_2) (tptp.hAPP tptp.int _let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_3) tptp.setS A_2) P_4))) (tptp.hAPP tptp.int tptp.int tptp.zfact (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) P_4) (tptp.one_one tptp.int))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) S))) (let ((_let_3 (tptp.hAPP X_b (tptp.fun tptp.nat X_b) (tptp.power_power X_b) C_1))) (let ((_let_4 (tptp.fun X_a _let_1))) (let ((_let_5 (tptp.fun X_b X_b))) (let ((_let_6 (tptp.fun X_b _let_5))) (let ((_let_7 (tptp.fun X_a _let_6))) (let ((_let_8 (tptp.fun X_a _let_5))) (let ((_let_9 (tptp.fun X_a X_b))) (let ((_let_10 (tptp.hAPP _let_1 X_b (tptp.hAPP _let_9 (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) (tptp.hAPP X_b _let_9 (tptp.hAPP _let_8 (tptp.fun X_b _let_9) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_9 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_9 _let_8) (tptp.combs X_a X_b _let_5) (tptp.hAPP _let_1 _let_7 (tptp.hAPP (tptp.fun tptp.bool _let_6) (tptp.fun _let_1 _let_7) (tptp.combb tptp.bool _let_6 X_a) (tptp.if X_b)) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_4 _let_4 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) A_2))) B_1)) C_1)) S))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) A_2) S)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) S)) (and (=> _let_11 (= _let_10 (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_5 (tptp.times_times X_b) (tptp.hAPP X_a X_b B_1 A_2)) (tptp.hAPP tptp.nat X_b _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) _let_2) (tptp.one_one tptp.nat)))))) (=> (not _let_11) (= _let_10 (tptp.hAPP tptp.nat X_b _let_3 _let_2))))))))))))))))))) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.nat_nat_set A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int F X_2)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP _let_1 tptp.int (tptp.hAPP (tptp.fun tptp.int tptp.int) (tptp.fun _let_1 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) F) A_3))))))) (forall ((X_a $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) F_1)) (= (= (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co302546470etprod X_a tptp.nat) F) F_1) (tptp.one_one tptp.nat)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) F_1)) (= (tptp.hAPP X_a tptp.nat F X_2) (tptp.one_one tptp.nat))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) S)) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co302546470etprod X_a tptp.nat) F) S))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) S)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP X_a tptp.nat F X_2)))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.fun X_a tptp.int))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP _let_4 tptp.int (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.int) (tptp.big_co302546470etprod X_a tptp.int) F) A_3)) (tptp.hAPP _let_4 tptp.real (tptp.hAPP _let_2 (tptp.fun _let_4 tptp.real) (tptp.big_co302546470etprod X_a tptp.real) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.int tptp.real) (tptp.fun _let_3 _let_2) (tptp.combb tptp.int tptp.real X_a) _let_1) F)) A_3))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.fun X_a tptp.nat))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co302546470etprod X_a tptp.nat) F) A_3)) (tptp.hAPP _let_4 tptp.real (tptp.hAPP _let_2 (tptp.fun _let_4 tptp.real) (tptp.big_co302546470etprod X_a tptp.real) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.real) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.real X_a) _let_1) F)) A_3))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun X_a tptp.int))) (let ((_let_3 (tptp.fun X_a tptp.nat))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co302546470etprod X_a tptp.nat) F) A_3)) (tptp.hAPP _let_4 tptp.int (tptp.hAPP _let_2 (tptp.fun _let_4 tptp.int) (tptp.big_co302546470etprod X_a tptp.int) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.int X_a) _let_1) F)) A_3))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.int))) (let ((_let_2 (tptp.fun X_a tptp.nat))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_3 tptp.nat (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.nat) (tptp.big_co302546470etprod X_a tptp.nat) F) A_3) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP _let_3 tptp.int (tptp.hAPP _let_1 (tptp.fun _let_3 tptp.int) (tptp.big_co302546470etprod X_a tptp.int) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.combb tptp.nat tptp.int X_a) (tptp.semiring_1_of_nat tptp.int)) F)) A_3))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.comm_monoid_mult X_a)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.int X_a))) (let ((_let_4 (tptp.fun tptp.int tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_5 (tptp.fun _let_2 X_a) (tptp.big_co302546470etprod tptp.nat X_a) F) A_3) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 (tptp.fun _let_1 X_a) (tptp.big_co302546470etprod tptp.int X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.combb tptp.nat X_a tptp.int) F) tptp.nat_1)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) A_3))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.comm_monoid_mult X_a)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (let ((_let_5 (tptp.fun tptp.int X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set A_3)) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_5 (tptp.fun _let_2 X_a) (tptp.big_co302546470etprod tptp.int X_a) F) A_3) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 (tptp.fun _let_1 X_a) (tptp.big_co302546470etprod tptp.nat X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.combb tptp.int X_a tptp.nat) F) (tptp.semiring_1_of_nat tptp.int))) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.image tptp.int tptp.nat) tptp.nat_1) A_3)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_b X_a))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.times_times X_a))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.fun X_b _let_6))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_b X_a X_a) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_a _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_a _let_6 X_b) _let_5) F)) G)) A_3) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 _let_5 (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 G) A_3))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_3 X_a (tptp.hAPP _let_2 (tptp.fun _let_3 X_a) (tptp.big_co302546470etprod X_b X_a) (tptp.hAPP X_a _let_2 (tptp.combk X_a X_b) _let_1)) A_3) _let_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.linordered_field X_a) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.big_co302546470etprod X_b X_a))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.fun _let_4 X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP _let_4 X_a (tptp.hAPP _let_2 _let_5 _let_3 F) A_3)) (tptp.hAPP _let_4 X_a (tptp.hAPP _let_2 _let_5 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a X_b) _let_1) F)) A_3)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.comm_semiring_1 X_b) (tptp.no_zero_divisors X_b)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F) A_3) (tptp.zero_zero X_b)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (= (tptp.hAPP X_a X_b F X_2) (tptp.zero_zero X_b))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_semiring_1 X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (= (tptp.hAPP X_a X_b F X_2) (tptp.zero_zero X_b))))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F) A_3) (tptp.zero_zero X_b)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F) A_3) (tptp.one_one X_b))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) G) A_3) (tptp.one_one X_b))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_semiring_1 X_b) (forall ((F $$unsorted) (I $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.dvd_dvd X_b) (tptp.hAPP X_a X_b F I)) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F) A_3))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.times_times X_b))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.fun X_a _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_b _let_6 X_a) _let_5) G)) H)) A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 _let_5 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 H) A_3)))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.one_one X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a _let_3))) (let ((_let_7 (tptp.fun X_a X_b))) (let ((_let_8 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_7 (tptp.fun _let_2 X_b) (tptp.big_co302546470etprod X_a X_b) (tptp.hAPP X_b _let_7 (tptp.hAPP _let_6 (tptp.fun X_b _let_7) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_7 _let_6) (tptp.combs X_a X_b _let_3) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_a) (tptp.if X_b)) (tptp.hAPP X_a _let_2 (tptp.fequal X_a) A_2))) B_1)) _let_1)) S))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) A_2) S)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) S)) (and (=> _let_9 (= _let_8 (tptp.hAPP X_a X_b B_1 A_2))) (=> (not _let_9) (= _let_8 _let_1)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.one_one X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_a _let_5))) (let ((_let_7 (tptp.fun X_a _let_4))) (let ((_let_8 (tptp.fun X_a X_b))) (let ((_let_9 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_8 (tptp.fun _let_2 X_b) (tptp.big_co302546470etprod X_a X_b) (tptp.hAPP X_b _let_8 (tptp.hAPP _let_7 (tptp.fun X_b _let_8) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combs X_a X_b _let_4) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_2 _let_6) (tptp.combb tptp.bool _let_5 X_a) (tptp.if X_b)) (tptp.hAPP X_a _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) A_2))) B_1)) _let_1)) S))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) A_2) S)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) S)) (and (=> _let_10 (= _let_9 (tptp.hAPP X_a X_b B_1 A_2))) (=> (not _let_10) (= _let_9 _let_1))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.field_inverse_zero X_b) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.inverse_divide X_b))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.fun X_a _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_b _let_6 X_a) _let_5) F)) G)) A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 _let_5 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3)))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.comm_monoid_mult X_b) (tptp.dvd X_b)) (forall ((F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.dvd_dvd X_b) (tptp.hAPP _let_1 X_b _let_2 A_3)) (tptp.hAPP _let_1 X_b _let_2 B_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((Y_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (tptp.hAPP _let_1 X_b (tptp.hAPP _let_2 (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) (tptp.hAPP X_b _let_2 (tptp.combk X_b X_a) Y_1)) A_3) (tptp.hAPP tptp.nat X_b (tptp.hAPP X_b (tptp.fun tptp.nat X_b) (tptp.power_power X_b) Y_1) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_3))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((F $$unsorted) (S $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) T_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) S) T_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) T_3) S))) (= (tptp.hAPP X_a X_b F X_2) (tptp.one_one X_b))))) (= (tptp.hAPP _let_1 X_b _let_2 S) (tptp.hAPP _let_1 X_b _let_2 T_3)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((F $$unsorted) (S $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) T_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) S) T_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) T_3) S))) (= (tptp.hAPP X_a X_b F X_2) (tptp.one_one X_b))))) (= (tptp.hAPP _let_1 X_b _let_2 T_3) (tptp.hAPP _let_1 X_b _let_2 S)))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.comm_monoid_mult X_a)) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod tptp.int X_a))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.fun tptp.int X_a))) (=> (= A_3 B_2) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set B_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (= (tptp.hAPP tptp.int X_a F X_2) (tptp.hAPP tptp.int X_a G X_2)))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 F) A_3) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 G) B_2)))))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) S)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) S)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP X_a tptp.nat F X_2)))))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co302546470etprod X_a tptp.nat) F) S))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) B_1) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_a) (tptp.fun _let_2 _let_1) (tptp.image X_b X_a) F) A_3))) (not (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (= (tptp.ti X_a B_1) (tptp.hAPP X_b X_a F X_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) A_3))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_semiring_1 X_b) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) A_3) B_2)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.dvd_dvd X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b G X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.dvd_dvd X_b) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) B_2))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.nat _let_2 tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.times_times tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.one_one tptp.nat)))) (let ((_let_5 (tptp.power_power tptp.real))) (let ((_let_6 (tptp.fun tptp.nat tptp.real))) (let ((_let_7 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_8 (tptp.fun _let_2 _let_6))) (let ((_let_9 (tptp.one_one tptp.real))) (let ((_let_10 (tptp.fun tptp.real tptp.real))) (let ((_let_11 (tptp.fun _let_6 _let_6))) (let ((_let_12 (tptp.fun tptp.nat _let_10))) (let ((_let_13 (tptp.hAPP (tptp.fun tptp.real _let_10) (tptp.fun _let_6 _let_12) (tptp.combb tptp.real _let_10 tptp.nat) (tptp.times_times tptp.real)))) (let ((_let_14 (tptp.combs tptp.nat tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X_1)) _let_9)) (= (tptp.hAPP tptp.real tptp.real tptp.arctan X_1) (tptp.hAPP _let_6 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_12 _let_11 _let_14 (tptp.hAPP _let_6 _let_12 _let_13 (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_12 _let_11 _let_14 (tptp.hAPP _let_6 _let_12 _let_13 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_10 _let_11 (tptp.combb tptp.real tptp.real tptp.nat) (tptp.hAPP tptp.real _let_10 (tptp.inverse_divide tptp.real) _let_9)) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_6 _let_8 _let_7 (tptp.real_1 tptp.nat)) _let_4)))) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_6 _let_8 _let_7 (tptp.hAPP tptp.real _let_6 _let_5 X_1)) _let_4))))))))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.times_times tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_5 (tptp.power_power tptp.real))) (let ((_let_6 (tptp.fun tptp.nat tptp.real))) (let ((_let_7 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_8 (tptp.fun _let_2 _let_6))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.hAPP (tptp.fun tptp.real _let_9) (tptp.fun _let_6 _let_10) (tptp.combb tptp.real _let_9 tptp.nat) (tptp.times_times tptp.real)))) (let ((_let_12 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_13 (tptp.fun _let_6 _let_6))) (let ((_let_14 (tptp.hAPP _let_10 _let_13 _let_12 (tptp.hAPP _let_6 _let_10 _let_11 (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))))) (let ((_let_15 (tptp.suminf tptp.real))) (let ((_let_16 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.nat _let_2 tptp.nat) (tptp.plus_plus tptp.nat)) _let_4)) (tptp.one_one tptp.nat)))) (let ((_let_17 (tptp.fun tptp.real _let_8))) (let ((_let_18 (tptp.fun tptp.real _let_6))) (let ((_let_19 (tptp.one_one tptp.real))) (let ((_let_20 (tptp.combb _let_6 _let_6 tptp.real))) (let ((_let_21 (tptp.fun _let_18 _let_18))) (let ((_let_22 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_22 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X_1)) _let_19)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_22 (tptp.hAPP _let_9 (tptp.fun tptp.real _let_22) (tptp.deriv tptp.real) (tptp.hAPP _let_18 _let_9 (tptp.hAPP (tptp.fun _let_6 tptp.real) (tptp.fun _let_18 _let_9) (tptp.combb _let_6 tptp.real tptp.real) _let_15) (tptp.hAPP _let_18 _let_18 (tptp.hAPP _let_13 _let_21 _let_20 _let_14) (tptp.hAPP _let_18 _let_18 (tptp.hAPP _let_13 _let_21 _let_20 (tptp.hAPP _let_10 _let_13 _let_12 (tptp.hAPP _let_6 _let_10 _let_11 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_9 _let_13 (tptp.combb tptp.real tptp.real tptp.nat) (tptp.hAPP tptp.real _let_9 (tptp.inverse_divide tptp.real) _let_19)) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_6 _let_8 _let_7 (tptp.real_1 tptp.nat)) _let_16))))) (tptp.hAPP _let_2 _let_18 (tptp.hAPP _let_17 (tptp.fun _let_2 _let_18) (tptp.combc tptp.real _let_2 _let_6) (tptp.hAPP _let_18 _let_17 (tptp.hAPP (tptp.fun _let_6 _let_8) (tptp.fun _let_18 _let_17) (tptp.combb _let_6 _let_8 tptp.real) _let_7) _let_5)) _let_16))))) X_1) (tptp.hAPP _let_6 tptp.real _let_15 (tptp.hAPP _let_6 _let_6 _let_14 (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_6 _let_8 _let_7 (tptp.hAPP tptp.real _let_6 _let_5 X_1)) _let_4))))))))))))))))))))))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (=> (and (tptp.comm_monoid_add X_a) (tptp.t2_space X_a)) (= (tptp.hAPP _let_2 X_a (tptp.suminf X_a) (tptp.hAPP X_a _let_2 (tptp.combk X_a tptp.nat) _let_1)) _let_1))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP tptp.real tptp.real tptp.sin X_2) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) tptp.sin_coeff)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_2)))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP tptp.real tptp.real tptp.sin X_1) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) tptp.sin_coeff)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1)))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP tptp.real tptp.real tptp.cos X_2) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) tptp.cos_coeff)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_2)))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP tptp.real tptp.real tptp.cos X_1) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) tptp.cos_coeff)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n2089651433ebra_1 X_a) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP _let_1 X_a (tptp.suminf X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_1 _let_3) (tptp.combb X_a _let_2 tptp.nat) (tptp.times_times X_a)) F)) (tptp.hAPP X_a _let_1 (tptp.power_power X_a) (tptp.zero_zero X_a)))) (tptp.hAPP tptp.nat X_a F (tptp.zero_zero tptp.nat))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.uminus_uminus tptp.real))) (= (tptp.hAPP tptp.real tptp.real _let_5 (tptp.hAPP tptp.real tptp.real tptp.sin X_1)) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 _let_4 (tptp.combb tptp.real tptp.real tptp.nat) _let_5) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 _let_4 (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) tptp.sin_coeff)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_6 (tptp.fun _let_1 _let_4))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.nat _let_8))) (let ((_let_10 (tptp.plus_plus tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.exp tptp.real) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_8 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_8 _let_10 (tptp.one_one tptp.real)) X_1)) (tptp.hAPP _let_4 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_7 (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.real _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.real _let_8 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_8 _let_7 (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.real_1 tptp.nat)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb tptp.nat tptp.nat tptp.nat) (tptp.fact_fact tptp.nat)) _let_3))))) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.real _let_4 (tptp.power_power tptp.real) X_1)) _let_3)))))))))))))))) (= _let_189 (tptp.hAPP _let_49 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_49 _let_49 (tptp.hAPP _let_185 _let_50 (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_49 _let_185 (tptp.hAPP _let_38 _let_186 _let_184 _let_32) (tptp.hAPP tptp.real _let_49 (tptp.hAPP _let_185 (tptp.fun tptp.real _let_49) (tptp.combc tptp.nat tptp.real tptp.real) (tptp.hAPP _let_49 _let_185 (tptp.hAPP _let_38 _let_186 _let_184 _let_132) (tptp.hAPP tptp.real _let_49 _let_139 _let_183))) _let_136))) (tptp.hAPP _let_25 _let_49 _let_83 (tptp.hAPP tptp.nat _let_25 (tptp.hAPP _let_181 _let_181 _let_180 (tptp.hAPP _let_25 _let_181 (tptp.hAPP _let_181 (tptp.fun _let_25 _let_181) (tptp.combb tptp.nat _let_25 tptp.nat) _let_182) (tptp.hAPP tptp.nat _let_25 (tptp.hAPP _let_181 _let_181 _let_180 (tptp.times_times tptp.nat)) _let_6))) _let_179))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat tptp.nat))) (let ((_let_7 (tptp.fun _let_6 _let_4))) (let ((_let_8 (tptp.fun tptp.nat _let_6))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (let ((_let_10 (tptp.number_number_of tptp.real))) (let ((_let_11 (tptp.fun tptp.nat _let_2))) (let ((_let_12 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_4 _let_11) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)))) (let ((_let_13 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_14 (tptp.ord_less tptp.real))) (let ((_let_15 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_15 _let_14 (tptp.zero_zero tptp.real)) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_15 _let_14 X_1) (tptp.hAPP tptp.int tptp.real _let_10 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (= (tptp.hAPP tptp.real tptp.real tptp.ln X_1) (tptp.hAPP _let_4 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_11 _let_9 _let_13 (tptp.hAPP _let_4 _let_11 _let_12 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_11 _let_9 _let_13 (tptp.hAPP _let_4 _let_11 _let_12 (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.int tptp.real _let_10 tptp.min_1)))) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_2 _let_9 (tptp.combb tptp.real tptp.real tptp.nat) (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) _let_1)) (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.real_1 tptp.nat)) (tptp.hAPP tptp.nat _let_6 (tptp.hAPP _let_8 _let_8 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.one_one tptp.nat))))))) (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) X_1) _let_1))) tptp.suc)))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((K $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.ring_1_of_int X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.fun tptp.int X_a))) (let ((_let_6 (tptp.fun X_a _let_3))) (let ((_let_7 (tptp.hAPP _let_6 (tptp.fun _let_5 _let_4) (tptp.combb X_a _let_3 tptp.int) (tptp.plus_plus X_a)))) (let ((_let_8 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_5) (tptp.combs tptp.int X_a X_a) (tptp.hAPP _let_5 _let_4 _let_7 _let_2)) _let_2))) (let ((_let_9 (tptp.combc tptp.int X_a X_a))) (let ((_let_10 (tptp.fun X_a _let_5))) (let ((_let_11 (tptp.zero_zero tptp.int))) (let ((_let_12 (tptp.fun tptp.int tptp.bool))) (let ((_let_13 (tptp.fun tptp.int _let_12))) (let ((_let_14 (tptp.fun tptp.int _let_6))) (let ((_let_15 (tptp.fun X_a _let_4))) (let ((_let_16 (tptp.fun tptp.int _let_4))) (let ((_let_17 (tptp.fun tptp.int _let_10))) (let ((_let_18 (tptp.fun tptp.int _let_5))) (let ((_let_19 (tptp.hAPP tptp.int X_a _let_2 K))) (let ((_let_20 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_12 (tptp.ord_less tptp.int) K) _let_11)))) (let ((_let_21 (= (tptp.ti tptp.int K) _let_11))) (and (=> _let_21 (= _let_19 (tptp.zero_zero X_a))) (=> (not _let_21) (and (=> _let_20 (= _let_19 (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP tptp.int X_a _let_2 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) K))))) (=> (not _let_20) (= _let_19 (tptp.hAPP _let_1 X_a (tptp.hAPP _let_18 (tptp.fun _let_1 X_a) (tptp.product_prod_case tptp.int tptp.int X_a) (tptp.hAPP _let_5 _let_18 (tptp.hAPP _let_17 (tptp.fun _let_5 _let_18) (tptp.combs tptp.int X_a _let_5) (tptp.hAPP _let_16 _let_17 (tptp.hAPP (tptp.fun _let_4 _let_10) (tptp.fun _let_16 _let_17) (tptp.combb _let_4 _let_10 tptp.int) _let_9) (tptp.hAPP _let_5 _let_16 (tptp.hAPP _let_15 (tptp.fun _let_5 _let_16) (tptp.combb X_a _let_4 tptp.int) (tptp.hAPP _let_14 _let_15 (tptp.combc tptp.int X_a _let_3) (tptp.hAPP _let_12 _let_14 (tptp.hAPP (tptp.fun tptp.bool _let_6) (tptp.fun _let_12 _let_14) (tptp.combb tptp.bool _let_6 tptp.int) (tptp.if X_a)) (tptp.hAPP tptp.int _let_12 (tptp.hAPP _let_13 _let_13 (tptp.combc tptp.int tptp.int tptp.bool) (tptp.fequal tptp.int)) _let_11)))) _let_8))) (tptp.hAPP X_a _let_5 (tptp.hAPP _let_4 _let_10 _let_9 (tptp.hAPP _let_5 _let_4 _let_7 _let_8)) (tptp.one_one X_a)))) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.divmod_int K) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))))))))))))))))))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.nat _let_2 tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.times_times tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.one_one tptp.nat)))) (let ((_let_5 (tptp.power_power tptp.real))) (let ((_let_6 (tptp.fun tptp.nat tptp.real))) (let ((_let_7 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_8 (tptp.fun _let_2 _let_6))) (let ((_let_9 (tptp.one_one tptp.real))) (let ((_let_10 (tptp.fun tptp.real tptp.real))) (let ((_let_11 (tptp.fun _let_6 _let_6))) (let ((_let_12 (tptp.fun tptp.nat _let_10))) (let ((_let_13 (tptp.hAPP (tptp.fun tptp.real _let_10) (tptp.fun _let_6 _let_12) (tptp.combb tptp.real _let_10 tptp.nat) (tptp.times_times tptp.real)))) (let ((_let_14 (tptp.combs tptp.nat tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X_1)) _let_9)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_12 _let_11 _let_14 (tptp.hAPP _let_6 _let_12 _let_13 (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_12 _let_11 _let_14 (tptp.hAPP _let_6 _let_12 _let_13 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_10 _let_11 (tptp.combb tptp.real tptp.real tptp.nat) (tptp.hAPP tptp.real _let_10 (tptp.inverse_divide tptp.real) _let_9)) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_6 _let_8 _let_7 (tptp.real_1 tptp.nat)) _let_4)))) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_6 _let_8 _let_7 (tptp.hAPP tptp.real _let_6 _let_5 X_1)) _let_4))))))))))))))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) (tptp.hAPP X_a _let_1 (tptp.combk X_a tptp.nat) (tptp.zero_zero X_a))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_c tptp.bool))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_5 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_2) B_1)) A_3)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_c (tptp.fun _let_4 tptp.bool) (tptp.member X_c) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_3 F A_2) B_1)) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_5 _let_4) (tptp.image _let_1 X_c) (tptp.hAPP (tptp.fun X_a _let_3) _let_2 (tptp.product_prod_case X_a X_b X_c) F)) A_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.suminf X_a))) (let ((_let_6 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_6 X_3)) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_6 Y_3)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_4 X_a _let_5 X_3)) (tptp.hAPP _let_4 X_a _let_5 Y_3)) (tptp.hAPP _let_4 X_a _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_3)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.suminf X_a))) (let ((_let_6 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_6 X_3)) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool _let_6 Y_3)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_4 X_a _let_5 X_3)) (tptp.hAPP _let_4 X_a _let_5 Y_3)) (tptp.hAPP _let_4 X_a _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_3)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((C_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.suminf X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.inverse_divide X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable X_a) F)) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP X_a _let_2 (tptp.hAPP _let_5 (tptp.fun X_a _let_2) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun X_a _let_4) (tptp.fun _let_2 _let_5) (tptp.combb X_a _let_4 tptp.nat) _let_3) F)) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP _let_2 X_a _let_1 F)) C_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.suminf X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.summable X_a) X_3)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_4 X_a _let_5 X_3)) Y_1) (tptp.hAPP _let_4 X_a _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.suminf X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable X_a) X_3)) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) _let_3) X_3)) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP _let_2 X_a _let_1 X_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.suminf X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.summable X_a) X_3)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_4 X_a _let_5 X_3)) Y_1) (tptp.hAPP _let_4 X_a _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.suminf X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.summable X_a) X_3)) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP _let_3 X_a _let_4 X_3)) (tptp.hAPP _let_3 X_a _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_3 _let_3) (tptp.combb X_a X_a tptp.nat) _let_2) X_3))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((C_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.suminf X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.summable X_a) F)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_4 X_a _let_5 F)) C_1) (tptp.hAPP _let_4 X_a _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) F)) C_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((C_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.suminf X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.hAPP X_a _let_3 (tptp.times_times X_a) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable X_a) F)) (= (tptp.hAPP _let_2 X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) _let_4) F)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP _let_2 X_a _let_1 F))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.fun X_c X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_1 X_a) (tptp.product_prod_case X_b X_c X_a) F) P_4) (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_2 F (tptp.hAPP _let_1 X_b (tptp.product_fst X_b X_c) P_4)) (tptp.hAPP _let_1 X_c (tptp.product_snd X_b X_c) P_4)))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.product_prod X_b X_c))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 X_a) (tptp.product_prod_case X_b X_c X_a) F1) (tptp.hAPP X_c _let_2 (tptp.hAPP X_b (tptp.fun X_c _let_2) (tptp.product_Pair X_b X_c) A_2) B_1)) (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_1 F1 A_2) B_1))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c X_a))) (let ((_let_2 (tptp.product_prod X_b X_c))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_2 X_a) (tptp.product_prod_case X_b X_c X_a) F) (tptp.hAPP X_c _let_2 (tptp.hAPP X_b (tptp.fun X_c _let_2) (tptp.product_Pair X_b X_c) A_2) B_1)) (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_1 F A_2) B_1))))) (forall ((X_a $$unsorted)) (=> (tptp.banach X_a) (forall ((F $$unsorted) (G $$unsorted)) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a F N_2))) (tptp.hAPP tptp.nat tptp.real G N_2)))))) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.real) tptp.bool (tptp.summable tptp.real) G)) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.summable X_a) F))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (C_1 $$unsorted) (P_4 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_c)) (tptp.fun _let_1 X_c) (tptp.product_prod_case X_a X_b X_c) C_1))) (=> (= (tptp.ti _let_1 P_4) (tptp.ti _let_1 Q_2)) (= (tptp.hAPP _let_1 X_c _let_2 P_4) (tptp.hAPP _let_1 X_c _let_2 Q_2)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((Z $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_2) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_2 _let_4 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_2 _let_4) (tptp.combb X_a _let_3 tptp.nat) (tptp.times_times X_a)) F)))) (let ((_let_6 (tptp.norm_norm X_a))) (let ((_let_7 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable X_a) (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP X_a _let_2 _let_1 X_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real _let_6 Z)) (tptp.hAPP X_a tptp.real _let_6 X_1))) (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_2 _let_7 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_2 _let_7) (tptp.combb X_a tptp.real tptp.nat) _let_6) (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP X_a _let_2 _let_1 Z))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((C_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 F)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) (tptp.hAPP X_a _let_1 (tptp.times_times X_a) C_1)) F)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((C_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 F)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_a _let_1 tptp.nat) (tptp.times_times X_a)) F)) C_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 X_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X_1)) X_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 X_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_a _let_1 tptp.nat) (tptp.times_times X_a)) X_3)) Y_1))))))))))) (forall ((F $$unsorted)) (let ((_let_1 (tptp.summable tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_2 _let_2) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.abs_abs tptp.real)) F))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_1 F)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_1 _let_1) (tptp.combb X_a X_a tptp.nat) (tptp.uminus_uminus X_a)) X_3))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.product_prod X_b X_a))) (= (tptp.hAPP _let_3 X_a (tptp.product_snd X_b X_a) P_4) (tptp.hAPP _let_3 X_a (tptp.hAPP _let_2 (tptp.fun _let_3 X_a) (tptp.product_prod_case X_b X_a X_a) (tptp.hAPP _let_1 _let_2 (tptp.combk _let_1 X_b) (tptp.combi X_a))) P_4)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (= (tptp.hAPP _let_1 X_a (tptp.product_fst X_a X_b) P_4) (tptp.hAPP _let_1 X_a (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_a)) (tptp.fun _let_1 X_a) (tptp.product_prod_case X_a X_b X_a) (tptp.combk X_a X_b)) P_4)))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (X_d $$unsorted) (X_e $$unsorted) (F $$unsorted) (G $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.fun _let_1 X_a))) (let ((_let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_a)) _let_2 (tptp.product_prod_case X_b X_c X_a) F))) (let ((_let_4 (tptp.fun X_e X_a))) (let ((_let_5 (tptp.fun X_e _let_1))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (let ((_let_7 (tptp.fun X_d _let_4))) (let ((_let_8 (tptp.fun X_d _let_5))) (let ((_let_9 (tptp.product_prod X_d X_e))) (= (tptp.hAPP _let_1 X_a _let_3 (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_8 (tptp.fun _let_9 _let_1) (tptp.product_prod_case X_d X_e _let_1) G) P_4)) (tptp.hAPP _let_9 X_a (tptp.hAPP _let_7 (tptp.fun _let_9 X_a) (tptp.product_prod_case X_d X_e X_a) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combb _let_5 _let_4 X_d) (tptp.hAPP _let_2 _let_6 (tptp.combb _let_1 X_a X_e) _let_3)) G)) P_4)))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable tptp.real) X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun _let_2 _let_1) (tptp.combb tptp.real X_a tptp.nat) (tptp.of_real X_a)) X_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.banach X_a) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_1 _let_2) (tptp.combb X_a tptp.real tptp.nat) (tptp.norm_norm X_a)) F))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) F)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 X_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_a _let_1 tptp.nat) (tptp.inverse_divide X_a)) X_3)) Y_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((C_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 F)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_a _let_1 tptp.nat) (tptp.inverse_divide X_a)) F)) C_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((K $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 F)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_3) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) K)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 X_3)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 Y_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_a _let_1 tptp.nat) (tptp.plus_plus X_a)) X_3)) Y_3)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 X_3)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 Y_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_a _let_1 tptp.nat) (tptp.minus_minus X_a)) X_3)) Y_3)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 X_c))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_b _let_1))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.fun X_a _let_3))) (let ((_let_7 (tptp.fun X_a _let_4))) (= (tptp.hAPP _let_6 _let_2 (tptp.product_prod_case X_a X_b X_c) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_7 _let_6) (tptp.combb _let_4 _let_3 X_a) (tptp.hAPP _let_2 _let_5 (tptp.combb _let_1 X_c X_b) F)) (tptp.product_Pair X_a X_b))) (tptp.ti _let_2 F)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b X_c))) (= (tptp.hAPP _let_1 X_c (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_1 X_c) (tptp.product_prod_case X_a X_b X_c) X_2) Xa) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_2 X_2 (tptp.hAPP _let_1 X_a (tptp.product_fst X_a X_b) Xa)) (tptp.hAPP _let_1 X_b (tptp.product_snd X_a X_b) Xa)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (X_d $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_d))) (let ((_let_4 (tptp.fun X_d _let_1))) (let ((_let_5 (tptp.product_prod X_a X_b))) (let ((_let_6 (tptp.fun _let_5 X_c))) (let ((_let_7 (tptp.fun _let_5 X_d))) (let ((_let_8 (tptp.fun _let_5 X_a))) (let ((_let_9 (tptp.fun _let_5 _let_1))) (let ((_let_10 (tptp.fun _let_5 X_b))) (= (tptp.hAPP _let_10 _let_6 (tptp.hAPP _let_9 (tptp.fun _let_10 _let_6) (tptp.combs _let_5 X_b X_c) (tptp.hAPP _let_7 _let_9 (tptp.hAPP _let_4 (tptp.fun _let_7 _let_9) (tptp.combb X_d _let_1 _let_5) F) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_3 (tptp.fun _let_8 _let_7) (tptp.combb X_a X_d _let_5) G) (tptp.product_fst X_a X_b)))) (tptp.product_snd X_a X_b)) (tptp.hAPP _let_2 _let_6 (tptp.product_prod_case X_a X_b X_c) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.combb X_d _let_1 X_a) F) G)))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (P_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.fun X_c X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_1 X_a) (tptp.product_prod_case X_b X_c X_a) P_1) Z) (tptp.hAPP X_c X_a (tptp.hAPP X_b _let_2 P_1 (tptp.hAPP _let_1 X_b (tptp.product_fst X_b X_c) Z)) (tptp.hAPP _let_1 X_c (tptp.product_snd X_b X_c) Z)))))) (forall ((X_a $$unsorted)) (=> (tptp.banach X_a) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.summable tptp.real))) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP tptp.nat X_a F N_2))) (tptp.hAPP tptp.nat tptp.real G N_2)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 G)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb X_a tptp.real tptp.nat) (tptp.norm_norm X_a)) F))))))))))) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.summable tptp.real))) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.nat tptp.real F N_2))) (tptp.hAPP tptp.nat tptp.real G N_2)))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 G)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_1 _let_1) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.abs_abs tptp.real)) F)))))))) (forall ((F $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_2 _let_2) (tptp.combb tptp.real tptp.real tptp.nat) _let_1) F))) (let ((_let_4 (tptp.suminf tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable tptp.real) _let_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP _let_2 tptp.real _let_4 F))) (tptp.hAPP _let_2 tptp.real _let_4 _let_3))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.summable tptp.real) X_3)) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP _let_3 tptp.real (tptp.suminf tptp.real) X_3)) (tptp.hAPP _let_2 X_a (tptp.suminf X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real X_a tptp.nat) _let_1) X_3)))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) tptp.sin_coeff)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1)))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) tptp.cos_coeff)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.banach X_a) (forall ((F $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_3 _let_2) (tptp.combb X_a tptp.real tptp.nat) _let_1) F))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable tptp.real) _let_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP _let_3 X_a (tptp.suminf X_a) F))) (tptp.hAPP _let_2 tptp.real (tptp.suminf tptp.real) _let_4))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((Z $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_2) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_2 _let_4 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_2 _let_4) (tptp.combb X_a _let_3 tptp.nat) (tptp.times_times X_a)) F)))) (let ((_let_6 (tptp.summable X_a))) (let ((_let_7 (tptp.norm_norm X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_6 (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP X_a _let_2 _let_1 X_1)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real _let_7 Z)) (tptp.hAPP X_a tptp.real _let_7 X_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_6 (tptp.hAPP _let_2 _let_2 _let_5 (tptp.hAPP X_a _let_2 _let_1 Z)))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_n2089651433ebra_1 X_a) (tptp.banach X_a)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X_1)) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) (tptp.hAPP X_a _let_1 (tptp.power_power X_a) X_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X_1)) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) (tptp.hAPP X_a _let_1 (tptp.power_power X_a) X_1)))))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP tptp.rat tptp.int (tptp.archim2085082626_floor tptp.rat) P_4) (tptp.hAPP _let_1 tptp.int (tptp.hAPP (tptp.fun tptp.int (tptp.fun tptp.int tptp.int)) (tptp.fun _let_1 tptp.int) (tptp.product_prod_case tptp.int tptp.int tptp.int) (tptp.div_div tptp.int)) (tptp.hAPP tptp.rat _let_1 tptp.quotient_of P_4))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of (tptp.hAPP tptp.rat tptp.rat (tptp.uminus_uminus tptp.rat) P_4)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.product_prod_case tptp.int tptp.int _let_1) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_3) (tptp.combb tptp.int _let_2 tptp.int) (tptp.product_Pair tptp.int tptp.int)) (tptp.uminus_uminus tptp.int))) (tptp.hAPP tptp.rat _let_1 tptp.quotient_of P_4)))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.real _let_4 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) (tptp.fact_fact tptp.nat))))) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1)))))))))) (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of (tptp.hAPP tptp.rat tptp.rat (tptp.abs_abs tptp.rat) P_4)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.product_prod_case tptp.int tptp.int _let_1) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_3) (tptp.combb tptp.int _let_2 tptp.int) (tptp.product_Pair tptp.int tptp.int)) (tptp.abs_abs tptp.int))) (tptp.hAPP tptp.rat _let_1 tptp.quotient_of P_4)))))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (let ((_let_2 (tptp.ord_less_eq tptp.int))) (let ((_let_3 (tptp.combc tptp.int tptp.int tptp.bool))) (let ((_let_4 (tptp.fun tptp.int tptp.bool))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.ord_less tptp.int))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun tptp.int _let_7))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.hAPP (tptp.fun tptp.bool _let_7) _let_9 (tptp.combb tptp.bool _let_7 tptp.int) tptp.fconj))) (let ((_let_11 (tptp.combs tptp.int tptp.bool tptp.bool))) (let ((_let_12 (tptp.fun _let_4 _let_4))) (let ((_let_13 (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_4 _let_6 _let_1) B_1))) (let ((_let_14 (tptp.combb tptp.bool tptp.bool tptp.int))) (let ((_let_15 (tptp.fun tptp.int tptp.int))) (let ((_let_16 (tptp.fun tptp.int _let_15))) (let ((_let_17 (tptp.fun _let_15 _let_4))) (let ((_let_18 (tptp.fun tptp.int _let_8))) (let ((_let_19 (tptp.fun tptp.int _let_12))) (let ((_let_20 (tptp.fun (tptp.product_prod tptp.int tptp.int) tptp.bool))) (= (tptp.hAPP tptp.int _let_20 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_20) tptp.divmod_int_rel A_2) B_1) (tptp.hAPP _let_5 _let_20 (tptp.product_prod_case tptp.int tptp.int tptp.bool) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_19 (tptp.fun _let_4 _let_5) (tptp.combc tptp.int _let_4 _let_4) (tptp.hAPP _let_18 _let_19 (tptp.hAPP (tptp.fun _let_8 _let_12) (tptp.fun _let_18 _let_19) (tptp.combb _let_8 _let_12 tptp.int) _let_11) (tptp.hAPP _let_5 _let_18 (tptp.hAPP _let_9 (tptp.fun _let_5 _let_18) (tptp.combb _let_4 _let_8 tptp.int) _let_10) (tptp.hAPP _let_16 _let_5 (tptp.hAPP _let_17 (tptp.fun _let_16 _let_5) (tptp.combb _let_15 _let_4 tptp.int) (tptp.hAPP _let_4 _let_17 (tptp.combb tptp.int tptp.bool tptp.int) (tptp.hAPP tptp.int _let_4 (tptp.fequal tptp.int) A_2))) (tptp.hAPP _let_15 _let_16 (tptp.hAPP _let_16 (tptp.fun _let_15 _let_16) (tptp.combb tptp.int _let_15 tptp.int) (tptp.plus_plus tptp.int)) (tptp.hAPP tptp.int _let_15 (tptp.times_times tptp.int) B_1)))))) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_8 _let_12 _let_11 (tptp.hAPP _let_4 _let_8 _let_10 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 _let_12 _let_14 (tptp.hAPP tptp.bool _let_7 tptp.fimplies _let_13)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_8 _let_12 _let_11 (tptp.hAPP _let_4 _let_8 _let_10 (tptp.hAPP tptp.int _let_4 _let_2 _let_1))) (tptp.hAPP tptp.int _let_4 (tptp.hAPP _let_5 _let_5 _let_3 _let_6) B_1))))) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 _let_12 _let_14 (tptp.hAPP tptp.bool _let_7 tptp.fimplies (tptp.hAPP tptp.bool tptp.bool tptp.fNot _let_13))) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_8 _let_12 _let_11 (tptp.hAPP _let_4 _let_8 _let_10 (tptp.hAPP tptp.int _let_4 _let_6 B_1))) (tptp.hAPP tptp.int _let_4 (tptp.hAPP _let_5 _let_5 _let_3 _let_2) _let_1)))))))))))))))))))))))))))) _let_178 (forall ((P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_1))) (let ((_let_6 (tptp.fun tptp.int _let_5))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun tptp.int _let_6))) (let ((_let_9 (tptp.fun _let_6 _let_6))) (let ((_let_10 (tptp.zero_zero tptp.int))) (let ((_let_11 (tptp.fun tptp.int tptp.bool))) (let ((_let_12 (tptp.fun tptp.int _let_11))) (let ((_let_13 (tptp.fun _let_1 _let_1))) (let ((_let_14 (tptp.fun _let_1 _let_13))) (let ((_let_15 (tptp.fun tptp.int _let_14))) (let ((_let_16 (tptp.fun tptp.int _let_13))) (let ((_let_17 (tptp.fun _let_5 _let_5))) (let ((_let_18 (tptp.fun tptp.int _let_17))) (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of (tptp.hAPP tptp.rat tptp.rat (tptp.inverse_inverse tptp.rat) P_4)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_6 _let_13 (tptp.product_prod_case tptp.int tptp.int _let_1) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_18 _let_9 (tptp.combs tptp.int _let_5 _let_5) (tptp.hAPP _let_16 _let_18 (tptp.hAPP (tptp.fun _let_13 _let_17) (tptp.fun _let_16 _let_18) (tptp.combb _let_13 _let_17 tptp.int) (tptp.combb _let_1 _let_1 tptp.int)) (tptp.hAPP _let_1 _let_16 (tptp.hAPP _let_15 (tptp.fun _let_1 _let_16) (tptp.combc tptp.int _let_1 _let_13) (tptp.hAPP _let_11 _let_15 (tptp.hAPP (tptp.fun tptp.bool _let_14) (tptp.fun _let_11 _let_15) (tptp.combb tptp.bool _let_14 tptp.int) (tptp.if _let_1)) (tptp.hAPP tptp.int _let_11 (tptp.hAPP _let_12 _let_12 (tptp.combc tptp.int tptp.int tptp.bool) (tptp.fequal tptp.int)) _let_10))) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_5 _let_4 _let_10) (tptp.one_one tptp.int))))) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_8 _let_7 (tptp.combs tptp.int tptp.int _let_5) (tptp.hAPP _let_8 _let_8 (tptp.hAPP _let_9 (tptp.fun _let_8 _let_8) (tptp.combb _let_6 _let_6 tptp.int) (tptp.combc tptp.int tptp.int _let_1)) (tptp.hAPP _let_3 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_3 _let_8) (tptp.combb _let_2 _let_6 tptp.int) (tptp.hAPP _let_6 _let_7 (tptp.combb tptp.int _let_5 tptp.int) _let_4)) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.int _let_2 tptp.int) (tptp.times_times tptp.int)) (tptp.sgn_sgn tptp.int))))) (tptp.abs_abs tptp.int)))) (tptp.hAPP tptp.rat _let_1 tptp.quotient_of P_4)))))))))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_6 (tptp.fun _let_1 _let_4))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.fun tptp.nat _let_8))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_7 (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.real _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.real _let_8 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_8 _let_7 (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.real_1 tptp.nat)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb tptp.nat tptp.nat tptp.nat) (tptp.fact_fact tptp.nat)) _let_3))))) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.real _let_4 (tptp.power_power tptp.real) X_1)) _let_3)))))))))))))) (forall ((B_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int _let_3))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.fun _let_1 _let_5))) (let ((_let_7 (tptp.hAPP _let_5 _let_6 (tptp.combb tptp.int _let_4 tptp.int) (tptp.product_Pair tptp.int tptp.int)))) (let ((_let_8 (tptp.combc tptp.int tptp.int tptp.int))) (let ((_let_9 (tptp.fun tptp.int _let_1))) (let ((_let_10 (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_9 _let_9 _let_8 (tptp.minus_minus tptp.int)) B_1))) (let ((_let_11 (tptp.fun _let_1 _let_4))) (let ((_let_12 (tptp.fun tptp.int _let_11))) (let ((_let_13 (tptp.fun tptp.int tptp.bool))) (let ((_let_14 (tptp.fun _let_3 _let_3))) (let ((_let_15 (tptp.fun _let_3 _let_14))) (let ((_let_16 (tptp.fun tptp.int _let_15))) (let ((_let_17 (tptp.fun tptp.int _let_14))) (let ((_let_18 (tptp.fun _let_4 _let_17))) (let ((_let_19 (tptp.fun tptp.int _let_17))) (let ((_let_20 (tptp.fun _let_4 _let_4))) (let ((_let_21 (tptp.fun tptp.int _let_20))) (= (tptp.hAPP tptp.int _let_14 tptp.adjust B_1) (tptp.hAPP _let_5 _let_14 (tptp.product_prod_case tptp.int tptp.int _let_3) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_21 (tptp.fun _let_5 _let_5) (tptp.combs tptp.int _let_4 _let_4) (tptp.hAPP _let_19 _let_21 (tptp.hAPP (tptp.fun _let_17 _let_20) (tptp.fun _let_19 _let_21) (tptp.combb _let_17 _let_20 tptp.int) (tptp.combs tptp.int _let_3 _let_3)) (tptp.hAPP _let_5 _let_19 (tptp.hAPP _let_18 (tptp.fun _let_5 _let_19) (tptp.combb _let_4 _let_17 tptp.int) (tptp.hAPP _let_16 _let_18 (tptp.combs tptp.int _let_3 _let_14) (tptp.hAPP _let_13 _let_16 (tptp.hAPP (tptp.fun tptp.bool _let_15) (tptp.fun _let_13 _let_16) (tptp.combb tptp.bool _let_15 tptp.int) (tptp.if _let_3)) (tptp.hAPP _let_1 _let_13 (tptp.hAPP _let_13 (tptp.fun _let_1 _let_13) (tptp.combb tptp.int tptp.bool tptp.int) (tptp.hAPP tptp.int _let_13 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int))) _let_10)))) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_12 _let_6 (tptp.combc tptp.int _let_1 _let_4) (tptp.hAPP _let_5 _let_12 (tptp.hAPP (tptp.fun _let_4 _let_11) (tptp.fun _let_5 _let_12) (tptp.combb _let_4 _let_11 tptp.int) (tptp.combb tptp.int _let_3 tptp.int)) (tptp.hAPP _let_1 _let_5 _let_7 (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_9 _let_9 _let_8 (tptp.hAPP _let_1 _let_9 (tptp.hAPP _let_9 (tptp.fun _let_1 _let_9) (tptp.combb tptp.int _let_1 tptp.int) (tptp.plus_plus tptp.int)) _let_2)) (tptp.one_one tptp.int))))) _let_10)))) (tptp.hAPP _let_1 _let_5 _let_7 _let_2)))))))))))))))))))))))))) (forall ((X0 $$unsorted) (F $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun _let_4 _let_2))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.hAPP (tptp.fun tptp.real _let_6) (tptp.fun _let_2 _let_7) (tptp.combb tptp.real _let_6 tptp.nat) (tptp.times_times tptp.real)))) (let ((_let_9 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (let ((_let_11 (tptp.hAPP _let_7 _let_10 _let_9 (tptp.hAPP _let_2 _let_7 _let_8 F)))) (let ((_let_12 (tptp.suminf tptp.real))) (let ((_let_13 (tptp.fun tptp.real _let_5))) (let ((_let_14 (tptp.fun tptp.real _let_2))) (let ((_let_15 (tptp.fun tptp.real tptp.bool))) (let ((_let_16 (tptp.fun tptp.real _let_15))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.hAPP (tptp.fun tptp.real _let_3) (tptp.fun _let_1 _let_4) (tptp.combb tptp.real _let_3 tptp.nat) (tptp.times_times tptp.real)))) (let ((_let_6 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_8 tptp.bool) (tptp.member tptp.real) X_2) (tptp.hAPP tptp.real _let_8 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_8) (tptp.ord_gr676655987ssThan tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) R_3)) R_3))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_1 _let_4 _let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_1 _let_4 _let_5 F)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) tptp.suc)))) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_2)))))))))))))) (=> (tptp.hBOOL (tptp.hAPP _let_15 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_15 tptp.bool) (tptp.member tptp.real) X0) (tptp.hAPP tptp.real _let_15 (tptp.hAPP tptp.real _let_16 (tptp.ord_gr676655987ssThan tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) R_3)) R_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_15 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_3)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_15 (tptp.hAPP _let_6 _let_16 (tptp.deriv tptp.real) (tptp.hAPP _let_14 _let_6 (tptp.hAPP (tptp.fun _let_2 tptp.real) (tptp.fun _let_14 _let_6) (tptp.combb _let_2 tptp.real tptp.real) _let_12) (tptp.hAPP _let_14 _let_14 (tptp.hAPP _let_10 (tptp.fun _let_14 _let_14) (tptp.combb _let_2 _let_2 tptp.real) _let_11) (tptp.hAPP _let_4 _let_14 (tptp.hAPP _let_13 (tptp.fun _let_4 _let_14) (tptp.combc tptp.real _let_4 _let_2) (tptp.hAPP _let_14 _let_13 (tptp.hAPP (tptp.fun _let_2 _let_5) (tptp.fun _let_14 _let_13) (tptp.combb _let_2 _let_5 tptp.real) _let_3) _let_1)) tptp.suc)))) X0) (tptp.hAPP _let_2 tptp.real _let_12 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_7 _let_10 _let_9 (tptp.hAPP _let_2 _let_7 _let_8 (tptp.hAPP _let_2 _let_2 _let_11 (tptp.hAPP _let_4 _let_2 (tptp.hAPP _let_2 _let_5 _let_3 (tptp.real_1 tptp.nat)) tptp.suc)))) (tptp.hAPP tptp.real _let_2 _let_1 X0))))))))))))))))))))))))) _let_174 (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (Z $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_c _let_2))) (let ((_let_4 (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) Z))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP X_c _let_2 (tptp.hAPP X_b _let_3 C_1 A_2) B_1))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_4 (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_b _let_3) (tptp.fun _let_1 _let_2) (tptp.product_prod_case X_b X_c _let_2) C_1) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) A_2) B_1)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_2 F1 A_2) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_1 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) F1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_2) B_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_2 F A_2) B_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_1 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) F) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_2) B_1))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.complex))) (let ((_let_2 (tptp.suminf tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.complex) X_3)) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP _let_1 tptp.complex _let_2 X_3)) (tptp.hAPP _let_1 tptp.complex _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun _let_1 _let_1) (tptp.combb tptp.complex tptp.complex tptp.nat) tptp.cnj) X_3))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (R_3 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.product_prod X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_3 _let_1 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_3 _let_1) (tptp.product_prod_case X_a X_b _let_1) R_3) (tptp.hAPP X_b _let_3 (tptp.hAPP X_a (tptp.fun X_b _let_3) (tptp.product_Pair X_a X_b) A_2) B_1)) C_1)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_b _let_1 (tptp.hAPP X_a _let_2 R_3 A_2) B_1) C_1))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_2 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) F) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) A_2) B_1))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 F A_2) B_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod_case X_a X_b tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun _let_4 _let_4))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_5 _let_3 _let_1 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_5) (tptp.combb _let_4 _let_4 X_a) (tptp.hAPP _let_6 _let_7 (tptp.combb tptp.bool tptp.bool X_b) (tptp.hAPP tptp.bool _let_6 tptp.fconj P_1))) Q_1)) X_2)) (and (tptp.hBOOL P_1) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_5 _let_3 _let_1 Q_1) X_2)))))))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.complex))) (let ((_let_2 (tptp.summable tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun _let_1 _let_1) (tptp.combb tptp.complex tptp.complex tptp.nat) tptp.cnj) X_3))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable tptp.complex) X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.re) X_3))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable tptp.complex) X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.im) X_3))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable tptp.complex) X_3)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP _let_2 tptp.complex (tptp.suminf tptp.complex) X_3)) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.re) X_3))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable tptp.complex) X_3)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP _let_2 tptp.complex (tptp.suminf tptp.complex) X_3)) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.im) X_3))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.fun _let_1 _let_3))) (let ((_let_7 (tptp.fun _let_1 _let_4))) (let ((_let_8 (tptp.fun _let_4 _let_4))) (let ((_let_9 (tptp.fun _let_1 _let_8))) (let ((_let_10 (tptp.product_prod _let_1 _let_1))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (= (tptp.finite_psubset X_a) (tptp.hAPP _let_11 _let_11 (tptp.collect _let_10) (tptp.hAPP _let_7 _let_11 (tptp.product_prod_case _let_1 _let_1 tptp.bool) (tptp.hAPP _let_4 _let_7 (tptp.hAPP _let_9 (tptp.fun _let_4 _let_7) (tptp.combc _let_1 _let_4 _let_4) (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun _let_3 _let_8) (tptp.fun _let_6 _let_9) (tptp.combb _let_3 _let_8 _let_1) (tptp.combs _let_1 tptp.bool tptp.bool)) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_7 _let_6) (tptp.combb _let_4 _let_3 _let_1) (tptp.hAPP (tptp.fun tptp.bool _let_2) _let_5 (tptp.combb tptp.bool _let_2 _let_1) tptp.fconj)) (tptp.ord_less _let_1)))) (tptp.finite_finite_1 X_a))))))))))))))))) _let_170 (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.product_Pair tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat _let_3))) (let ((_let_6 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 tptp.divmod_nat Ma) N_1))) (let ((_let_7 (tptp.zero_zero tptp.nat))) (let ((_let_8 (or (= N_1 _let_7) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) Ma) N_1))))) (and (=> _let_8 (= _let_6 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_4 _let_7) Ma))) (=> (not _let_8) (= _let_6 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_2) (tptp.product_prod_case tptp.nat tptp.nat _let_2) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_1 _let_5) (tptp.combb tptp.nat _let_3 tptp.nat) _let_4) tptp.suc)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 tptp.divmod_nat (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) Ma) N_1)) N_1)))))))))))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.fun _let_6 _let_7))) (let ((_let_9 (tptp.fun tptp.real _let_7))) (let ((_let_10 (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_9 _let_9 (tptp.combc tptp.real tptp.real _let_6) (tptp.hAPP _let_9 _let_9 (tptp.hAPP (tptp.fun _let_7 _let_7) (tptp.fun _let_9 _let_9) (tptp.combb _let_7 _let_7 tptp.real) (tptp.combc tptp.real tptp.real tptp.real)) (tptp.hAPP _let_7 _let_9 (tptp.hAPP _let_8 (tptp.fun _let_7 _let_9) (tptp.combb _let_6 _let_7 tptp.real) (tptp.hAPP _let_7 _let_8 (tptp.combb tptp.real _let_6 tptp.real) (tptp.inverse_divide tptp.real))) (tptp.plus_plus tptp.real)))) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_11 (tptp.product_Pair tptp.real tptp.real))) (let ((_let_12 (tptp.fun tptp.real _let_1))) (let ((_let_13 (tptp.fun _let_6 _let_12))) (let ((_let_14 (tptp.fun tptp.real _let_13))) (let ((_let_15 (tptp.fun tptp.real _let_12))) (let ((_let_16 (tptp.hAPP _let_7 _let_15 (tptp.hAPP _let_14 (tptp.fun _let_7 _let_15) (tptp.combs tptp.real _let_6 _let_12) (tptp.hAPP _let_15 _let_14 (tptp.hAPP (tptp.fun _let_12 _let_13) (tptp.fun _let_15 _let_14) (tptp.combb _let_12 _let_13 tptp.real) (tptp.combb tptp.real _let_1 tptp.real)) _let_11)) _let_10))) (let ((_let_17 (tptp.fun _let_6 _let_15))) (let ((_let_18 (tptp.fun tptp.real _let_15))) (let ((_let_19 (tptp.fun tptp.real tptp.bool))) (let ((_let_20 (tptp.fun _let_12 _let_19))) (let ((_let_21 (tptp.fun tptp.real _let_19))) (let ((_let_22 (tptp.fun _let_1 _let_1))) (let ((_let_23 (tptp.fun _let_1 _let_22))) (let ((_let_24 (tptp.fun tptp.real _let_23))) (let ((_let_25 (tptp.fun _let_19 _let_24))) (let ((_let_26 (tptp.fun tptp.real _let_24))) (let ((_let_27 (tptp.fun tptp.real _let_22))) (let ((_let_28 (tptp.fun _let_12 _let_27))) (let ((_let_29 (tptp.fun tptp.real _let_28))) (let ((_let_30 (tptp.fun tptp.real _let_27))) (let ((_let_31 (tptp.fun _let_12 _let_12))) (let ((_let_32 (tptp.fun tptp.real _let_31))) (= (tptp.hAPP tptp.nat _let_1 _let_5 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_15 _let_22 (tptp.product_prod_case tptp.real tptp.real _let_1) (tptp.hAPP _let_15 _let_15 (tptp.hAPP _let_32 (tptp.fun _let_15 _let_15) (tptp.combs tptp.real _let_12 _let_12) (tptp.hAPP _let_30 _let_32 (tptp.hAPP (tptp.fun _let_27 _let_31) (tptp.fun _let_30 _let_32) (tptp.combb _let_27 _let_31 tptp.real) (tptp.combs tptp.real _let_1 _let_1)) (tptp.hAPP _let_15 _let_30 (tptp.hAPP _let_29 (tptp.fun _let_15 _let_30) (tptp.combs tptp.real _let_12 _let_27) (tptp.hAPP _let_26 _let_29 (tptp.hAPP (tptp.fun _let_24 _let_28) (tptp.fun _let_26 _let_29) (tptp.combb _let_24 _let_28 tptp.real) (tptp.combs tptp.real _let_1 _let_22)) (tptp.hAPP _let_21 _let_26 (tptp.hAPP _let_25 (tptp.fun _let_21 _let_26) (tptp.combb _let_19 _let_24 tptp.real) (tptp.hAPP (tptp.fun tptp.bool _let_23) _let_25 (tptp.combb tptp.bool _let_23 tptp.real) (tptp.if _let_1))) (tptp.hAPP _let_15 _let_21 (tptp.hAPP _let_20 (tptp.fun _let_15 _let_21) (tptp.combb _let_12 _let_19 tptp.real) (tptp.hAPP _let_4 _let_20 (tptp.combb _let_1 tptp.bool tptp.real) P_1)) _let_16)))) (tptp.hAPP _let_6 _let_15 (tptp.hAPP _let_14 _let_17 (tptp.combc tptp.real _let_6 _let_12) (tptp.hAPP _let_18 _let_14 (tptp.hAPP (tptp.fun _let_15 _let_13) (tptp.fun _let_18 _let_14) (tptp.combb _let_15 _let_13 tptp.real) (tptp.combs tptp.real tptp.real _let_1)) (tptp.hAPP _let_7 _let_18 (tptp.hAPP _let_17 (tptp.fun _let_7 _let_18) (tptp.combb _let_6 _let_15 tptp.real) (tptp.hAPP _let_15 _let_17 (tptp.combb tptp.real _let_12 tptp.real) _let_11)) _let_10))) (tptp.combi tptp.real))))) _let_16)) (tptp.hAPP tptp.nat _let_1 _let_5 N_1)))))))))))))))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.banach X_a) (forall ((F $$unsorted) (N_4 $$unsorted) (C_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) C_1) (tptp.one_one tptp.real))) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_4) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) C_1) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP tptp.nat X_a F N_2)))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.summable X_a) F))))))) (forall ((X_a $$unsorted)) (=> (tptp.banach X_a) (forall ((F $$unsorted) (C_1 $$unsorted) (N_4 $$unsorted)) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_4) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2)))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) C_1) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP tptp.nat X_a F N_2)))))))) (or (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) C_1)) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.summable X_a) F))))))) (forall ((A_2 $$unsorted) (R_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_1)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.real) tptp.bool (tptp.summable tptp.real) A_2)) (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP _let_3 tptp.real (tptp.suminf tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_3) (tptp.combb tptp.nat tptp.real tptp.nat) A_2) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) N_2))))) R_1))))))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (Z $$unsorted) (C_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (= (tptp.ti _let_2 P_4) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) A_4) B_4)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) Z) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) C_1 A_4) B_4))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c (tptp.fun _let_1 tptp.bool) (tptp.member X_c) Z) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b _let_1)) (tptp.fun _let_2 _let_1) (tptp.product_prod_case X_a X_b _let_1) C_1) P_4))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted) (C_1 $$unsorted) (P_4 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b _let_1)) (tptp.fun _let_2 _let_1) (tptp.product_prod_case X_a X_b _let_1) C_1) P_4) Z)) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (= (tptp.ti _let_2 P_4) (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) C_1 X_2) Y_2) Z)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (Z $$unsorted) (C_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.product_prod X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Z) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_c _let_1)) (tptp.fun _let_2 _let_1) (tptp.product_prod_case X_b X_c _let_1) C_1) P_4))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.product_prod X_b X_c))) (=> (= (tptp.ti _let_2 P_4) (tptp.hAPP X_c _let_2 (tptp.hAPP X_b (tptp.fun X_c _let_2) (tptp.product_Pair X_b X_c) X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Z) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) C_1 X_2) Y_2))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (C_1 $$unsorted) (X_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) A_4) B_4) (tptp.ti _let_2 P_4)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) C_1 A_4) B_4) X_1)))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun X_b _let_1)) (tptp.fun _let_2 _let_1) (tptp.product_prod_case X_a X_b _let_1) C_1) P_4) X_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (C_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (=> (= (tptp.ti _let_1 P_4) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) A_4) B_4)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) C_1 A_4) B_4))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_1 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) C_1) P_4))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (C_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun X_a (tptp.fun X_b tptp.bool)) (tptp.fun _let_1 tptp.bool) (tptp.product_prod_case X_a X_b tptp.bool) C_1) P_4)) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (=> (= (tptp.ti _let_1 P_4) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) C_1 X_2) Y_2)))))))))) (forall ((L $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.pdivmod K) L))) (let ((_let_4 (tptp.minus_minus tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (let ((_let_6 (tptp.uminus_uminus tptp.int))) (let ((_let_7 (tptp.fun tptp.int _let_5))) (let ((_let_8 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_9 (tptp.fun tptp.int _let_2))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.hAPP _let_9 _let_10 (tptp.combb tptp.int _let_2 tptp.int) _let_8))) (let ((_let_12 (tptp.fun _let_5 _let_2))) (let ((_let_13 (tptp.fun tptp.int _let_12))) (let ((_let_14 (tptp.zero_zero tptp.int))) (let ((_let_15 (tptp.fun tptp.int tptp.bool))) (let ((_let_16 (tptp.fun tptp.int _let_15))) (let ((_let_17 (tptp.if _let_1))) (let ((_let_18 (tptp.fun _let_1 _let_1))) (let ((_let_19 (tptp.fun _let_1 _let_18))) (let ((_let_20 (tptp.fun tptp.int _let_19))) (let ((_let_21 (tptp.fun tptp.int _let_18))) (let ((_let_22 (tptp.fun _let_1 _let_21))) (let ((_let_23 (tptp.fun tptp.int _let_21))) (let ((_let_24 (tptp.fun _let_2 _let_2))) (let ((_let_25 (tptp.fun tptp.int _let_24))) (let ((_let_26 (tptp.ord_less tptp.int))) (let ((_let_27 (tptp.fun tptp.bool tptp.bool))) (let ((_let_28 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.divmod_int K) L))) (let ((_let_29 (= (tptp.ti tptp.int L) _let_14))) (let ((_let_30 (tptp.hAPP tptp.int _let_2 _let_8 _let_14))) (let ((_let_31 (= (tptp.ti tptp.int K) _let_14))) (and (=> _let_31 (= _let_28 (tptp.hAPP tptp.int _let_1 _let_30 _let_14))) (=> (not _let_31) (and (=> _let_29 (= _let_28 (tptp.hAPP tptp.int _let_1 _let_30 K))) (=> (not _let_29) (= _let_28 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_18 (tptp.product_apsnd tptp.int tptp.int tptp.int) (tptp.hAPP tptp.int _let_5 (tptp.times_times tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.sgn_sgn tptp.int) L))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_18 (tptp.hAPP tptp.bool _let_19 _let_17 (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool _let_27 tptp.fdisj (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool _let_27 tptp.fconj (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_26 _let_14) L)) (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 (tptp.ord_less_eq tptp.int) _let_14) K))) (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool _let_27 tptp.fconj (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_26 L) _let_14)) (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_15 _let_26 K) _let_14)))) _let_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_9 _let_18 (tptp.product_prod_case tptp.int tptp.int _let_1) (tptp.hAPP _let_9 _let_9 (tptp.hAPP _let_25 (tptp.fun _let_9 _let_9) (tptp.combs tptp.int _let_2 _let_2) (tptp.hAPP _let_23 _let_25 (tptp.hAPP (tptp.fun _let_21 _let_24) (tptp.fun _let_23 _let_25) (tptp.combb _let_21 _let_24 tptp.int) (tptp.combs tptp.int _let_1 _let_1)) (tptp.hAPP _let_2 _let_23 (tptp.hAPP _let_22 (tptp.fun _let_2 _let_23) (tptp.combb _let_1 _let_21 tptp.int) (tptp.hAPP _let_20 _let_22 (tptp.combc tptp.int _let_1 _let_18) (tptp.hAPP _let_15 _let_20 (tptp.hAPP (tptp.fun tptp.bool _let_19) (tptp.fun _let_15 _let_20) (tptp.combb tptp.bool _let_19 tptp.int) _let_17) (tptp.hAPP tptp.int _let_15 (tptp.hAPP _let_16 _let_16 (tptp.combc tptp.int tptp.int tptp.bool) (tptp.fequal tptp.int)) _let_14)))) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_9 _let_9 (tptp.combc tptp.int tptp.int _let_1) (tptp.hAPP _let_5 _let_9 _let_11 _let_6)) _let_14)))) (tptp.hAPP _let_5 _let_9 (tptp.hAPP _let_13 _let_10 (tptp.combc tptp.int _let_5 _let_2) (tptp.hAPP _let_9 _let_13 (tptp.hAPP (tptp.fun _let_2 _let_12) (tptp.fun _let_9 _let_13) (tptp.combb _let_2 _let_12 tptp.int) (tptp.combb tptp.int _let_1 tptp.int)) (tptp.hAPP _let_5 _let_9 _let_11 (tptp.hAPP tptp.int _let_5 (tptp.hAPP _let_7 _let_7 (tptp.combc tptp.int tptp.int tptp.int) (tptp.hAPP _let_5 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_7) (tptp.combb tptp.int _let_5 tptp.int) _let_4) _let_6)) (tptp.one_one tptp.int))))) (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) L))))) _let_3)))))))))))))))))))))))))))))))))))))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.product_prod X_a X_c))) (= (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_2 _let_1) (tptp.product_apsnd X_c X_b X_a) F) (tptp.hAPP X_c _let_2 (tptp.hAPP X_a (tptp.fun X_c _let_2) (tptp.product_Pair X_a X_c) X_1) Y_1)) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_1) (tptp.hAPP X_c X_b F Y_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_c))) (let ((_let_2 (tptp.product_prod X_a X_b))) (= (tptp.hAPP _let_2 X_a (tptp.product_fst X_a X_b) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_c X_b) (tptp.fun _let_1 _let_2) (tptp.product_apsnd X_c X_b X_a) F) X_1)) (tptp.hAPP _let_1 X_a (tptp.product_fst X_a X_c) X_1))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (F $$unsorted) (X_1 $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_c))) (let ((_let_2 (tptp.hAPP _let_1 X_c (tptp.product_snd X_a X_c) X_1))) (let ((_let_3 (tptp.product_apsnd X_c X_b X_a))) (let ((_let_4 (tptp.product_prod X_a X_b))) (let ((_let_5 (tptp.fun _let_1 _let_4))) (let ((_let_6 (tptp.fun X_c X_b))) (= (= (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_6 _let_5 _let_3 F) X_1) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_6 _let_5 _let_3 G) X_1)) (= (tptp.hAPP X_c X_b F _let_2) (tptp.hAPP X_c X_b G _let_2)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_c $$unsorted) (F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (let ((_let_2 (tptp.product_prod X_b X_a))) (= (tptp.hAPP _let_2 X_a (tptp.product_snd X_b X_a) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_c X_a) (tptp.fun _let_1 _let_2) (tptp.product_apsnd X_c X_a X_b) F) X_1)) (tptp.hAPP X_c X_a F (tptp.hAPP _let_1 X_c (tptp.product_snd X_b X_c) X_1)))))) _let_143 (forall ((L $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.pdivmod K) L))) (let ((_let_4 (tptp.minus_minus tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (let ((_let_6 (tptp.uminus_uminus tptp.int))) (let ((_let_7 (tptp.fun tptp.int _let_5))) (let ((_let_8 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_9 (tptp.fun tptp.int _let_2))) (let ((_let_10 (tptp.fun _let_5 _let_9))) (let ((_let_11 (tptp.hAPP _let_9 _let_10 (tptp.combb tptp.int _let_2 tptp.int) _let_8))) (let ((_let_12 (tptp.fun _let_5 _let_2))) (let ((_let_13 (tptp.fun tptp.int _let_12))) (let ((_let_14 (tptp.zero_zero tptp.int))) (let ((_let_15 (tptp.fequal tptp.int))) (let ((_let_16 (tptp.fun tptp.int tptp.bool))) (let ((_let_17 (tptp.fun tptp.int _let_16))) (let ((_let_18 (tptp.if _let_1))) (let ((_let_19 (tptp.fun _let_1 _let_1))) (let ((_let_20 (tptp.fun _let_1 _let_19))) (let ((_let_21 (tptp.fun tptp.int _let_20))) (let ((_let_22 (tptp.fun tptp.int _let_19))) (let ((_let_23 (tptp.fun _let_1 _let_22))) (let ((_let_24 (tptp.fun tptp.int _let_22))) (let ((_let_25 (tptp.fun _let_2 _let_2))) (let ((_let_26 (tptp.fun tptp.int _let_25))) (let ((_let_27 (tptp.sgn_sgn tptp.int))) (let ((_let_28 (tptp.hAPP tptp.int tptp.int _let_27 L))) (let ((_let_29 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.divmod_int K) L))) (let ((_let_30 (= (tptp.ti tptp.int L) _let_14))) (let ((_let_31 (tptp.hAPP tptp.int _let_2 _let_8 _let_14))) (let ((_let_32 (= (tptp.ti tptp.int K) _let_14))) (and (=> _let_32 (= _let_29 (tptp.hAPP tptp.int _let_1 _let_31 _let_14))) (=> (not _let_32) (and (=> _let_30 (= _let_29 (tptp.hAPP tptp.int _let_1 _let_31 K))) (=> (not _let_30) (= _let_29 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_19 (tptp.product_apsnd tptp.int tptp.int tptp.int) (tptp.hAPP tptp.int _let_5 (tptp.times_times tptp.int) _let_28)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 _let_19 (tptp.hAPP tptp.bool _let_20 _let_18 (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_16 _let_15 (tptp.hAPP tptp.int tptp.int _let_27 K)) _let_28)) _let_3) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_9 _let_19 (tptp.product_prod_case tptp.int tptp.int _let_1) (tptp.hAPP _let_9 _let_9 (tptp.hAPP _let_26 (tptp.fun _let_9 _let_9) (tptp.combs tptp.int _let_2 _let_2) (tptp.hAPP _let_24 _let_26 (tptp.hAPP (tptp.fun _let_22 _let_25) (tptp.fun _let_24 _let_26) (tptp.combb _let_22 _let_25 tptp.int) (tptp.combs tptp.int _let_1 _let_1)) (tptp.hAPP _let_2 _let_24 (tptp.hAPP _let_23 (tptp.fun _let_2 _let_24) (tptp.combb _let_1 _let_22 tptp.int) (tptp.hAPP _let_21 _let_23 (tptp.combc tptp.int _let_1 _let_19) (tptp.hAPP _let_16 _let_21 (tptp.hAPP (tptp.fun tptp.bool _let_20) (tptp.fun _let_16 _let_21) (tptp.combb tptp.bool _let_20 tptp.int) _let_18) (tptp.hAPP tptp.int _let_16 (tptp.hAPP _let_17 _let_17 (tptp.combc tptp.int tptp.int tptp.bool) _let_15) _let_14)))) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_9 _let_9 (tptp.combc tptp.int tptp.int _let_1) (tptp.hAPP _let_5 _let_9 _let_11 _let_6)) _let_14)))) (tptp.hAPP _let_5 _let_9 (tptp.hAPP _let_13 _let_10 (tptp.combc tptp.int _let_5 _let_2) (tptp.hAPP _let_9 _let_13 (tptp.hAPP (tptp.fun _let_2 _let_12) (tptp.fun _let_9 _let_13) (tptp.combb _let_2 _let_12 tptp.int) (tptp.combb tptp.int _let_1 tptp.int)) (tptp.hAPP _let_5 _let_9 _let_11 (tptp.hAPP tptp.int _let_5 (tptp.hAPP _let_7 _let_7 (tptp.combc tptp.int tptp.int tptp.int) (tptp.hAPP _let_5 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_7) (tptp.combb tptp.int _let_5 tptp.int) _let_4) _let_6)) (tptp.one_one tptp.int))))) (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) L))))) _let_3))))))))))))))))))))))))))))))))))))))))) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.suminf tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.summable tptp.real))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.nat tptp.real F N_2))) (tptp.hAPP tptp.nat tptp.real G N_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 G)) (and (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 F)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_2 tptp.real _let_1 F)) (tptp.hAPP _let_2 tptp.real _let_1 G)))))))))) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) F)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real F N_2)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) F))))))) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) F)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real F N_2)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) F))))))) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real F N_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) F)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) F))))))) (forall ((D_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (let ((_let_6 (tptp.fun tptp.int _let_1))) (let ((_let_7 (tptp.product_prod tptp.int tptp.int))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (= (tptp.hAPP tptp.int _let_8 tptp.int_ge_less_than D_1) (tptp.hAPP _let_8 _let_8 (tptp.collect _let_7) (tptp.hAPP _let_6 _let_8 (tptp.product_prod_case tptp.int tptp.int tptp.bool) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_6 _let_6) (tptp.combs tptp.int _let_1 _let_1) (tptp.hAPP _let_3 _let_5 (tptp.hAPP (tptp.fun _let_2 _let_4) (tptp.fun _let_3 _let_5) (tptp.combb _let_2 _let_4 tptp.int) (tptp.combb tptp.bool tptp.bool tptp.int)) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.bool _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.bool _let_2 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) D_1)))) (tptp.ord_less tptp.int)))))))))))))) (forall ((D_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun tptp.int _let_1))) (let ((_let_6 (tptp.product_prod tptp.int tptp.int))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (= (tptp.hAPP tptp.int _let_7 tptp.int_ge_less_than2 D_1) (tptp.hAPP _let_7 _let_7 (tptp.collect _let_6) (tptp.hAPP _let_5 _let_7 (tptp.product_prod_case tptp.int tptp.int tptp.bool) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_5) (tptp.combb _let_1 _let_1 tptp.int) (tptp.hAPP _let_3 _let_4 (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.bool _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.bool _let_2 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) D_1)))) (tptp.ord_less tptp.int))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.hAPP _let_1 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_2) (tptp.combb tptp.nat _let_1 tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.one_one tptp.nat)))) (let ((_let_4 (tptp.power_power tptp.real))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (let ((_let_6 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_7 (tptp.fun _let_1 _let_5))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.combb tptp.real _let_8 tptp.nat))) (let ((_let_10 (tptp.fun tptp.nat _let_8))) (let ((_let_11 (tptp.fun _let_5 _let_10))) (let ((_let_12 (tptp.fun tptp.real _let_8))) (let ((_let_13 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_14 (tptp.fun _let_5 _let_5))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_5 (tptp.fun tptp.real tptp.bool) (tptp.sums tptp.real) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_10 _let_14 _let_13 (tptp.hAPP _let_5 _let_10 (tptp.hAPP _let_12 _let_11 _let_9 (tptp.times_times tptp.real)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_10 _let_14 _let_13 (tptp.hAPP _let_5 _let_10 (tptp.hAPP _let_12 _let_11 _let_9 (tptp.inverse_divide tptp.real)) (tptp.hAPP tptp.real _let_5 _let_4 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_5 _let_7 _let_6 (tptp.real_1 tptp.nat)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb tptp.nat tptp.nat tptp.nat) (tptp.fact_fact tptp.nat)) _let_3))))) (tptp.hAPP _let_1 _let_5 (tptp.hAPP _let_5 _let_7 _let_6 (tptp.hAPP tptp.real _let_5 _let_4 X_1)) _let_3))) (tptp.hAPP tptp.real tptp.real tptp.sin X_1)))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.cauchy tptp.real) X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.cauchy X_a) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun _let_2 _let_1) (tptp.combb tptp.real X_a tptp.nat) (tptp.of_real X_a)) X_3))))))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 (tptp.fun X_a tptp.bool) (tptp.sums X_a) (tptp.hAPP X_a _let_2 (tptp.combk X_a tptp.nat) _let_1)) _let_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((C_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) C_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.sums X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 F) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_3 _let_3) (tptp.combb X_a X_a tptp.nat) _let_2) F)) (tptp.hAPP X_a X_a _let_2 A_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((C_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.sums X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 F) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) F)) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) C_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.sums X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 X_3) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_3 _let_3) (tptp.combb X_a X_a tptp.nat) _let_2) X_3)) (tptp.hAPP X_a X_a _let_2 A_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.sums X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 X_3) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) Y_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.sums X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 _let_4 _let_3 X_3) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 _let_4 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) _let_1) X_3)) (tptp.hAPP X_a X_a _let_1 A_2))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_3 (tptp.fun tptp.real tptp.bool) (tptp.sums tptp.real) X_3) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 (tptp.fun X_a tptp.bool) (tptp.sums X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real X_a tptp.nat) _let_1) X_3)) (tptp.hAPP tptp.real X_a _let_1 A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.sums X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 X_3) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) Y_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((C_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.sums X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 F) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) F)) C_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) C_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_3 $$unsorted) (B_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.sums X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 X_3) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 Y_3) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_3)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_3 $$unsorted) (B_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.sums X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 X_3) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 Y_3) B_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_3)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.t2_space X_a)) (forall ((F $$unsorted) (Sa $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.sums X_a) F) Sa)) (= (tptp.ti X_a Sa) (tptp.hAPP _let_1 X_a (tptp.suminf X_a) F))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (forall ((F $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.summable X_a) F)) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun X_a tptp.bool) (tptp.sums X_a) F) X1))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (forall ((F $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.sums X_a) F) L)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) F))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.t2_space X_a)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) F)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.sums X_a) F) (tptp.hAPP _let_1 X_a (tptp.suminf X_a) F)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.t2_space X_a)) (forall ((F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.sums X_a) F) X_1)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) F)) (= (tptp.hAPP _let_1 X_a (tptp.suminf X_a) F) (tptp.ti X_a X_1)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (forall ((Sa $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.sums X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (= (tptp.hAPP tptp.nat X_a F (tptp.zero_zero tptp.nat)) (tptp.zero_zero X_a)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_3) (tptp.combb tptp.nat X_a tptp.nat) F) tptp.suc)) Sa)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_2 _let_1 F) Sa))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((F $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.sums X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_2 _let_1 (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_3) (tptp.combb tptp.nat X_a tptp.nat) F) tptp.suc)) L)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_2 _let_1 F) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) L) (tptp.hAPP tptp.nat X_a F (tptp.zero_zero tptp.nat))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_1 (tptp.fun tptp.real tptp.bool) (tptp.sums tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) tptp.sin_coeff)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (tptp.hAPP tptp.real tptp.real tptp.sin X_1))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_1 (tptp.fun tptp.real tptp.bool) (tptp.sums tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) tptp.cos_coeff)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (tptp.hAPP tptp.real tptp.real tptp.cos X_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X_1)) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 (tptp.fun X_a tptp.bool) (tptp.sums X_a) (tptp.hAPP X_a _let_3 (tptp.power_power X_a) X_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.inverse_divide X_a) _let_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.minus_minus X_a) _let_1) X_1))))))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_49 _let_55 (tptp.sums tptp.real) (tptp.hAPP _let_25 _let_49 (tptp.hAPP _let_49 _let_82 _let_81 (tptp.hAPP tptp.real _let_49 _let_139 _let_138)) tptp.suc)) _let_136)) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.cauchy X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 X_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X_1)) X_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.cauchy X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 X_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_a _let_1 tptp.nat) (tptp.times_times X_a)) X_3)) Y_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.cauchy X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 X_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool _let_4 (tptp.hAPP X_a _let_3 (tptp.hAPP _let_2 (tptp.fun X_a _let_3) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_a _let_1 tptp.nat) (tptp.inverse_divide X_a)) X_3)) Y_1))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X_1) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_1)))) (let ((_let_5 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) _let_1))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_3 (tptp.fun tptp.real tptp.bool) (tptp.sums tptp.real) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_7 (tptp.fun _let_3 _let_3) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.hAPP tptp.real _let_7 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 _let_6 _let_4) _let_5))) (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 _let_6 (tptp.one_one tptp.real)) _let_5)))) _let_4)))))))))) (forall ((G $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat _let_5))) (let ((_let_10 (tptp.sums tptp.real))) (let ((_let_11 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_4 _let_11 _let_10 G) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_4 _let_11 _let_10 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP tptp.real _let_9 (tptp.hAPP _let_7 (tptp.fun tptp.real _let_9) (tptp.combc tptp.nat tptp.real _let_5) (tptp.hAPP _let_8 _let_7 (tptp.hAPP (tptp.fun tptp.bool _let_6) (tptp.fun _let_8 _let_7) (tptp.combb tptp.bool _let_6 tptp.nat) (tptp.if tptp.real)) (tptp.even_odd_even tptp.nat))) (tptp.zero_zero tptp.real))) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_4) (tptp.combb tptp.nat tptp.real tptp.nat) G) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.nat _let_2 tptp.nat) (tptp.div_div tptp.nat)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.minus_minus tptp.nat)) (tptp.one_one tptp.nat)))) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) X_1))))))))))))))) (forall ((F $$unsorted) (Y_1 $$unsorted) (G $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))) (let ((_let_3 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.div_div tptp.nat))) (let ((_let_7 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_8 (tptp.fun tptp.nat tptp.real))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.fun tptp.real _let_1))) (let ((_let_11 (tptp.fun tptp.nat _let_10))) (let ((_let_12 (tptp.fun tptp.nat tptp.bool))) (let ((_let_13 (tptp.fun tptp.nat _let_1))) (let ((_let_14 (tptp.sums tptp.real))) (let ((_let_15 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_8 _let_15 _let_14 G) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_8 _let_15 _let_14 F) Y_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_8 _let_15 _let_14 (tptp.hAPP _let_8 _let_8 (tptp.hAPP _let_13 (tptp.fun _let_8 _let_8) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_8 _let_13 (tptp.hAPP _let_11 (tptp.fun _let_8 _let_13) (tptp.combs tptp.nat tptp.real _let_1) (tptp.hAPP _let_12 _let_11 (tptp.hAPP (tptp.fun tptp.bool _let_10) (tptp.fun _let_12 _let_11) (tptp.combb tptp.bool _let_10 tptp.nat) (tptp.if tptp.real)) (tptp.even_odd_even tptp.nat))) (tptp.hAPP _let_4 _let_8 (tptp.hAPP _let_8 _let_9 _let_7 F) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_5 _let_5 _let_3 _let_6) _let_2)))) (tptp.hAPP _let_4 _let_8 (tptp.hAPP _let_8 _let_9 _let_7 G) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_5 _let_5 _let_3 (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_5) (tptp.combb tptp.nat _let_4 tptp.nat) _let_6) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_5 _let_5 _let_3 (tptp.minus_minus tptp.nat)) (tptp.one_one tptp.nat)))) _let_2)))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.plus_plus tptp.real) X_1) Y_1))))))))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_6 (tptp.fun _let_1 _let_4))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.combb tptp.real _let_7 tptp.nat))) (let ((_let_9 (tptp.fun tptp.nat _let_7))) (let ((_let_10 (tptp.fun _let_4 _let_9))) (let ((_let_11 (tptp.fun tptp.real _let_7))) (let ((_let_12 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_13 (tptp.fun _let_4 _let_4))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_4 (tptp.fun tptp.real tptp.bool) (tptp.sums tptp.real) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_13 _let_12 (tptp.hAPP _let_4 _let_9 (tptp.hAPP _let_11 _let_10 _let_8 (tptp.times_times tptp.real)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_13 _let_12 (tptp.hAPP _let_4 _let_9 (tptp.hAPP _let_11 _let_10 _let_8 (tptp.inverse_divide tptp.real)) (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.real_1 tptp.nat)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb tptp.nat tptp.nat tptp.nat) (tptp.fact_fact tptp.nat)) _let_2))))) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP tptp.real _let_4 _let_3 X_1)) _let_2))) (tptp.hAPP tptp.real tptp.real tptp.cos X_1))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_vector X_a) (tptp.ring_1 X_a)) (forall ((C_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.power_power X_a) X_1))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_1 _let_4) (tptp.combb X_a _let_3 tptp.nat) (tptp.times_times X_a)))) (let ((_let_6 (tptp.combs tptp.nat X_a X_a))) (let ((_let_7 (tptp.fun _let_1 _let_1))) (let ((_let_8 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_1 _let_4 _let_5 (tptp.hAPP _let_1 _let_1 (tptp.diffs X_a) C_1))) _let_2))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) _let_8)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.sums X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_1 _let_4 _let_5 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_1 _let_4 _let_5 (tptp.semiring_1_of_nat X_a))) C_1))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat X_a tptp.nat) _let_2) (tptp.hAPP tptp.nat _let_9 (tptp.hAPP _let_10 _let_10 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.minus_minus tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))))) (tptp.hAPP _let_1 X_a (tptp.suminf X_a) _let_8))))))))))))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (F $$unsorted) (V_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP X_a (tptp.fun _let_4 _let_4) (tptp.nat_case X_a) A_2) F))) (let ((_let_6 (tptp.fun X_a X_a))) (= (tptp.hAPP tptp.nat X_a _let_5 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 (tptp.hAPP tptp.bool (tptp.fun X_a _let_6) (tptp.if X_a) (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)) (tptp.hAPP tptp.nat X_a _let_5 N_1)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)) N_1))))))))))) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.complex))) (let ((_let_2 (tptp.sums tptp.complex))) (let ((_let_3 (tptp.fun tptp.complex tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.complex tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 X_3) A_2)) (tptp.hBOOL (tptp.hAPP tptp.complex tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun _let_1 _let_1) (tptp.combb tptp.complex tptp.complex tptp.nat) tptp.cnj) X_3)) (tptp.hAPP tptp.complex tptp.complex tptp.cnj A_2)))))))) (forall ((X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Nat $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.nat_case X_a) F1) F2) (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat)) (tptp.hAPP tptp.nat X_a F2 Nat)))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((F $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.of_real X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_3 (tptp.diffs X_a) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real X_a tptp.nat) _let_2) F)) X_2) (tptp.hAPP tptp.real X_a _let_2 (tptp.hAPP tptp.nat tptp.real (tptp.hAPP _let_1 _let_1 (tptp.diffs tptp.real) F) X_2))))))))) (forall ((X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_1 _let_1 (tptp.hAPP X_a (tptp.fun _let_1 _let_1) (tptp.nat_case X_a) F1) F2) (tptp.zero_zero tptp.nat)) (tptp.ti X_a F1)))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((C_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.diffs X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.uminus_uminus X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 _let_2 _let_1 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) _let_3) C_1)) X_2) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 _let_2 _let_1 C_1) X_2))))))))) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP tptp.complex tptp.bool (tptp.hAPP _let_2 (tptp.fun tptp.complex tptp.bool) (tptp.sums tptp.complex) X_3) A_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_1 (tptp.fun tptp.real tptp.bool) (tptp.sums tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.re) X_3)) (tptp.hAPP tptp.complex tptp.real tptp.re A_2))))))) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (=> (tptp.hBOOL (tptp.hAPP tptp.complex tptp.bool (tptp.hAPP _let_2 (tptp.fun tptp.complex tptp.bool) (tptp.sums tptp.complex) X_3) A_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_1 (tptp.fun tptp.real tptp.bool) (tptp.sums tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.im) X_3)) (tptp.hAPP tptp.complex tptp.real tptp.im A_2))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP _let_1 _let_1 (tptp.diffs tptp.real) tptp.sin_coeff) N_1) (tptp.hAPP tptp.nat tptp.real tptp.cos_coeff N_1)))) _let_135 (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((C_1 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc X_2))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 _let_2 (tptp.diffs X_a) C_1) X_2) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) _let_1)) (tptp.hAPP tptp.nat X_a C_1 _let_1)))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.nat))) (let ((_let_2 (tptp.real_1 tptp.nat))) (let ((_let_3 (tptp.inverse_inverse tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP _let_4 _let_4 (tptp.diffs tptp.real) (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_4 _let_4) (tptp.combb tptp.real tptp.real tptp.nat) _let_3) (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_4) (tptp.combb tptp.nat tptp.real tptp.nat) _let_2) _let_1))) X_2) (tptp.hAPP tptp.real tptp.real _let_3 (tptp.hAPP tptp.nat tptp.real _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 X_2)))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.bool (tptp.fun _let_2 _let_2) (tptp.nat_case tptp.bool) tptp.fFalse) (tptp.hAPP tptp.nat _let_2 _let_1 Ma)) N_1)))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP _let_1 _let_1 (tptp.diffs tptp.real) tptp.cos_coeff) N_1) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.nat tptp.real tptp.sin_coeff N_1))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP tptp.nat tptp.real (tptp.hAPP _let_1 _let_1 (tptp.diffs tptp.real) tptp.cos_coeff) X_2) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) (tptp.hAPP tptp.nat tptp.real tptp.sin_coeff X_2))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) Ma))) (= (tptp.hAPP tptp.nat tptp.nat _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP _let_1 _let_1 (tptp.hAPP tptp.nat (tptp.fun _let_1 _let_1) (tptp.nat_case tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.combi tptp.nat)) (tptp.hAPP tptp.nat tptp.nat _let_2 N_1)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X_1 $$unsorted) (C_1 $$unsorted) (K_3 $$unsorted)) (let ((_let_1 (tptp.power_power X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.diffs X_a))) (let ((_let_4 (tptp.hAPP _let_2 _let_2 _let_3 C_1))) (let ((_let_5 (tptp.fun X_a X_a))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.hAPP (tptp.fun X_a _let_5) (tptp.fun _let_2 _let_6) (tptp.combb X_a _let_5 tptp.nat) (tptp.times_times X_a)))) (let ((_let_8 (tptp.combs tptp.nat X_a X_a))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.hAPP _let_6 _let_9 _let_8 (tptp.hAPP _let_2 _let_6 _let_7 _let_4)))) (let ((_let_11 (tptp.suminf X_a))) (let ((_let_12 (tptp.hAPP _let_6 _let_9 _let_8 (tptp.hAPP _let_2 _let_6 _let_7 C_1)))) (let ((_let_13 (tptp.fun X_a _let_2))) (let ((_let_14 (tptp.fun X_a tptp.bool))) (let ((_let_15 (tptp.norm_norm X_a))) (let ((_let_16 (tptp.hAPP X_a _let_2 _let_1 K_3))) (let ((_let_17 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_17 (tptp.hAPP _let_2 _let_2 _let_12 _let_16))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_17 (tptp.hAPP _let_2 _let_2 _let_10 _let_16))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_17 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_6 _let_9 _let_8 (tptp.hAPP _let_2 _let_6 _let_7 (tptp.hAPP _let_2 _let_2 _let_3 _let_4))) _let_16))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real _let_15 X_1)) (tptp.hAPP X_a tptp.real _let_15 K_3))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_14 (tptp.hAPP _let_5 (tptp.fun X_a _let_14) (tptp.deriv X_a) (tptp.hAPP _let_13 _let_5 (tptp.hAPP (tptp.fun _let_2 X_a) (tptp.fun _let_13 _let_5) (tptp.combb _let_2 X_a X_a) _let_11) (tptp.hAPP _let_13 _let_13 (tptp.hAPP _let_9 (tptp.fun _let_13 _let_13) (tptp.combb _let_2 _let_2 X_a) _let_12) _let_1))) X_1) (tptp.hAPP _let_2 X_a _let_11 (tptp.hAPP _let_2 _let_2 _let_10 (tptp.hAPP X_a _let_2 _let_1 X_1))))))))))))))))))))))))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (F $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_3 _let_3 (tptp.hAPP X_a (tptp.fun _let_3 _let_3) (tptp.nat_case X_a) A_2) F) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.hAPP tptp.bool (tptp.fun X_a _let_2) (tptp.if X_a) (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)) A_2) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (F $$unsorted) (P_1 $$unsorted) (P_4 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_a))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) P_1 (tptp.hAPP _let_1 X_a (tptp.product_snd X_b X_a) P_4)) (tptp.hAPP _let_1 X_b (tptp.product_fst X_b X_a) P_4))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a (tptp.fun X_b tptp.bool) P_1 Y_2) X_2)) (tptp.hBOOL (tptp.hAPP X_c tptp.bool Q_1 (tptp.hAPP X_a X_c (tptp.hAPP X_b (tptp.fun X_a X_c) F X_2) Y_2))))) (tptp.hBOOL (tptp.hAPP X_c tptp.bool Q_1 (tptp.hAPP _let_1 X_c (tptp.hAPP (tptp.fun X_b (tptp.fun X_a X_c)) (tptp.fun _let_1 X_c) (tptp.product_prod_case X_b X_a X_c) F) P_4))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.finite_finite_1 X_a) A_3)) (exists ((N_2 $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.ti _let_3 A_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_1 _let_3) (tptp.image tptp.nat X_a) F_3) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.ord_less tptp.nat)) N_2)))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I_2) A_3)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) (tptp.hAPP X_a tptp.nat F I_2)) X_1) (tptp.one_one tptp.nat))))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co302546470etprod X_a tptp.nat) F) A_3)) X_1) (tptp.one_one tptp.nat))))) (forall ((F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.suminf tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.summable tptp.real))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real F N_2)) (tptp.hAPP tptp.nat tptp.real G N_2)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 F)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 G)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_2 tptp.real _let_1 F)) (tptp.hAPP _let_2 tptp.real _let_1 G)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_3 $$unsorted)) (=> (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) (tptp.hAPP tptp.nat X_a X_3 M_2))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.monoseq X_a) X_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_3 $$unsorted)) (=> (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a X_3 M_2)) (tptp.hAPP tptp.nat X_a X_3 N_2))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.monoseq X_a) X_3)))))) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.combc tptp.real tptp.real tptp.bool))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_6 (tptp.ord_less tptp.real))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.hAPP (tptp.fun tptp.bool _let_7) (tptp.fun _let_1 _let_8) (tptp.combb tptp.bool _let_7 tptp.real) tptp.fconj))) (let ((_let_10 (tptp.combs tptp.real tptp.bool tptp.bool))) (let ((_let_11 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP tptp.real tptp.real tptp.arctan Y_1) (tptp.hAPP _let_1 tptp.real (tptp.the tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_11 _let_10 (tptp.hAPP _let_1 _let_8 _let_9 (tptp.hAPP tptp.real _let_1 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_5)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_11 _let_10 (tptp.hAPP _let_1 _let_8 _let_9 (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_2 _let_2 _let_4 _let_6) _let_5))) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.real _let_1 tptp.real) (tptp.fequal tptp.real)) tptp.tan)) Y_1))))))))))))))))) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.combc tptp.real tptp.real tptp.bool))) (let ((_let_5 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) tptp.pi) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_6 (tptp.ord_less_eq tptp.real))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun tptp.real _let_7))) (let ((_let_9 (tptp.hAPP (tptp.fun tptp.bool _let_7) (tptp.fun _let_1 _let_8) (tptp.combb tptp.bool _let_7 tptp.real) tptp.fconj))) (let ((_let_10 (tptp.combs tptp.real tptp.bool tptp.bool))) (let ((_let_11 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP tptp.real tptp.real tptp.arcsin Y_1) (tptp.hAPP _let_1 tptp.real (tptp.the tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_11 _let_10 (tptp.hAPP _let_1 _let_8 _let_9 (tptp.hAPP tptp.real _let_1 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) _let_5)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_8 _let_11 _let_10 (tptp.hAPP _let_1 _let_8 _let_9 (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_2 _let_2 _let_4 _let_6) _let_5))) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.real _let_1 tptp.real) (tptp.fequal tptp.real)) tptp.sin)) Y_1))))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real tptp.ln X_1) (tptp.hAPP _let_1 tptp.real (tptp.the tptp.real) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.real tptp.real tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.real _let_1 tptp.real) (tptp.fequal tptp.real)) (tptp.exp tptp.real))) X_1))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP _let_2 X_a (tptp.suminf X_a) F) (tptp.hAPP _let_1 X_a (tptp.the X_a) (tptp.hAPP _let_2 _let_1 (tptp.sums X_a) F)))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_2 tptp.root N_1) X_1))) (let ((_let_4 (tptp.ord_less tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 _let_4 X_1) _let_1)))) (let ((_let_7 (tptp.uminus_uminus tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_5))) (let ((_let_9 (tptp.hAPP _let_8 _let_8 (tptp.combc tptp.real tptp.real tptp.bool) (tptp.hAPP _let_2 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_2 _let_8) (tptp.combb tptp.real _let_5 tptp.real) (tptp.fequal tptp.real)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP (tptp.fun tptp.real (tptp.fun tptp.nat tptp.real)) (tptp.fun tptp.nat _let_2) (tptp.combc tptp.real tptp.nat tptp.real) (tptp.power_power tptp.real)) N_1))))) (let ((_let_10 (tptp.hAPP tptp.real _let_5 _let_4 _let_1))) (let ((_let_11 (tptp.fun tptp.bool tptp.bool))) (let ((_let_12 (tptp.fun tptp.real _let_11))) (let ((_let_13 (tptp.hAPP _let_12 (tptp.fun _let_5 _let_5) (tptp.combs tptp.real tptp.bool tptp.bool) (tptp.hAPP _let_5 _let_12 (tptp.hAPP (tptp.fun tptp.bool _let_11) (tptp.fun _let_5 _let_12) (tptp.combb tptp.bool _let_11 tptp.real) tptp.fconj) _let_10)))) (let ((_let_14 (tptp.the tptp.real))) (let ((_let_15 (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool _let_10 X_1)))) (and (=> _let_15 (= _let_3 (tptp.hAPP _let_5 tptp.real _let_14 (tptp.hAPP _let_5 _let_5 _let_13 (tptp.hAPP tptp.real _let_5 _let_9 X_1))))) (=> (not _let_15) (and (=> _let_6 (= _let_3 (tptp.hAPP tptp.real tptp.real _let_7 (tptp.hAPP _let_5 tptp.real _let_14 (tptp.hAPP _let_5 _let_5 _let_13 (tptp.hAPP tptp.real _let_5 _let_9 (tptp.hAPP tptp.real tptp.real _let_7 X_1))))))) (=> (not _let_6) (= _let_3 _let_1))))))))))))))))))))) (forall ((Y_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real _let_1))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.combc tptp.real tptp.real tptp.bool))) (let ((_let_5 (tptp.ord_less_eq tptp.real))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (let ((_let_8 (tptp.hAPP (tptp.fun tptp.bool _let_6) (tptp.fun _let_1 _let_7) (tptp.combb tptp.bool _let_6 tptp.real) tptp.fconj))) (let ((_let_9 (tptp.combs tptp.real tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun _let_1 _let_1))) (= (tptp.hAPP tptp.real tptp.real tptp.arccos Y_1) (tptp.hAPP _let_1 tptp.real (tptp.the tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_7 _let_10 _let_9 (tptp.hAPP _let_1 _let_7 _let_8 (tptp.hAPP tptp.real _let_1 _let_5 (tptp.zero_zero tptp.real)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_7 _let_10 _let_9 (tptp.hAPP _let_1 _let_7 _let_8 (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_2 _let_2 _let_4 _let_5) tptp.pi))) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_2 _let_2 _let_4 (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.real _let_1 tptp.real) (tptp.fequal tptp.real)) tptp.cos)) Y_1)))))))))))))))) _let_134 (= _let_35 _let_131) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_3 $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a X_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hAPP tptp.nat X_a X_3 N_2)))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.monoseq X_a) X_3)))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_3 $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) (tptp.hAPP tptp.nat X_a X_3 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.monoseq X_a) X_3)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun X_a _let_6))) (let ((_let_8 (tptp.fun X_a _let_2))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (= (tptp.hAPP _let_9 _let_1 (tptp.the _let_1) (tptp.hAPP _let_8 _let_9 (tptp.product_prod_case X_a X_b tptp.bool) (tptp.hAPP _let_2 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_2 _let_8) (tptp.combc X_a _let_2 _let_2) (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun _let_4 _let_6) (tptp.fun _let_5 _let_7) (tptp.combb _let_4 _let_6 X_a) (tptp.combb tptp.bool tptp.bool X_b)) (tptp.hAPP _let_3 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_3 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) (tptp.hAPP X_a _let_3 (tptp.fequal X_a) X_1)))) (tptp.hAPP X_b _let_2 (tptp.fequal X_b) Y_1)))) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_1) Y_1)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_2))) (let ((_let_7 (tptp.fun X_a _let_3))) (let ((_let_8 (tptp.the _let_1))) (= (tptp.hAPP _let_5 _let_1 _let_8 P_1) (tptp.hAPP _let_5 _let_1 _let_8 (tptp.hAPP _let_6 _let_5 (tptp.product_prod_case X_a X_b tptp.bool) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_4 (tptp.fun _let_7 _let_6) (tptp.combb _let_3 _let_2 X_a) (tptp.hAPP _let_5 _let_4 (tptp.combb _let_1 tptp.bool X_b) P_1)) (tptp.product_Pair X_a X_b)))))))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) tptp.divmod_nat Ma) N_1) (tptp.hAPP _let_2 _let_1 (tptp.the _let_1) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) tptp.divmod_nat_rel Ma) N_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun X_a _let_2))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 X_b))) (let ((_let_8 (tptp.the _let_1))) (= (tptp.hAPP _let_6 _let_1 _let_8 (tptp.hAPP _let_5 _let_6 (tptp.product_prod_case X_a X_b tptp.bool) P_1)) (tptp.hAPP _let_6 _let_1 _let_8 (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_3 (tptp.fun _let_7 _let_6) (tptp.combs _let_1 X_b tptp.bool) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 _let_1) P_1) (tptp.product_fst X_a X_b))) (tptp.product_snd X_a X_b))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.ring_1_of_int tptp.real))) (let ((_let_4 (tptp.fun tptp.int tptp.real))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.fun tptp.int _let_5))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun tptp.int _let_8))) (= (tptp.hAPP tptp.real tptp.int (tptp.archim2085082626_floor tptp.real) X_1) (tptp.hAPP _let_6 tptp.int (tptp.the tptp.int) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_9 (tptp.fun _let_6 _let_6) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_6 _let_9) (tptp.combb tptp.bool _let_8 tptp.int) tptp.fconj) (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_7 (tptp.fun tptp.real _let_6) (tptp.combc tptp.int tptp.real tptp.bool) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun tptp.real _let_5) (tptp.fun _let_4 _let_7) (tptp.combb tptp.real _let_5 tptp.int) (tptp.ord_less_eq tptp.real)) _let_3)) X_1))) (tptp.hAPP _let_4 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_6) (tptp.combb tptp.real tptp.bool tptp.int) (tptp.hAPP tptp.real _let_5 (tptp.ord_less tptp.real) X_1)) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_4) (tptp.combb tptp.int tptp.real tptp.int) _let_3) (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.int tptp.int tptp.int) (tptp.plus_plus tptp.int)) (tptp.one_one tptp.int))))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (let ((_let_3 (tptp.ring_1_of_int tptp.rat))) (let ((_let_4 (tptp.fun tptp.int tptp.rat))) (let ((_let_5 (tptp.fun tptp.rat tptp.bool))) (let ((_let_6 (tptp.fun tptp.int tptp.bool))) (let ((_let_7 (tptp.fun tptp.int _let_5))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun tptp.int _let_8))) (= (tptp.hAPP tptp.rat tptp.int (tptp.archim2085082626_floor tptp.rat) X_1) (tptp.hAPP _let_6 tptp.int (tptp.the tptp.int) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_9 (tptp.fun _let_6 _let_6) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_6 _let_9) (tptp.combb tptp.bool _let_8 tptp.int) tptp.fconj) (tptp.hAPP tptp.rat _let_6 (tptp.hAPP _let_7 (tptp.fun tptp.rat _let_6) (tptp.combc tptp.int tptp.rat tptp.bool) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun tptp.rat _let_5) (tptp.fun _let_4 _let_7) (tptp.combb tptp.rat _let_5 tptp.int) (tptp.ord_less_eq tptp.rat)) _let_3)) X_1))) (tptp.hAPP _let_4 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_6) (tptp.combb tptp.rat tptp.bool tptp.int) (tptp.hAPP tptp.rat _let_5 (tptp.ord_less tptp.rat) X_1)) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_1 _let_4) (tptp.combb tptp.int tptp.rat tptp.int) _let_3) (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.int tptp.int tptp.int) (tptp.plus_plus tptp.int)) (tptp.one_one tptp.int))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (= (tptp.hAPP X_a X_b G X_2) (tptp.one_one X_b))))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) G) A_3) (tptp.one_one X_b)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.zero_zero X_b)) (tptp.hAPP X_a X_b F X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less X_b) (tptp.zero_zero X_b)) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F) A_3)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((G $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a X_b F X_2))) (let ((_let_2 (tptp.ord_less_eq X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) X_2) A_3)) (and (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 (tptp.zero_zero X_b)) _let_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 _let_2 _let_1) (tptp.hAPP X_a X_b G X_2)))))))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.linordered_semidom X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) (tptp.hAPP X_a X_b F X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F) A_3)))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (F $$unsorted) (V_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.plus_plus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)) N_1))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.hAPP _let_7 _let_5 (tptp.hAPP X_a (tptp.fun _let_7 _let_5) (tptp.nat_rec X_a) A_2) F))) (= (tptp.hAPP tptp.nat X_a _let_8 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 (tptp.hAPP tptp.bool (tptp.fun X_a _let_6) (tptp.if X_a) (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)) (tptp.hAPP tptp.nat X_a _let_8 N_1)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.nat _let_6 F _let_4) (tptp.hAPP tptp.nat X_a _let_8 _let_4))))))))))))) (forall ((A_2 $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_2 (tptp.fun tptp.int _let_1) tptp.rRset2norRR A_3) Ma) A_2))) (let ((_let_4 (tptp.member tptp.int))) (let ((_let_5 (tptp.fun _let_2 tptp.bool))) (let ((_let_6 (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_2 _let_2 tptp.is_RRset A_3) Ma)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 A_2) A_3))))) (let ((_let_7 (tptp.fun _let_2 _let_2))) (let ((_let_8 (tptp.fun tptp.int _let_2))) (let ((_let_9 (tptp.fun tptp.bool tptp.bool))) (let ((_let_10 (tptp.fun tptp.int _let_9))) (and (=> _let_6 (= _let_3 (tptp.hAPP _let_2 tptp.int (tptp.hilbert_Eps tptp.int) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_10 _let_7 (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_10 (tptp.hAPP (tptp.fun tptp.bool _let_9) (tptp.fun _let_2 _let_10) (tptp.combb tptp.bool _let_9 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_2 (tptp.hAPP _let_8 _let_8 (tptp.combc tptp.int tptp.int tptp.bool) (tptp.hAPP tptp.int _let_8 tptp.zcong A_2)) Ma))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.int _let_5) _let_7 (tptp.combc tptp.int _let_2 tptp.bool) _let_4) (tptp.hAPP tptp.int _let_2 tptp.norRRset Ma)))))) (=> (not _let_6) (= _let_3 (tptp.zero_zero tptp.int))))))))))))))) (forall ((X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted) (Nat $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP _let_3 _let_1 (tptp.hAPP X_a (tptp.fun _let_3 _let_1) (tptp.nat_rec X_a) F1) F2))) (= (tptp.hAPP tptp.nat X_a _let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc Nat)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.nat _let_2 F2 Nat) (tptp.hAPP tptp.nat X_a _let_4 Nat)))))))) (forall ((X_a $$unsorted) (F1 $$unsorted) (F2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat (tptp.fun X_a X_a)))) (= (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_a (tptp.fun _let_2 _let_1) (tptp.nat_rec X_a) F1) F2) (tptp.zero_zero tptp.nat)) (tptp.ti X_a F1))))) (forall ((A_2 $$unsorted) (A_3 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 tptp.norRRset Ma))) (let ((_let_3 (tptp.member tptp.int))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun tptp.int _let_1))) (let ((_let_7 (tptp.hAPP tptp.int _let_6 tptp.zcong A_2))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun tptp.int _let_8))) (let ((_let_10 (tptp.hAPP _let_1 tptp.int (tptp.hilbert_Eps tptp.int) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_9 _let_4 (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_1 _let_9) (tptp.combb tptp.bool _let_8 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.int tptp.int tptp.bool) _let_7) Ma))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.int _let_5) _let_4 (tptp.combc tptp.int _let_1 tptp.bool) _let_3) _let_2))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.one_one tptp.int)) Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP _let_1 _let_1 tptp.is_RRset A_3) Ma)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_3 A_2) A_3)) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 _let_7 _let_10) Ma)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int _let_5 _let_3 _let_10) _let_2))))))))))))))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (F $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.hAPP _let_5 _let_3 (tptp.hAPP X_a (tptp.fun _let_5 _let_3) (tptp.nat_rec X_a) A_2) F))) (= (tptp.hAPP tptp.nat X_a _let_6 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.hAPP tptp.bool (tptp.fun X_a _let_4) (tptp.if X_a) (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)) A_2) (tptp.hAPP X_a X_a (tptp.hAPP tptp.nat _let_4 F _let_2) (tptp.hAPP tptp.nat X_a _let_6 _let_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (= (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_1) (tptp.hAPP X_a X_a (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_1) (tptp.semiri532925092at_aux X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_a X_a X_a) (tptp.plus_plus X_a)) (tptp.one_one X_a))) N_1) (tptp.zero_zero X_a)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a _let_2))) (let ((_let_7 (tptp.fun X_a _let_1))) (let ((_let_8 (tptp.product_prod X_a X_b))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (= (tptp.hAPP _let_1 _let_9 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_9) (tptp.prod X_a X_b) A_3) B_2) (tptp.hAPP _let_9 _let_9 (tptp.collect _let_8) (tptp.hAPP _let_7 _let_9 (tptp.product_prod_case X_a X_b tptp.bool) (tptp.hAPP _let_1 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_1 _let_7) (tptp.combc X_a _let_1 _let_1) (tptp.hAPP _let_5 _let_6 (tptp.hAPP (tptp.fun _let_4 _let_2) (tptp.fun _let_5 _let_6) (tptp.combb _let_4 _let_2 X_a) (tptp.combb tptp.bool tptp.bool X_b)) (tptp.hAPP _let_3 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_3 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) (tptp.hAPP _let_3 _let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_3 tptp.bool)) (tptp.fun _let_3 _let_3) (tptp.combc X_a _let_3 tptp.bool) (tptp.member X_a)) A_3)))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) B_2))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((Inc $$unsorted) (I $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_1) (tptp.semiri532925092at_aux X_a) Inc) (tptp.zero_zero tptp.nat)) I) (tptp.ti X_a I)))))) (forall ((X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((Inc $$unsorted) (N_1 $$unsorted) (I $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP _let_1 (tptp.fun tptp.nat _let_1) (tptp.semiri532925092at_aux X_a) Inc))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) I) (tptp.hAPP X_a X_a (tptp.hAPP tptp.nat _let_1 _let_2 N_1) (tptp.hAPP X_a X_a Inc I)))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.real))) (let ((_let_2 (tptp.power_power tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fact_fact tptp.nat))) (let ((_let_5 (tptp.real_1 tptp.nat))) (let ((_let_6 (tptp.times_times tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.zero_zero tptp.nat))) (let ((_let_9 (tptp.fun tptp.nat tptp.bool))) (let ((_let_10 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_11 (tptp.fun tptp.nat tptp.nat))) (let ((_let_12 (tptp.fun _let_11 _let_3))) (let ((_let_13 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_14 (tptp.fun tptp.nat _let_11))) (let ((_let_15 (tptp.combb tptp.real _let_7 tptp.nat))) (let ((_let_16 (tptp.fun tptp.nat _let_7))) (let ((_let_17 (tptp.fun _let_3 _let_16))) (let ((_let_18 (tptp.fun tptp.real _let_7))) (let ((_let_19 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_20 (tptp.fun _let_3 _let_3))) (let ((_let_21 (tptp.fun tptp.nat _let_18))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 (tptp.minus_minus tptp.real) (tptp.hAPP tptp.real tptp.real tptp.sin X_1)) (tptp.hAPP _let_9 tptp.real (tptp.hAPP _let_3 (tptp.fun _let_9 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_16 _let_20 _let_19 (tptp.hAPP _let_3 _let_16 (tptp.hAPP _let_18 _let_17 _let_15 _let_6) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_16 _let_20 _let_19 (tptp.hAPP tptp.real _let_16 (tptp.hAPP _let_21 (tptp.fun tptp.real _let_16) (tptp.combc tptp.nat tptp.real _let_7) (tptp.hAPP _let_9 _let_21 (tptp.hAPP (tptp.fun tptp.bool _let_18) (tptp.fun _let_9 _let_21) (tptp.combb tptp.bool _let_18 tptp.nat) (tptp.if tptp.real)) (tptp.even_odd_even tptp.nat))) (tptp.zero_zero tptp.real))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_16 _let_20 _let_19 (tptp.hAPP _let_3 _let_16 (tptp.hAPP _let_18 _let_17 _let_15 (tptp.inverse_divide tptp.real)) (tptp.hAPP _let_11 _let_3 (tptp.hAPP _let_3 _let_12 _let_10 (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1))) (tptp.hAPP tptp.nat _let_11 (tptp.hAPP _let_14 _let_14 _let_13 (tptp.hAPP _let_11 _let_14 (tptp.hAPP _let_14 (tptp.fun _let_11 _let_14) (tptp.combb tptp.nat _let_11 tptp.nat) (tptp.div_div tptp.nat)) (tptp.hAPP tptp.nat _let_11 (tptp.hAPP _let_14 _let_14 _let_13 (tptp.minus_minus tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_8)))) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (tptp.hAPP _let_11 _let_3 (tptp.hAPP _let_3 _let_12 _let_10 _let_5) _let_4))))) (tptp.hAPP tptp.real _let_3 _let_2 X_1))) (tptp.hAPP tptp.nat _let_9 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_9) (tptp.ord_atLeastLessThan tptp.nat) _let_8) N_1))))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.nat tptp.real _let_5 (tptp.hAPP tptp.nat tptp.nat _let_4 N_1)))) (tptp.hAPP tptp.nat tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real _let_1 X_1)) N_1)))))))))))))))))))))))))) (forall ((U_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_2) (tptp.hAPP tptp.nat tptp.nat F N_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.collect tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat _let_1 tptp.nat) (tptp.ord_less_eq tptp.nat)) F)) U_1))))))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) L) U_1))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.fun _let_4 X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_1 (tptp.hAPP _let_4 X_a (tptp.hAPP _let_2 _let_5 _let_3 F) A_3))) (tptp.hAPP _let_4 X_a (tptp.hAPP _let_2 _let_5 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a X_b) _let_1) F)) A_3))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.zero_zero X_a)) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_1 (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum X_b X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_1 _let_1) (tptp.combb X_a X_a X_b) (tptp.abs_abs X_a)) F)) A_3)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((K $$unsorted) (F $$unsorted) (Sa $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.sums X_a))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 _let_6 _let_5 F) Sa)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 _let_6 _let_5 (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_4 _let_4 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) K))) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) Sa) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_2 (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) K))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((K $$unsorted) (Sa $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.suminf X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable X_a) F)) (=> (= (tptp.hAPP _let_2 X_a _let_5 F) (tptp.ti X_a Sa)) (= (tptp.hAPP _let_2 X_a _let_5 (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_4 _let_4 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) K))) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) Sa) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_2 (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) K)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((K $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.suminf X_a))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.summable X_a) F)) (= (tptp.hAPP _let_3 X_a _let_4 F) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP _let_5 X_a (tptp.hAPP _let_3 (tptp.fun _let_5 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_5) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) K))) (tptp.hAPP _let_3 X_a _let_4 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_3) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) K)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.ring_1_of_int X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.int))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP tptp.int X_a _let_1 (tptp.hAPP _let_4 tptp.int (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.int) (tptp.big_co1399186613setsum X_b tptp.int) F) A_3)) (tptp.hAPP _let_4 X_a (tptp.hAPP _let_2 (tptp.fun _let_4 X_a) (tptp.big_co1399186613setsum X_b X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.int X_a) (tptp.fun _let_3 _let_2) (tptp.combb tptp.int X_a X_b) _let_1) F)) A_3))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.nat))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co1399186613setsum X_b tptp.nat) F) A_3)) (tptp.hAPP _let_4 X_a (tptp.hAPP _let_2 (tptp.fun _let_4 X_a) (tptp.big_co1399186613setsum X_b X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat X_a X_b) _let_1) F)) A_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((F $$unsorted) (N_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun tptp.nat X_a))) (let ((_let_7 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_8 (tptp.fun _let_1 X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP _let_1 X_a (tptp.hAPP _let_6 _let_8 _let_7 F) _let_2)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_1)) R_1)) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_6 _let_8 _let_7 (tptp.hAPP X_a _let_6 (tptp.hAPP _let_5 (tptp.fun X_a _let_6) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun X_a _let_4) (tptp.fun _let_6 _let_5) (tptp.combb X_a _let_4 tptp.nat) _let_3) F)) R_1)) _let_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.times_times tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_atLeastLessThan tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.hAPP tptp.nat _let_5 _let_3 (tptp.zero_zero tptp.nat)))) (let ((_let_7 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_8 (tptp.fun _let_4 X_a))) (let ((_let_9 (tptp.fun tptp.nat X_a))) (let ((_let_10 (tptp.hAPP _let_9 _let_8 _let_7 F))) (let ((_let_11 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_12 (tptp.fun tptp.nat _let_2))) (let ((_let_13 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_12 _let_12 _let_11 _let_1) K))) (let ((_let_14 (tptp.fun tptp.nat _let_5))) (= (tptp.hAPP _let_4 X_a (tptp.hAPP _let_9 _let_8 _let_7 (tptp.hAPP _let_5 _let_9 (tptp.hAPP _let_8 (tptp.fun _let_5 _let_9) (tptp.combb _let_4 X_a tptp.nat) _let_10) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_14 (tptp.fun _let_2 _let_5) (tptp.combs tptp.nat tptp.nat _let_4) (tptp.hAPP _let_2 _let_14 (tptp.hAPP _let_14 (tptp.fun _let_2 _let_14) (tptp.combb tptp.nat _let_5 tptp.nat) _let_3) _let_13)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_12 _let_12 _let_11 (tptp.hAPP _let_2 _let_12 (tptp.hAPP _let_12 (tptp.fun _let_2 _let_12) (tptp.combb tptp.nat _let_2 tptp.nat) (tptp.plus_plus tptp.nat)) _let_13)) K)))) (tptp.hAPP tptp.nat _let_4 _let_6 N_1)) (tptp.hAPP _let_4 X_a _let_10 (tptp.hAPP tptp.nat _let_4 _let_6 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 N_1) K))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.monoid_mult X_a) (tptp.comm_semiring_0 X_a)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) _let_1))) (let ((_let_4 (tptp.minus_minus tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.power_power X_a))) (let ((_let_7 (tptp.fun tptp.nat X_a))) (let ((_let_8 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_7) (tptp.combb tptp.nat X_a tptp.nat) (tptp.hAPP X_a _let_7 _let_6 Y_1)))) (let ((_let_9 (tptp.times_times X_a))) (let ((_let_10 (tptp.fun X_a X_a))) (let ((_let_11 (tptp.fun tptp.nat _let_10))) (let ((_let_12 (tptp.hAPP _let_11 (tptp.fun _let_7 _let_7) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_7 _let_11 (tptp.hAPP (tptp.fun X_a _let_10) (tptp.fun _let_7 _let_11) (tptp.combb X_a _let_10 tptp.nat) _let_9) (tptp.hAPP X_a _let_7 _let_6 X_1))))) (let ((_let_13 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_14 (tptp.fun _let_2 X_a))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_7 _let_14 _let_13 (tptp.hAPP _let_7 _let_7 _let_12 (tptp.hAPP _let_5 _let_7 _let_8 (tptp.hAPP tptp.nat _let_5 _let_4 _let_1)))) _let_3) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_10 _let_9 Y_1) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_7 _let_14 _let_13 (tptp.hAPP _let_7 _let_7 _let_12 (tptp.hAPP _let_5 _let_7 _let_8 (tptp.hAPP tptp.nat _let_5 _let_4 N_1)))) _let_3)))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.power X_a)) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)))) (let ((_let_3 (tptp.power_power X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.hAPP X_a _let_4 _let_3 Y_1))) (let ((_let_6 (tptp.fun tptp.nat tptp.nat))) (let ((_let_7 (tptp.hAPP tptp.nat _let_6 (tptp.minus_minus tptp.nat) N_1))) (let ((_let_8 (tptp.hAPP X_a _let_4 _let_3 X_1))) (let ((_let_9 (tptp.combb tptp.nat X_a tptp.nat))) (let ((_let_10 (tptp.fun _let_6 _let_4))) (let ((_let_11 (tptp.fun X_a X_a))) (let ((_let_12 (tptp.fun tptp.nat _let_11))) (let ((_let_13 (tptp.hAPP (tptp.fun X_a _let_11) (tptp.fun _let_4 _let_12) (tptp.combb X_a _let_11 tptp.nat) (tptp.times_times X_a)))) (let ((_let_14 (tptp.combs tptp.nat X_a X_a))) (let ((_let_15 (tptp.fun _let_4 _let_4))) (let ((_let_16 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_17 (tptp.fun _let_1 X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP _let_4 _let_17 _let_16 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_12 _let_15 _let_14 (tptp.hAPP _let_4 _let_12 _let_13 _let_8)) (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_4 _let_10 _let_9 _let_5) _let_7))) _let_2) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_4 _let_17 _let_16 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_12 _let_15 _let_14 (tptp.hAPP _let_4 _let_12 _let_13 (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_4 _let_10 _let_9 _let_8) _let_7))) _let_5)) _let_2)))))))))))))))))))))) (forall ((F $$unsorted) (N_1 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (let ((_let_3 (tptp.minus_minus tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun tptp.nat tptp.real))) (let ((_let_7 (tptp.big_co1399186613setsum tptp.nat tptp.real))) (let ((_let_8 (tptp.fun _let_1 tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP _let_1 tptp.real (tptp.hAPP _let_6 _let_8 _let_7 F) _let_2)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_4 (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) R_1)) (tptp.hAPP _let_1 tptp.real (tptp.hAPP _let_6 _let_8 _let_7 (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_5 (tptp.fun tptp.real _let_6) (tptp.combc tptp.nat tptp.real tptp.real) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_6 _let_5) (tptp.combb tptp.real _let_4 tptp.nat) _let_3) F)) R_1)) _let_2))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.fun X_b tptp.real))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP _let_4 X_a (tptp.hAPP _let_3 (tptp.fun _let_4 X_a) (tptp.big_co1399186613setsum X_b X_a) F) A_3))) (tptp.hAPP _let_4 tptp.real (tptp.hAPP _let_2 (tptp.fun _let_4 tptp.real) (tptp.big_co1399186613setsum X_b tptp.real) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_3 _let_2) (tptp.combb X_a tptp.real X_b) _let_1) F)) A_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.fun tptp.nat X_a))) (let ((_let_8 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_9 (tptp.fun _let_2 X_a))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_7 _let_9 _let_8 F) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 N_1) K))) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_7 _let_9 _let_8 (tptp.hAPP _let_5 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_7) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_4) K))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 Ma) N_1))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.minus_minus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.hAPP X_a _let_4 (tptp.power_power X_a) X_1))) (let ((_let_6 (tptp.fun tptp.nat tptp.bool))) (=> (not (= (tptp.ti X_a X_1) _let_1)) (= (tptp.hAPP _let_6 X_a (tptp.hAPP _let_4 (tptp.fun _let_6 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) _let_5) (tptp.hAPP tptp.nat _let_6 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_6) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 (tptp.inverse_divide X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_5 N_1)) _let_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 X_1) _let_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((F $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) (let ((_let_3 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.hAPP _let_5 _let_4 _let_3 F))) (let ((_let_7 (tptp.plus_plus tptp.nat))) (let ((_let_8 (tptp.fun tptp.nat tptp.nat))) (let ((_let_9 (tptp.fun tptp.nat _let_8))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP _let_5 _let_4 _let_3 (tptp.hAPP _let_8 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_8 _let_5) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP _let_9 _let_9 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_7) K))) (tptp.hAPP tptp.nat _let_1 _let_2 N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP _let_1 X_a _let_6 (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_8 _let_7 N_1) K)))) (tptp.hAPP _let_1 X_a _let_6 (tptp.hAPP tptp.nat _let_1 _let_2 K)))))))))))))))) (forall ((K $$unsorted) (N_1 $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) (let ((_let_3 (tptp.big_co1399186613setsum tptp.nat tptp.real))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (let ((_let_6 (tptp.hAPP _let_5 _let_4 _let_3 F_3))) (let ((_let_7 (tptp.plus_plus tptp.nat))) (let ((_let_8 (tptp.fun tptp.nat tptp.nat))) (let ((_let_9 (tptp.fun tptp.nat _let_8))) (= (tptp.hAPP _let_1 tptp.real (tptp.hAPP _let_5 _let_4 _let_3 (tptp.hAPP _let_8 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_8 _let_5) (tptp.combb tptp.nat tptp.real tptp.nat) F_3) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP _let_9 _let_9 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_7) K))) (tptp.hAPP tptp.nat _let_1 _let_2 N_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) (tptp.hAPP _let_1 tptp.real _let_6 (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_8 _let_7 N_1) K)))) (tptp.hAPP _let_1 tptp.real _let_6 (tptp.hAPP tptp.nat _let_1 _let_2 K)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (N_1 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) (let ((_let_3 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.hAPP _let_5 _let_4 _let_3 F))) (let ((_let_7 (tptp.plus_plus tptp.nat))) (let ((_let_8 (tptp.fun tptp.nat tptp.nat))) (let ((_let_9 (tptp.fun tptp.nat _let_8))) (= (tptp.hAPP _let_1 X_a _let_6 (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_8 _let_7 N_1) K))) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_5 _let_4 _let_3 (tptp.hAPP _let_8 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_8 _let_5) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP _let_9 _let_9 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_7) K))) (tptp.hAPP tptp.nat _let_1 _let_2 N_1))) (tptp.hAPP _let_1 X_a _let_6 (tptp.hAPP tptp.nat _let_1 _let_2 K)))))))))))))))) (forall ((K $$unsorted) (N_2 $$unsorted) (F_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) (let ((_let_3 (tptp.big_co1399186613setsum tptp.nat tptp.real))) (let ((_let_4 (tptp.fun _let_1 tptp.real))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (let ((_let_6 (tptp.hAPP _let_5 _let_4 _let_3 F_3))) (let ((_let_7 (tptp.plus_plus tptp.nat))) (let ((_let_8 (tptp.fun tptp.nat tptp.nat))) (let ((_let_9 (tptp.fun tptp.nat _let_8))) (= (tptp.hAPP _let_1 tptp.real _let_6 (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_8 _let_7 N_2) K))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP _let_1 tptp.real (tptp.hAPP _let_5 _let_4 _let_3 (tptp.hAPP _let_8 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_8 _let_5) (tptp.combb tptp.nat tptp.real tptp.nat) F_3) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP _let_9 _let_9 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_7) K))) (tptp.hAPP tptp.nat _let_1 _let_2 N_2))) (tptp.hAPP _let_1 tptp.real _let_6 (tptp.hAPP tptp.nat _let_1 _let_2 K)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((G $$unsorted) (A_3 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (let ((_let_7 (tptp.fun _let_6 X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_6 X_a (tptp.hAPP _let_4 _let_7 _let_5 G) A_3)) Y_1) (tptp.hAPP _let_6 X_a (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc X_b X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 X_b) _let_1) G)) Y_1)) A_3)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 _let_1))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 tptp.bool)) _let_2 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 _let_3 B_2))) (let ((_let_5 (tptp.fun X_b X_b))) (let ((_let_6 (tptp.fun X_b _let_5))) (let ((_let_7 (tptp.fun X_a _let_6))) (let ((_let_8 (tptp.fun X_a _let_5))) (let ((_let_9 (tptp.fun X_a X_b))) (let ((_let_10 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_11 (tptp.fun _let_1 X_b))) (let ((_let_12 (tptp.fun tptp.bool tptp.bool))) (let ((_let_13 (tptp.fun X_a _let_12))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (tptp.hAPP _let_1 X_b (tptp.hAPP _let_9 _let_11 _let_10 F) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_13 _let_2 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_13 (tptp.hAPP (tptp.fun tptp.bool _let_12) (tptp.fun _let_1 _let_13) (tptp.combb tptp.bool _let_12 X_a) tptp.fconj) (tptp.hAPP _let_1 _let_1 _let_3 A_3))) _let_4))) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_9 _let_11 _let_10 (tptp.hAPP X_b _let_9 (tptp.hAPP _let_8 (tptp.fun X_b _let_9) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_9 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_9 _let_8) (tptp.combs X_a X_b _let_5) (tptp.hAPP _let_1 _let_7 (tptp.hAPP (tptp.fun tptp.bool _let_6) (tptp.fun _let_1 _let_7) (tptp.combb tptp.bool _let_6 X_a) (tptp.if X_b)) _let_4)) F)) (tptp.zero_zero X_b))) A_3))))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (P_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_1))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_8 (tptp.fun _let_4 X_b))) (let ((_let_9 (tptp.fun _let_4 _let_4))) (let ((_let_10 (tptp.fun tptp.bool tptp.bool))) (let ((_let_11 (tptp.fun X_a _let_10))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (tptp.hAPP _let_4 X_b (tptp.hAPP _let_6 _let_8 _let_7 F) (tptp.hAPP _let_4 _let_4 (tptp.collect X_a) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_11 _let_9 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_11 (tptp.hAPP (tptp.fun tptp.bool _let_10) (tptp.fun _let_4 _let_11) (tptp.combb tptp.bool _let_10 X_a) tptp.fconj) (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_4 tptp.bool)) _let_9 (tptp.combc X_a _let_4 tptp.bool) (tptp.member X_a)) A_3))) P_1))) (tptp.hAPP _let_4 X_b (tptp.hAPP _let_6 _let_8 _let_7 (tptp.hAPP X_b _let_6 (tptp.hAPP _let_5 (tptp.fun X_b _let_6) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_6 _let_5 (tptp.hAPP _let_3 (tptp.fun _let_6 _let_5) (tptp.combs X_a X_b _let_1) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.bool _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.bool _let_2 X_a) (tptp.if X_b)) P_1)) F)) (tptp.zero_zero X_b))) A_3))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_7 (tptp.fun _let_2 X_a))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_7 _let_6 F) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_4) (tptp.combb tptp.nat X_a tptp.nat) F) tptp.suc)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 Ma) N_1))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_c $$unsorted)) (=> (tptp.comm_monoid_add X_c) (forall ((F $$unsorted) (R_3 $$unsorted) (T_3 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun _let_1 _let_1))) (let ((_let_6 (tptp.fun tptp.bool tptp.bool))) (let ((_let_7 (tptp.fun X_a _let_6))) (let ((_let_8 (tptp.fun tptp.bool _let_6))) (let ((_let_9 (tptp.combb _let_1 _let_1 X_b))) (let ((_let_10 (tptp.fun _let_2 _let_2))) (let ((_let_11 (tptp.fun X_a X_c))) (let ((_let_12 (tptp.fun X_b _let_11))) (let ((_let_13 (tptp.fun X_b X_c))) (let ((_let_14 (tptp.fun X_a _let_13))) (let ((_let_15 (tptp.big_co1399186613setsum X_a X_c))) (let ((_let_16 (tptp.fun _let_1 X_c))) (let ((_let_17 (tptp.fun X_b _let_16))) (let ((_let_18 (tptp.big_co1399186613setsum X_b X_c))) (let ((_let_19 (tptp.fun _let_3 X_c))) (let ((_let_20 (tptp.fun _let_3 _let_3))) (let ((_let_21 (tptp.fun X_b _let_6))) (let ((_let_22 (tptp.combb _let_3 _let_3 X_a))) (let ((_let_23 (tptp.fun _let_4 _let_4))) (let ((_let_24 (tptp.fun X_a _let_19))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) S)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_b) T_3)) (= (tptp.hAPP _let_1 X_c (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_24 (tptp.fun _let_4 _let_11) (tptp.combs X_a _let_3 X_c) (tptp.hAPP _let_14 _let_24 (tptp.hAPP (tptp.fun _let_13 _let_19) (tptp.fun _let_14 _let_24) (tptp.combb _let_13 _let_19 X_a) _let_18) F)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_20 _let_23 _let_22 (tptp.collect X_b)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_20 _let_23 _let_22 (tptp.hAPP _let_21 _let_20 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_21 (tptp.hAPP _let_8 (tptp.fun _let_3 _let_21) (tptp.combb tptp.bool _let_6 X_b) tptp.fconj) (tptp.hAPP _let_3 _let_3 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_3 tptp.bool)) _let_20 (tptp.combc X_b _let_3 tptp.bool) (tptp.member X_b)) T_3)))) R_3)))) S) (tptp.hAPP _let_3 X_c (tptp.hAPP _let_13 _let_19 _let_18 (tptp.hAPP _let_2 _let_13 (tptp.hAPP _let_17 (tptp.fun _let_2 _let_13) (tptp.combs X_b _let_1 X_c) (tptp.hAPP _let_12 _let_17 (tptp.hAPP (tptp.fun _let_11 _let_16) (tptp.fun _let_12 _let_17) (tptp.combb _let_11 _let_16 X_b) _let_15) (tptp.hAPP _let_14 _let_12 (tptp.combc X_a X_b X_c) F))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_10 _let_9 (tptp.collect X_a)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_10 _let_9 (tptp.hAPP _let_7 _let_5 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_7 (tptp.hAPP _let_8 (tptp.fun _let_1 _let_7) (tptp.combb tptp.bool _let_6 X_a) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 tptp.bool)) _let_5 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)) S)))) (tptp.hAPP _let_4 _let_2 (tptp.combc X_a X_b tptp.bool) R_3))))) T_3))))))))))))))))))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.real))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP _let_4 tptp.real (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.real) (tptp.big_co1399186613setsum X_b tptp.real) G) A_3)) (tptp.hAPP _let_4 X_a (tptp.hAPP _let_2 (tptp.fun _let_4 X_a) (tptp.big_co1399186613setsum X_b X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real X_a X_b) _let_1) G)) A_3))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((G $$unsorted) (A_3 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (let ((_let_7 (tptp.fun _let_6 X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_6 X_a (tptp.hAPP _let_4 _let_7 _let_5 G) A_3)) Y_1) (tptp.hAPP _let_6 X_a (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc X_b X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 X_b) _let_1) G)) Y_1)) A_3)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X_1))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (let ((_let_6 (tptp.fun _let_5 X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP _let_5 X_a (tptp.hAPP _let_3 _let_6 _let_4 G) A_3)) (tptp.hAPP _let_5 X_a (tptp.hAPP _let_3 _let_6 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_3 _let_3) (tptp.combb X_a X_a X_b) _let_2) G)) A_3))))))))))) (forall ((F $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (= (tptp.hAPP _let_2 tptp.real (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_3) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_3 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_3 _let_5) (tptp.combb tptp.real _let_4 tptp.nat) (tptp.times_times tptp.real)) F)) (tptp.hAPP tptp.real _let_3 (tptp.power_power tptp.real) _let_1))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastLessThan tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) N_1)) _let_1))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted)) (= (exists ((M_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 M_2)))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 X_2))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted)) (= (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 M_2)))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 X_2))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.ord_atLeastLessThan X_a))) (let ((_let_4 (tptp.fun X_a _let_2))) (=> (= (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 A_2) B_1) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 C_1) D_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) D_1)) (= (tptp.ti X_a B_1) (tptp.ti X_a D_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.ord_atLeastLessThan X_a))) (let ((_let_4 (tptp.fun X_a _let_2))) (=> (= (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 A_2) B_1) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 C_1) D_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) D_1)) (= (tptp.ti X_a A_2) (tptp.ti X_a C_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((C_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.ord_less X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 A_2) B_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 C_1) D_1)) (= (= (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 A_2) B_1) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 C_1) D_1)) (and (= (tptp.ti X_a A_2) (tptp.ti X_a C_1)) (= (tptp.ti X_a B_1) (tptp.ti X_a D_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((K $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.ord_atLeastLessThan tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_3 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F))) (=> (= (tptp.hAPP tptp.nat X_a F _let_1) (tptp.zero_zero X_a)) (= (tptp.hAPP _let_3 X_a _let_5 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.nat _let_4 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1)) K)) (tptp.hAPP _let_3 X_a _let_5 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.nat _let_4 _let_2 _let_1) K)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B_1))) (let ((_let_4 (tptp.ord_atLeastLessThan X_a))) (let ((_let_5 (tptp.fun X_a _let_2))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_5 _let_4 A_2) B_1)) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_5 _let_4 C_1) D_1))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_2)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 D_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((F $$unsorted) (P_4 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F))) (let ((_let_5 (tptp.hAPP tptp.nat _let_3 _let_1 Ma))) (let ((_let_6 (tptp.ord_less_eq tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_6 Ma) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_6 N_1) P_4)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP _let_2 X_a _let_4 (tptp.hAPP tptp.nat _let_2 _let_5 P_4))) (tptp.hAPP _let_2 X_a _let_4 (tptp.hAPP tptp.nat _let_2 _let_5 N_1))) (tptp.hAPP _let_2 X_a _let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_1) P_4)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (P_4 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_1 Ma))) (let ((_let_5 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F))) (let ((_let_6 (tptp.ord_less_eq tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_6 Ma) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_6 N_1) P_4)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP _let_2 X_a _let_5 (tptp.hAPP tptp.nat _let_2 _let_4 N_1))) (tptp.hAPP _let_2 X_a _let_5 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 N_1) P_4))) (tptp.hAPP _let_2 X_a _let_5 (tptp.hAPP tptp.nat _let_2 _let_4 P_4)))))))))))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) L) U_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) U_1) L)))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) Ma) N_1)) (= (tptp.hAPP _let_2 X_a _let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 Ma) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a F Ma)) (tptp.hAPP _let_2 X_a _let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma)) N_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) Ma))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F))) (let ((_let_4 (tptp.hAPP _let_1 X_a _let_3 (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) N_1) Ma)))) (and (=> _let_5 (= _let_4 (tptp.zero_zero X_a))) (=> (not _let_5) (= _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP _let_1 X_a _let_3 (tptp.hAPP tptp.nat _let_1 _let_2 N_1))) (tptp.hAPP tptp.nat X_a F N_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Ma $$unsorted) (I $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.hAPP X_a _let_3 _let_1 I))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less_eq X_a) I) N_1)) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.minus_minus _let_2) (tptp.hAPP X_a _let_2 _let_4 Ma)) (tptp.hAPP X_a _let_2 _let_4 N_1)) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 N_1) Ma)))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.real))) (let ((_let_2 (tptp.minus_minus tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.hAPP tptp.real _let_4 (tptp.power_power tptp.real) X_1))) (let ((_let_6 (tptp.fun tptp.nat tptp.bool))) (=> (not (= X_1 _let_1)) (= (tptp.hAPP _let_6 tptp.real (tptp.hAPP _let_4 (tptp.fun _let_6 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) _let_5) (tptp.hAPP tptp.nat _let_6 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_6) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 (tptp.inverse_divide tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.nat tptp.real _let_5 N_1)) _let_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 X_1) _let_1))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) G) A_3) (tptp.zero_zero X_b))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F) A_3) (tptp.zero_zero X_b))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring_0 X_a) (forall ((F $$unsorted) (A_3 $$unsorted) (G $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.fun X_c X_a))) (let ((_let_6 (tptp.fun _let_5 _let_5))) (let ((_let_7 (tptp.fun X_b _let_6))) (let ((_let_8 (tptp.fun X_b _let_5))) (let ((_let_9 (tptp.big_co1399186613setsum X_c X_a))) (let ((_let_10 (tptp.fun X_c tptp.bool))) (let ((_let_11 (tptp.fun _let_10 X_a))) (let ((_let_12 (tptp.fun X_b _let_11))) (let ((_let_13 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_14 (tptp.fun X_b tptp.bool))) (let ((_let_15 (tptp.fun _let_14 X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_14 X_a (tptp.hAPP _let_4 _let_15 _let_13 F) A_3)) (tptp.hAPP _let_10 X_a (tptp.hAPP _let_5 _let_11 _let_9 G) B_2)) (tptp.hAPP _let_14 X_a (tptp.hAPP _let_4 _let_15 _let_13 (tptp.hAPP _let_10 _let_4 (tptp.hAPP _let_12 (tptp.fun _let_10 _let_4) (tptp.combc X_b _let_10 X_a) (tptp.hAPP _let_8 _let_12 (tptp.hAPP (tptp.fun _let_5 _let_11) (tptp.fun _let_8 _let_12) (tptp.combb _let_5 _let_11 X_b) _let_9) (tptp.hAPP _let_5 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_8) (tptp.combc X_b _let_5 _let_5) (tptp.hAPP _let_3 _let_7 (tptp.hAPP (tptp.fun _let_2 _let_6) (tptp.fun _let_3 _let_7) (tptp.combb _let_2 _let_6 X_b) (tptp.combb X_a X_a X_c)) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 X_b) _let_1) F))) G))) B_2)) A_3)))))))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring_0 X_a) (forall ((F $$unsorted) (A_3 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (let ((_let_7 (tptp.fun _let_6 X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_6 X_a (tptp.hAPP _let_4 _let_7 _let_5 F) A_3)) R_1) (tptp.hAPP _let_6 X_a (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc X_b X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 X_b) _let_1) F)) R_1)) A_3)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring_0 X_a) (forall ((R_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) R_1))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_5 (tptp.fun X_b tptp.bool))) (let ((_let_6 (tptp.fun _let_5 X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP _let_5 X_a (tptp.hAPP _let_3 _let_6 _let_4 F) A_3)) (tptp.hAPP _let_5 X_a (tptp.hAPP _let_3 _let_6 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_3 _let_3) (tptp.combb X_a X_a X_b) _let_2) F)) A_3))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.ordere142940540dd_abs X_a) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.abs_abs X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.hAPP _let_3 X_a (tptp.hAPP _let_2 (tptp.fun _let_3 X_a) (tptp.big_co1399186613setsum X_b X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a X_b) _let_1) F)) A_3))) (= (tptp.hAPP X_a X_a _let_1 _let_4) _let_4)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.uminus_uminus X_a))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_4 _let_4) (tptp.combb X_a X_a X_b) _let_5) F)) A_3) (tptp.hAPP X_a X_a _let_5 (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 F) A_3))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_a))) (let ((_let_2 (tptp.fun X_c _let_1))) (let ((_let_3 (tptp.fun X_c X_a))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (let ((_let_7 (tptp.fun _let_6 X_a))) (let ((_let_8 (tptp.fun X_c _let_7))) (let ((_let_9 (tptp.big_co1399186613setsum X_c X_a))) (let ((_let_10 (tptp.fun X_c tptp.bool))) (let ((_let_11 (tptp.fun _let_10 X_a))) (let ((_let_12 (tptp.fun X_b _let_11))) (= (tptp.hAPP _let_6 X_a (tptp.hAPP _let_1 _let_7 _let_5 (tptp.hAPP _let_10 _let_1 (tptp.hAPP _let_12 (tptp.fun _let_10 _let_1) (tptp.combc X_b _let_10 X_a) (tptp.hAPP _let_4 _let_12 (tptp.hAPP (tptp.fun _let_3 _let_11) (tptp.fun _let_4 _let_12) (tptp.combb _let_3 _let_11 X_b) _let_9) F)) B_2)) A_3) (tptp.hAPP _let_10 X_a (tptp.hAPP _let_3 _let_11 _let_9 (tptp.hAPP _let_6 _let_3 (tptp.hAPP _let_8 (tptp.fun _let_6 _let_3) (tptp.combc X_c _let_6 X_a) (tptp.hAPP _let_2 _let_8 (tptp.hAPP (tptp.fun _let_1 _let_7) (tptp.fun _let_2 _let_8) (tptp.combb _let_1 _let_7 X_c) _let_5) (tptp.hAPP _let_4 _let_2 (tptp.combc X_b X_c X_a) F))) A_3)) B_2))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_a _let_5))) (let ((_let_7 (tptp.fun X_a _let_4))) (let ((_let_8 (tptp.fun X_a X_b))) (let ((_let_9 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_8 (tptp.fun _let_2 X_b) (tptp.big_co1399186613setsum X_a X_b) (tptp.hAPP X_b _let_8 (tptp.hAPP _let_7 (tptp.fun X_b _let_8) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combs X_a X_b _let_4) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun tptp.bool _let_5) (tptp.fun _let_2 _let_6) (tptp.combb tptp.bool _let_5 X_a) (tptp.if X_b)) (tptp.hAPP X_a _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) A_2))) B_1)) _let_1)) S))) (let ((_let_10 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) A_2) S)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) S)) (and (=> _let_10 (= _let_9 (tptp.hAPP X_a X_b B_1 A_2))) (=> (not _let_10) (= _let_9 _let_1))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a _let_3))) (let ((_let_7 (tptp.fun X_a X_b))) (let ((_let_8 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_7 (tptp.fun _let_2 X_b) (tptp.big_co1399186613setsum X_a X_b) (tptp.hAPP X_b _let_7 (tptp.hAPP _let_6 (tptp.fun X_b _let_7) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_7 _let_6) (tptp.combs X_a X_b _let_3) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_a) (tptp.if X_b)) (tptp.hAPP X_a _let_2 (tptp.fequal X_a) A_2))) B_1)) _let_1)) S))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) A_2) S)))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) S)) (and (=> _let_9 (= _let_8 (tptp.hAPP X_a X_b B_1 A_2))) (=> (not _let_9) (= _let_8 _let_1)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((A_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.fun X_b X_a))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (= (tptp.hAPP _let_3 X_a (tptp.hAPP _let_2 (tptp.fun _let_3 X_a) (tptp.big_co1399186613setsum X_b X_a) (tptp.hAPP X_a _let_2 (tptp.combk X_a X_b) _let_1)) A_3) _let_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.field X_a) (forall ((F $$unsorted) (A_3 $$unsorted) (R_1 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_b _let_2))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (let ((_let_7 (tptp.fun _let_6 X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP _let_6 X_a (tptp.hAPP _let_4 _let_7 _let_5 F) A_3)) R_1) (tptp.hAPP _let_6 X_a (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc X_b X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 X_b) _let_1) F)) R_1)) A_3)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.plus_plus X_b))) (let ((_let_6 (tptp.fun X_b X_b))) (let ((_let_7 (tptp.fun X_a _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_b _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_b _let_6 X_a) _let_5) G)) H)) A_3) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_6 _let_5 (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 H) A_3)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.plus_plus X_a))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.fun X_b _let_6))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_b X_a X_a) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_a _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_a _let_6 X_b) _let_5) F)) G)) A_3) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 _let_5 (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 G) A_3))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.minus_minus X_a))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.fun X_b _let_6))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_7 (tptp.fun _let_4 _let_4) (tptp.combs X_b X_a X_a) (tptp.hAPP _let_4 _let_7 (tptp.hAPP (tptp.fun X_a _let_6) (tptp.fun _let_4 _let_7) (tptp.combb X_a _let_6 X_b) _let_5) F)) G)) A_3) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_6 _let_5 (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 G) A_3))))))))))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.ord_atLeastLessThan tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc L)) U_1) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.ord_gr676655987ssThan tptp.nat) L) U_1))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_atLeastLessThan tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_4 _let_4) (tptp.image tptp.nat tptp.nat) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_1) K)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat _let_5 _let_3 I) J)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat _let_5 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K)))))))))) (forall ((X_c $$unsorted) (X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((G $$unsorted) (F $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_c tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a X_c))) (let ((_let_4 (tptp.fun X_a _let_1))) (let ((_let_5 (tptp.fun X_c _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (let ((_let_9 (tptp.combb _let_2 _let_2 X_c))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun _let_2 X_b))) (let ((_let_12 (tptp.hAPP (tptp.fun X_a X_b) _let_11 (tptp.big_co1399186613setsum X_a X_b) G))) (let ((_let_13 (tptp.fun X_c X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) S)) (= (tptp.hAPP _let_2 X_b _let_12 S) (tptp.hAPP _let_1 X_b (tptp.hAPP _let_13 (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_c X_b) (tptp.hAPP _let_5 _let_13 (tptp.hAPP _let_11 (tptp.fun _let_5 _let_13) (tptp.combb _let_2 X_b X_c) _let_12) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_6 _let_10 _let_9 (tptp.collect X_a)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_6 _let_10 _let_9 (tptp.hAPP _let_8 _let_6 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_8 (tptp.hAPP (tptp.fun tptp.bool _let_7) (tptp.fun _let_2 _let_8) (tptp.combb tptp.bool _let_7 X_a) tptp.fconj) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_2 tptp.bool)) _let_6 (tptp.combc X_a _let_2 tptp.bool) (tptp.member X_a)) S)))) (tptp.hAPP _let_4 _let_5 (tptp.combc X_a X_c tptp.bool) (tptp.hAPP _let_3 _let_4 (tptp.hAPP (tptp.fun X_c _let_1) (tptp.fun _let_3 _let_4) (tptp.combb X_c _let_1 X_a) (tptp.fequal X_c)) F)))))) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.image X_a X_c) F) S)))))))))))))))))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.nat) (tptp.fun _let_2 _let_2) (tptp.image tptp.nat tptp.nat) tptp.suc) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 I) J)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I)) (tptp.hAPP tptp.nat tptp.nat tptp.suc J))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.monoid_mult X_a) (tptp.comm_ring X_a)) (forall ((Z $$unsorted) (H $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) Ma))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 (tptp.minus_minus tptp.nat) Ma))) (let ((_let_5 (tptp.power_power X_a))) (let ((_let_6 (tptp.fun tptp.nat X_a))) (let ((_let_7 (tptp.hAPP X_a _let_6 _let_5 Z))) (let ((_let_8 (tptp.combb tptp.nat X_a tptp.nat))) (let ((_let_9 (tptp.fun _let_3 _let_6))) (let ((_let_10 (tptp.fun X_a X_a))) (let ((_let_11 (tptp.hAPP _let_3 _let_6 (tptp.hAPP _let_6 _let_9 _let_8 (tptp.hAPP X_a _let_6 _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_10 (tptp.plus_plus X_a) Z) H))) _let_4))) (let ((_let_12 (tptp.combb X_a _let_10 tptp.nat))) (let ((_let_13 (tptp.fun tptp.nat _let_10))) (let ((_let_14 (tptp.fun _let_6 _let_13))) (let ((_let_15 (tptp.fun X_a _let_10))) (let ((_let_16 (tptp.hAPP _let_15 _let_14 _let_12 (tptp.minus_minus X_a)))) (let ((_let_17 (tptp.combs tptp.nat X_a X_a))) (let ((_let_18 (tptp.fun _let_6 _let_6))) (let ((_let_19 (tptp.hAPP _let_15 _let_14 _let_12 (tptp.times_times X_a)))) (let ((_let_20 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_21 (tptp.fun _let_1 X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP _let_6 _let_21 _let_20 (tptp.hAPP X_a _let_6 (tptp.hAPP _let_13 (tptp.fun X_a _let_6) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_6 _let_13 _let_16 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_13 _let_18 _let_17 (tptp.hAPP _let_6 _let_13 _let_19 _let_11)) _let_7))) (tptp.hAPP tptp.nat X_a _let_7 Ma))) _let_2) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_6 _let_21 _let_20 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_13 _let_18 _let_17 (tptp.hAPP _let_6 _let_13 _let_19 _let_7)) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_13 _let_18 _let_17 (tptp.hAPP _let_6 _let_13 _let_16 _let_11)) (tptp.hAPP _let_3 _let_6 (tptp.hAPP _let_6 _let_9 _let_8 _let_7) _let_4)))) _let_2)))))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.monoid_mult X_a) (tptp.comm_ring X_a)) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.power_power X_a))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.hAPP X_a _let_5 _let_4 Y_1))) (let ((_let_7 (tptp.hAPP X_a _let_5 _let_4 X_1))) (let ((_let_8 (tptp.times_times X_a))) (let ((_let_9 (tptp.fun X_a X_a))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_9 _let_11 (tptp.hAPP tptp.nat X_a _let_7 _let_1)) (tptp.hAPP tptp.nat X_a _let_6 _let_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_9 _let_8 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_9 _let_11 X_1) Y_1)) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_5 (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_10 (tptp.fun _let_5 _let_5) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_5 _let_10 (tptp.hAPP (tptp.fun X_a _let_9) (tptp.fun _let_5 _let_10) (tptp.combb X_a _let_9 tptp.nat) _let_8) _let_7)) (tptp.hAPP _let_3 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_5) (tptp.combb tptp.nat X_a tptp.nat) _let_6) (tptp.hAPP tptp.nat _let_3 (tptp.minus_minus tptp.nat) N_1)))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) _let_1)))))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.semiring_1 X_a) (forall ((Y_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_b X_a))) (= (tptp.hAPP _let_1 X_a (tptp.hAPP _let_2 (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum X_b X_a) (tptp.hAPP X_a _let_2 (tptp.combk X_a X_b) Y_1)) A_3) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_b) A_3))) Y_1))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.real))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_3)) (tptp.hAPP _let_2 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.real) (tptp.big_co1399186613setsum X_a tptp.real) (tptp.hAPP tptp.real _let_1 (tptp.combk tptp.real X_a) (tptp.one_one tptp.real))) A_3))))) (forall ((Diff $$unsorted) (N_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.zero_zero tptp.nat))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (let ((_let_6 (tptp.fun tptp.nat tptp.nat))) (let ((_let_7 (tptp.fun tptp.nat _let_3))) (let ((_let_8 (tptp.combb tptp.real _let_3 tptp.nat))) (let ((_let_9 (tptp.fun _let_5 _let_7))) (let ((_let_10 (tptp.fun tptp.real _let_3))) (let ((_let_11 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_12 (tptp.fun _let_5 _let_5))) (=> (= X_1 _let_1) (=> (not (= N_1 _let_2)) (= (tptp.hAPP _let_4 tptp.real (tptp.hAPP _let_5 (tptp.fun _let_4 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_7 _let_12 _let_11 (tptp.hAPP _let_5 _let_7 (tptp.hAPP _let_10 _let_9 _let_8 (tptp.times_times tptp.real)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_7 _let_12 _let_11 (tptp.hAPP _let_5 _let_7 (tptp.hAPP _let_10 _let_9 _let_8 (tptp.inverse_divide tptp.real)) (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_7 (tptp.fun tptp.real _let_5) (tptp.combc tptp.nat tptp.real tptp.real) Diff) _let_1))) (tptp.hAPP _let_6 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_6 _let_5) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) (tptp.fact_fact tptp.nat))))) (tptp.hAPP tptp.real _let_5 (tptp.power_power tptp.real) X_1))) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_4) (tptp.ord_atLeastLessThan tptp.nat) _let_2) N_1)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_3 Diff _let_2) _let_1))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((K $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_4 _let_4 _let_2 (tptp.times_times tptp.nat)) K))) (let ((_let_6 (tptp.fun tptp.nat tptp.bool))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (let ((_let_9 (tptp.fun _let_6 X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) F)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_6 (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) K)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.sums X_a) (tptp.hAPP _let_7 _let_1 (tptp.hAPP _let_9 (tptp.fun _let_7 _let_1) (tptp.combb _let_6 X_a tptp.nat) (tptp.hAPP _let_1 _let_9 (tptp.big_co1399186613setsum tptp.nat X_a) F)) (tptp.hAPP _let_3 _let_7 (tptp.hAPP _let_8 (tptp.fun _let_3 _let_7) (tptp.combs tptp.nat tptp.nat _let_6) (tptp.hAPP _let_3 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_3 _let_8) (tptp.combb tptp.nat _let_7 tptp.nat) (tptp.ord_atLeastLessThan tptp.nat)) _let_5)) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_4 _let_4 _let_2 (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_4) (tptp.combb tptp.nat _let_3 tptp.nat) (tptp.plus_plus tptp.nat)) _let_5)) K)))) (tptp.hAPP _let_1 X_a (tptp.suminf X_a) F))))))))))))))))) (forall ((A_3 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) K) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) K) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) A_3))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) _let_2)) (= A_3 _let_2))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ab_group_add X_b) (forall ((F $$unsorted) (B_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) A_3)) (= (tptp.hAPP _let_1 X_b _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP _let_1 X_b _let_2 A_3)) (tptp.hAPP _let_1 X_b _let_2 B_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 (tptp.ord_gr676655987ssThan X_a) A_2) B_1)) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 (tptp.ord_atLeastLessThan X_a) C_1) D_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) A_2) B_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) D_1))))))))))) (forall ((F $$unsorted) (G $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 _let_2 N_1))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.hAPP tptp.nat _let_4 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (let ((_let_6 (tptp.fun tptp.nat _let_4))) (let ((_let_7 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_8 (tptp.fun tptp.nat tptp.real))) (let ((_let_9 (tptp.fun _let_4 _let_8))) (let ((_let_10 (tptp.big_co1399186613setsum tptp.nat tptp.real))) (let ((_let_11 (tptp.fun _let_1 tptp.real))) (let ((_let_12 (tptp.fun tptp.real tptp.real))) (let ((_let_13 (tptp.fun tptp.real _let_12))) (let ((_let_14 (tptp.fun tptp.nat _let_13))) (let ((_let_15 (tptp.fun tptp.nat _let_12))) (= (tptp.hAPP _let_1 tptp.real (tptp.hAPP _let_8 _let_11 _let_10 (tptp.hAPP _let_8 _let_8 (tptp.hAPP _let_15 (tptp.fun _let_8 _let_8) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_8 _let_15 (tptp.hAPP _let_14 (tptp.fun _let_8 _let_15) (tptp.combs tptp.nat tptp.real _let_12) (tptp.hAPP _let_1 _let_14 (tptp.hAPP (tptp.fun tptp.bool _let_13) (tptp.fun _let_1 _let_14) (tptp.combb tptp.bool _let_13 tptp.nat) (tptp.if tptp.real)) (tptp.even_odd_even tptp.nat))) F)) G)) (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_5 N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_12 (tptp.plus_plus tptp.real) (tptp.hAPP _let_1 tptp.real (tptp.hAPP _let_8 _let_11 _let_10 (tptp.hAPP _let_4 _let_8 (tptp.hAPP _let_8 _let_9 _let_7 F) _let_5)) _let_3)) (tptp.hAPP _let_1 tptp.real (tptp.hAPP _let_8 _let_11 _let_10 (tptp.hAPP _let_4 _let_8 (tptp.hAPP _let_8 _let_9 _let_7 G) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.hAPP _let_4 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_4 _let_6) (tptp.combb tptp.nat _let_4 tptp.nat) (tptp.plus_plus tptp.nat)) _let_5)) (tptp.one_one tptp.nat)))) _let_3))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.zero X_a) (forall ((Diff $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.nat))) (let ((_let_2 (tptp.real_1 tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 (tptp.power_power tptp.real) (tptp.zero_zero tptp.real)))) (let ((_let_5 (tptp.zero_zero X_a))) (let ((_let_6 (tptp.fun X_a tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.real tptp.real))) (let ((_let_9 (tptp.inverse_divide tptp.real))) (let ((_let_10 (tptp.zero_zero tptp.nat))) (let ((_let_11 (tptp.fun tptp.nat tptp.bool))) (let ((_let_12 (tptp.fun tptp.nat tptp.nat))) (let ((_let_13 (tptp.combb tptp.real _let_8 tptp.nat))) (let ((_let_14 (tptp.fun tptp.nat _let_8))) (let ((_let_15 (tptp.fun _let_3 _let_14))) (let ((_let_16 (tptp.fun tptp.real _let_8))) (let ((_let_17 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_18 (tptp.fun _let_3 _let_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_11 (tptp.ord_less tptp.nat) _let_10) N_1)) (= (tptp.hAPP X_a tptp.real (tptp.hAPP tptp.nat _let_6 Diff _let_10) _let_5) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_8 (tptp.plus_plus tptp.real) (tptp.hAPP _let_11 tptp.real (tptp.hAPP _let_3 (tptp.fun _let_11 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_14 _let_18 _let_17 (tptp.hAPP _let_3 _let_14 (tptp.hAPP _let_16 _let_15 _let_13 _let_9) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_14 _let_18 _let_17 (tptp.hAPP _let_3 _let_14 (tptp.hAPP _let_16 _let_15 _let_13 _let_7) (tptp.hAPP X_a _let_3 (tptp.hAPP (tptp.fun tptp.nat _let_6) (tptp.fun X_a _let_3) (tptp.combc tptp.nat X_a tptp.real) Diff) _let_5))) _let_4))) (tptp.hAPP _let_12 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_12 _let_3) (tptp.combb tptp.nat tptp.real tptp.nat) _let_2) _let_1))) (tptp.hAPP tptp.nat _let_11 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_11) (tptp.ord_atLeastLessThan tptp.nat) _let_10) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_8 _let_9 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_8 _let_7 (tptp.hAPP X_a tptp.real (tptp.hAPP tptp.nat _let_6 Diff N_1) _let_5)) (tptp.hAPP tptp.nat tptp.real _let_4 N_1))) (tptp.hAPP tptp.nat tptp.real _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N_1))))))))))))))))))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (= (tptp.hAPP _let_2 tptp.real (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_3) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.hAPP tptp.real _let_3 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1))) tptp.suc)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N_1))) (tptp.zero_zero tptp.real)))))) (forall ((X_a $$unsorted)) (=> (tptp.field X_a) (forall ((Z $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.minus_minus tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat _let_3 _let_2 N_1))) (let ((_let_5 (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_1)))) (let ((_let_6 (tptp.fun tptp.nat tptp.bool))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.hAPP tptp.nat _let_7 (tptp.ord_atLeastLessThan tptp.nat) _let_1))) (let ((_let_9 (tptp.power_power X_a))) (let ((_let_10 (tptp.fun tptp.nat X_a))) (let ((_let_11 (tptp.hAPP X_a _let_10 _let_9 Z))) (let ((_let_12 (tptp.fun X_a X_a))) (let ((_let_13 (tptp.hAPP X_a _let_10 _let_9 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_12 (tptp.plus_plus X_a) Z) H)))) (let ((_let_14 (tptp.times_times X_a))) (let ((_let_15 (tptp.fun tptp.nat _let_12))) (let ((_let_16 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_17 (tptp.fun _let_6 X_a))) (let ((_let_18 (tptp.minus_minus X_a))) (=> (not (= (tptp.ti X_a H) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_12 _let_18 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_12 (tptp.inverse_divide X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_12 _let_18 (tptp.hAPP tptp.nat X_a _let_13 N_1)) (tptp.hAPP tptp.nat X_a _let_11 N_1))) H)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_12 _let_14 (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_1)) (tptp.hAPP tptp.nat X_a _let_11 _let_5))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_12 _let_14 H) (tptp.hAPP _let_6 X_a (tptp.hAPP _let_10 _let_17 _let_16 (tptp.hAPP _let_7 _let_10 (tptp.hAPP _let_17 (tptp.fun _let_7 _let_10) (tptp.combb _let_6 X_a tptp.nat) (tptp.hAPP _let_10 _let_17 _let_16 (tptp.hAPP _let_10 _let_10 (tptp.hAPP _let_15 (tptp.fun _let_10 _let_10) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_10 _let_15 (tptp.hAPP (tptp.fun X_a _let_12) (tptp.fun _let_10 _let_15) (tptp.combb X_a _let_12 tptp.nat) _let_14) _let_13)) (tptp.hAPP _let_3 _let_10 (tptp.hAPP _let_10 (tptp.fun _let_3 _let_10) (tptp.combb tptp.nat X_a tptp.nat) _let_11) (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))))) (tptp.hAPP _let_3 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_3 _let_7) (tptp.combb tptp.nat _let_6 tptp.nat) _let_8) (tptp.hAPP tptp.nat _let_3 _let_2 _let_5)))) (tptp.hAPP tptp.nat _let_6 _let_8 _let_5)))))))))))))))))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat tptp.nat))) (let ((_let_7 (tptp.fun _let_6 _let_4))) (let ((_let_8 (tptp.fun tptp.nat _let_6))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.combb tptp.real _let_9 tptp.nat))) (let ((_let_11 (tptp.fun tptp.nat _let_9))) (let ((_let_12 (tptp.fun _let_4 _let_11))) (let ((_let_13 (tptp.fun tptp.real _let_9))) (let ((_let_14 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_15 (tptp.fun _let_4 _let_4))) (let ((_let_16 (tptp.fun tptp.nat _let_13))) (= (tptp.hAPP _let_2 tptp.real (tptp.hAPP _let_4 (tptp.fun _let_2 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_4) (tptp.combc tptp.nat tptp.real tptp.real) (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_16 _let_12 (tptp.combs tptp.nat tptp.real _let_9) (tptp.hAPP _let_2 _let_16 (tptp.hAPP (tptp.fun tptp.bool _let_13) (tptp.fun _let_2 _let_16) (tptp.combb tptp.bool _let_13 tptp.nat) (tptp.if tptp.real)) (tptp.even_odd_even tptp.nat))) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_11 _let_15 _let_14 (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_13 _let_12 _let_10 (tptp.times_times tptp.real)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_11 _let_15 _let_14 (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_13 _let_12 _let_10 (tptp.inverse_divide tptp.real)) (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1))) (tptp.hAPP tptp.nat _let_6 (tptp.hAPP _let_8 _let_8 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.div_div tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.real_1 tptp.nat)) (tptp.fact_fact tptp.nat))))) (tptp.hAPP tptp.real _let_4 _let_3 _let_1)))) _let_1)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastLessThan tptp.nat) (tptp.one_one tptp.nat)) N_1)) _let_1)))))))))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.zero_zero tptp.real))) (let ((_let_3 (tptp.power_power tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat tptp.nat))) (let ((_let_7 (tptp.fun _let_6 _let_4))) (let ((_let_8 (tptp.fun tptp.nat _let_6))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.combb tptp.real _let_9 tptp.nat))) (let ((_let_11 (tptp.fun tptp.nat _let_9))) (let ((_let_12 (tptp.fun _let_4 _let_11))) (let ((_let_13 (tptp.fun tptp.real _let_9))) (let ((_let_14 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_15 (tptp.fun _let_4 _let_4))) (let ((_let_16 (tptp.fun tptp.nat _let_13))) (= (tptp.hAPP _let_1 tptp.real (tptp.hAPP _let_4 (tptp.fun _let_1 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_11 _let_15 _let_14 (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_13 _let_12 _let_10 (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_4) (tptp.combc tptp.nat tptp.real tptp.real) (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_16 _let_12 (tptp.combs tptp.nat tptp.real _let_9) (tptp.hAPP _let_1 _let_16 (tptp.hAPP (tptp.fun tptp.bool _let_13) (tptp.fun _let_1 _let_16) (tptp.combb tptp.bool _let_13 tptp.nat) (tptp.if tptp.real)) (tptp.even_odd_even tptp.nat))) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_11 _let_15 _let_14 (tptp.hAPP _let_4 _let_11 (tptp.hAPP _let_13 _let_12 _let_10 (tptp.inverse_divide tptp.real)) (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP tptp.real _let_4 _let_3 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1))) (tptp.hAPP tptp.nat _let_6 (tptp.hAPP _let_8 _let_8 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.div_div tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (tptp.hAPP _let_6 _let_4 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.real_1 tptp.nat)) (tptp.fact_fact tptp.nat))))) _let_2))) (tptp.hAPP tptp.real _let_4 _let_3 _let_2))) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.one_one tptp.real))))))))))))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 X_1))) (let ((_let_4 (tptp.fact_fact tptp.nat))) (let ((_let_5 (tptp.real_1 tptp.nat))) (let ((_let_6 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_7 (tptp.number_number_of tptp.real))) (let ((_let_8 (tptp.inverse_divide tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.times_times tptp.real))) (let ((_let_11 (tptp.plus_plus tptp.real))) (let ((_let_12 (tptp.zero_zero tptp.nat))) (let ((_let_13 (tptp.fun tptp.nat tptp.bool))) (let ((_let_14 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_15 (tptp.fun tptp.nat tptp.nat))) (let ((_let_16 (tptp.fun _let_15 _let_2))) (let ((_let_17 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_18 (tptp.fun tptp.nat _let_15))) (let ((_let_19 (tptp.combb tptp.real _let_9 tptp.nat))) (let ((_let_20 (tptp.fun tptp.nat _let_9))) (let ((_let_21 (tptp.fun _let_2 _let_20))) (let ((_let_22 (tptp.fun tptp.real _let_9))) (let ((_let_23 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_24 (tptp.fun _let_2 _let_2))) (let ((_let_25 (tptp.fun tptp.nat _let_22))) (let ((_let_26 (tptp.abs_abs tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_26 T_4)) (tptp.hAPP tptp.real tptp.real _let_26 X_1))) (= (tptp.hAPP tptp.real tptp.real tptp.sin X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_11 (tptp.hAPP _let_13 tptp.real (tptp.hAPP _let_2 (tptp.fun _let_13 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_20 _let_24 _let_23 (tptp.hAPP _let_2 _let_20 (tptp.hAPP _let_22 _let_21 _let_19 _let_10) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_20 _let_24 _let_23 (tptp.hAPP tptp.real _let_20 (tptp.hAPP _let_25 (tptp.fun tptp.real _let_20) (tptp.combc tptp.nat tptp.real _let_9) (tptp.hAPP _let_13 _let_25 (tptp.hAPP (tptp.fun tptp.bool _let_22) (tptp.fun _let_13 _let_25) (tptp.combb tptp.bool _let_22 tptp.nat) (tptp.if tptp.real)) (tptp.even_odd_even tptp.nat))) (tptp.zero_zero tptp.real))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_20 _let_24 _let_23 (tptp.hAPP _let_2 _let_20 (tptp.hAPP _let_22 _let_21 _let_19 _let_8) (tptp.hAPP _let_15 _let_2 (tptp.hAPP _let_2 _let_16 _let_14 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real _let_7 tptp.min_1))) (tptp.hAPP tptp.nat _let_15 (tptp.hAPP _let_18 _let_18 _let_17 (tptp.hAPP _let_15 _let_18 (tptp.hAPP _let_18 (tptp.fun _let_15 _let_18) (tptp.combb tptp.nat _let_15 tptp.nat) (tptp.div_div tptp.nat)) (tptp.hAPP tptp.nat _let_15 (tptp.hAPP _let_18 _let_18 _let_17 (tptp.minus_minus tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_12)))) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_6))))) (tptp.hAPP _let_15 _let_2 (tptp.hAPP _let_2 _let_16 _let_14 _let_5) _let_4))))) _let_3)) (tptp.hAPP tptp.nat _let_13 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_13) (tptp.ord_atLeastLessThan tptp.nat) _let_12) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_8 (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_11 T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_8 (tptp.one_one tptp.real)) (tptp.hAPP tptp.int tptp.real _let_7 _let_6))) (tptp.hAPP tptp.nat tptp.real _let_5 N_1))) tptp.pi)))) (tptp.hAPP tptp.nat tptp.real _let_5 (tptp.hAPP tptp.nat tptp.nat _let_4 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_3 N_1))))))))))))))))))))))))))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 X_1))) (let ((_let_4 (tptp.fact_fact tptp.nat))) (let ((_let_5 (tptp.real_1 tptp.nat))) (let ((_let_6 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_7 (tptp.number_number_of tptp.real))) (let ((_let_8 (tptp.inverse_divide tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.times_times tptp.real))) (let ((_let_11 (tptp.plus_plus tptp.real))) (let ((_let_12 (tptp.fun tptp.nat tptp.bool))) (let ((_let_13 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_14 (tptp.fun tptp.nat tptp.nat))) (let ((_let_15 (tptp.fun _let_14 _let_2))) (let ((_let_16 (tptp.fun tptp.nat _let_14))) (let ((_let_17 (tptp.combb tptp.real _let_9 tptp.nat))) (let ((_let_18 (tptp.fun tptp.nat _let_9))) (let ((_let_19 (tptp.fun _let_2 _let_18))) (let ((_let_20 (tptp.fun tptp.real _let_9))) (let ((_let_21 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_22 (tptp.fun _let_2 _let_2))) (let ((_let_23 (tptp.fun tptp.nat _let_20))) (let ((_let_24 (tptp.abs_abs tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_24 T_4)) (tptp.hAPP tptp.real tptp.real _let_24 X_1))) (= (tptp.hAPP tptp.real tptp.real tptp.cos X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_11 (tptp.hAPP _let_12 tptp.real (tptp.hAPP _let_2 (tptp.fun _let_12 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_18 _let_22 _let_21 (tptp.hAPP _let_2 _let_18 (tptp.hAPP _let_20 _let_19 _let_17 _let_10) (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_18 (tptp.fun tptp.real _let_2) (tptp.combc tptp.nat tptp.real tptp.real) (tptp.hAPP _let_2 _let_18 (tptp.hAPP _let_23 _let_19 (tptp.combs tptp.nat tptp.real _let_9) (tptp.hAPP _let_12 _let_23 (tptp.hAPP (tptp.fun tptp.bool _let_20) (tptp.fun _let_12 _let_23) (tptp.combb tptp.bool _let_20 tptp.nat) (tptp.if tptp.real)) (tptp.even_odd_even tptp.nat))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_18 _let_22 _let_21 (tptp.hAPP _let_2 _let_18 (tptp.hAPP _let_20 _let_19 _let_17 _let_8) (tptp.hAPP _let_14 _let_2 (tptp.hAPP _let_2 _let_15 _let_13 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real _let_7 tptp.min_1))) (tptp.hAPP tptp.nat _let_14 (tptp.hAPP _let_16 _let_16 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.div_div tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_6))))) (tptp.hAPP _let_14 _let_2 (tptp.hAPP _let_2 _let_15 _let_13 _let_5) _let_4)))) (tptp.zero_zero tptp.real)))) _let_3)) (tptp.hAPP tptp.nat _let_12 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_12) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_8 (tptp.hAPP tptp.real tptp.real tptp.cos (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_11 T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_8 (tptp.one_one tptp.real)) (tptp.hAPP tptp.int tptp.real _let_7 _let_6))) (tptp.hAPP tptp.nat tptp.real _let_5 N_1))) tptp.pi)))) (tptp.hAPP tptp.nat tptp.real _let_5 (tptp.hAPP tptp.nat tptp.nat _let_4 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_3 N_1))))))))))))))))))))))))))))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastLessThan tptp.int) L) U_1))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) Y_1) X_1)) (= (tptp.hAPP _let_1 tptp.real (tptp.complete_Sup_Sup tptp.real) (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.ord_atLeastLessThan tptp.real) Y_1) X_1)) X_1)))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun X_a tptp.int))) (let ((_let_3 (tptp.fun X_a tptp.nat))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) F) A_3)) (tptp.hAPP _let_4 tptp.int (tptp.hAPP _let_2 (tptp.fun _let_4 tptp.int) (tptp.big_co1399186613setsum X_a tptp.int) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.int X_a) _let_1) F)) A_3))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.int))) (let ((_let_2 (tptp.fun X_a tptp.nat))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_3 tptp.nat (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) F) A_3) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP _let_3 tptp.int (tptp.hAPP _let_1 (tptp.fun _let_3 tptp.int) (tptp.big_co1399186613setsum X_a tptp.int) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.combb tptp.nat tptp.int X_a) (tptp.semiring_1_of_nat tptp.int)) F)) A_3))))))) (forall ((X_a $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.complex))) (let ((_let_2 (tptp.big_co1399186613setsum X_a tptp.complex))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP _let_3 tptp.complex (tptp.hAPP _let_1 _let_4 _let_2 G) A_3)) (tptp.hAPP _let_3 tptp.complex (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun _let_1 _let_1) (tptp.combb tptp.complex tptp.complex X_a) tptp.cnj) G)) A_3))))))) (forall ((X_a $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.real))) (let ((_let_2 (tptp.fun X_a tptp.complex))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP _let_3 tptp.complex (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.complex) (tptp.big_co1399186613setsum X_a tptp.complex) G) A_3)) (tptp.hAPP _let_3 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_3 tptp.real) (tptp.big_co1399186613setsum X_a tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real X_a) tptp.im) G)) A_3)))))) (forall ((X_a $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.real))) (let ((_let_2 (tptp.fun X_a tptp.complex))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP _let_3 tptp.complex (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.complex) (tptp.big_co1399186613setsum X_a tptp.complex) G) A_3)) (tptp.hAPP _let_3 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_3 tptp.real) (tptp.big_co1399186613setsum X_a tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real X_a) tptp.re) G)) A_3)))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.nat))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.fun X_a tptp.nat))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP tptp.nat tptp.real _let_1 (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) F) A_3)) (tptp.hAPP _let_4 tptp.real (tptp.hAPP _let_2 (tptp.fun _let_4 tptp.real) (tptp.big_co1399186613setsum X_a tptp.real) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.real) (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.real X_a) _let_1) F)) A_3))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.real_1 tptp.int))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.fun X_a tptp.int))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP tptp.int tptp.real _let_1 (tptp.hAPP _let_4 tptp.int (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.int) (tptp.big_co1399186613setsum X_a tptp.int) F) A_3)) (tptp.hAPP _let_4 tptp.real (tptp.hAPP _let_2 (tptp.fun _let_4 tptp.real) (tptp.big_co1399186613setsum X_a tptp.real) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.int tptp.real) (tptp.fun _let_3 _let_2) (tptp.combb tptp.int tptp.real X_a) _let_1) F)) A_3))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a tptp.int))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.int))) (let ((_let_4 (tptp.fun X_a tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (let ((_let_6 (tptp.hAPP tptp.int _let_5 (tptp.times_times tptp.int) C_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (tptp.hAPP _let_2 tptp.int (tptp.hAPP _let_4 _let_3 _let_1 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_4) (tptp.combb tptp.int tptp.int X_a) _let_6) F)) A_3) (tptp.hAPP tptp.int tptp.int _let_6 (tptp.hAPP _let_2 tptp.int (tptp.hAPP _let_4 _let_3 _let_1 F) A_3))))))))))) (forall ((U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastLessThan tptp.int) (tptp.zero_zero tptp.int)) U_1))))) (forall ((X_a $$unsorted) (F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) F_1)) (= (= (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) F) F_1) (tptp.zero_zero tptp.nat)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) F_1)) (= (tptp.hAPP X_a tptp.nat F X_2) (tptp.zero_zero tptp.nat))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.nat))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card X_a) A_3) (tptp.hAPP _let_2 tptp.nat (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.combk tptp.nat X_a) (tptp.one_one tptp.nat))) A_3))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (= (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) F) A_3) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (= (tptp.hAPP X_a tptp.nat F X_2) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) A_3)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a Xa))) (= (tptp.hAPP X_a tptp.nat F Xa) (tptp.zero_zero tptp.nat))))))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (= (= (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) F) A_3) (tptp.one_one tptp.nat)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (= (tptp.hAPP X_a tptp.nat F X_2) (tptp.one_one tptp.nat)) (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Xa) A_3)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a Xa))) (= (tptp.hAPP X_a tptp.nat F Xa) (tptp.zero_zero tptp.nat))))))))))))) (forall ((U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastLessThan tptp.int) (tptp.zero_zero tptp.int)) U_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 U_1)))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastLessThan tptp.int) L) U_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) U_1) L))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) B_2) A_3)) (= (tptp.hAPP _let_1 tptp.nat _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) A_3) B_2)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) (tptp.hAPP _let_1 tptp.nat _let_2 A_3)) (tptp.hAPP _let_1 tptp.nat _let_2 B_2)))))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (= (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 (tptp.ord_atLeastLessThan tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) L) (tptp.one_one tptp.int))) U_1) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 (tptp.ord_gr676655987ssThan tptp.int) L) U_1))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.int))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) X_3)) (= (tptp.hAPP _let_1 tptp.int (tptp.hAPP _let_2 (tptp.fun _let_1 tptp.int) (tptp.big_co1399186613setsum X_a tptp.int) (tptp.hAPP tptp.int _let_2 (tptp.combk tptp.int X_a) C_1)) X_3) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) C_1) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) X_3)))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_3 (tptp.fun X_a tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) X_3)) (= (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP _let_1 tptp.nat (tptp.hAPP _let_3 (tptp.fun _let_1 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) (tptp.hAPP tptp.nat _let_3 (tptp.combk tptp.nat X_a) C_1)) X_3)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) (tptp.hAPP tptp.nat tptp.int _let_2 C_1)) (tptp.hAPP tptp.nat tptp.int _let_2 (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) X_3))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.comm_monoid_mult X_a)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.int X_a))) (let ((_let_4 (tptp.fun tptp.int tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_5 (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F) A_3) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.int X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.combb tptp.nat X_a tptp.int) F) tptp.nat_1)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_2 _let_1) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) A_3))))))))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun tptp.int _let_4))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_2 _let_2) (tptp.image tptp.int tptp.int) (tptp.hAPP tptp.int _let_4 (tptp.hAPP _let_5 _let_5 (tptp.combc tptp.int tptp.int tptp.int) (tptp.plus_plus tptp.int)) L)) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 _let_1 (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.minus_minus tptp.int) U_1) L))) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int _let_3 _let_1 L) U_1)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.comm_monoid_mult X_a)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (let ((_let_5 (tptp.fun tptp.int X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set A_3)) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_5 (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum tptp.int X_a) F) A_3) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.combb tptp.int X_a tptp.nat) F) (tptp.semiring_1_of_nat tptp.int))) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.image tptp.int tptp.nat) tptp.nat_1) A_3)))))))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.power_power tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 X_1))) (let ((_let_4 (tptp.fact_fact tptp.nat))) (let ((_let_5 (tptp.real_1 tptp.nat))) (let ((_let_6 (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (let ((_let_7 (tptp.number_number_of tptp.real))) (let ((_let_8 (tptp.inverse_divide tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.times_times tptp.real))) (let ((_let_11 (tptp.plus_plus tptp.real))) (let ((_let_12 (tptp.zero_zero tptp.nat))) (let ((_let_13 (tptp.fun tptp.nat tptp.bool))) (let ((_let_14 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_15 (tptp.fun tptp.nat tptp.nat))) (let ((_let_16 (tptp.fun _let_15 _let_2))) (let ((_let_17 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_18 (tptp.fun tptp.nat _let_15))) (let ((_let_19 (tptp.combb tptp.real _let_9 tptp.nat))) (let ((_let_20 (tptp.fun tptp.nat _let_9))) (let ((_let_21 (tptp.fun _let_2 _let_20))) (let ((_let_22 (tptp.fun tptp.real _let_9))) (let ((_let_23 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_24 (tptp.fun _let_2 _let_2))) (let ((_let_25 (tptp.fun tptp.nat _let_22))) (= (tptp.hAPP tptp.real tptp.real tptp.sin X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_11 (tptp.hAPP _let_13 tptp.real (tptp.hAPP _let_2 (tptp.fun _let_13 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_20 _let_24 _let_23 (tptp.hAPP _let_2 _let_20 (tptp.hAPP _let_22 _let_21 _let_19 _let_10) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_20 _let_24 _let_23 (tptp.hAPP tptp.real _let_20 (tptp.hAPP _let_25 (tptp.fun tptp.real _let_20) (tptp.combc tptp.nat tptp.real _let_9) (tptp.hAPP _let_13 _let_25 (tptp.hAPP (tptp.fun tptp.bool _let_22) (tptp.fun _let_13 _let_25) (tptp.combb tptp.bool _let_22 tptp.nat) (tptp.if tptp.real)) (tptp.even_odd_even tptp.nat))) (tptp.zero_zero tptp.real))) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_20 _let_24 _let_23 (tptp.hAPP _let_2 _let_20 (tptp.hAPP _let_22 _let_21 _let_19 _let_8) (tptp.hAPP _let_15 _let_2 (tptp.hAPP _let_2 _let_16 _let_14 (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.int tptp.real _let_7 tptp.min_1))) (tptp.hAPP tptp.nat _let_15 (tptp.hAPP _let_18 _let_18 _let_17 (tptp.hAPP _let_15 _let_18 (tptp.hAPP _let_18 (tptp.fun _let_15 _let_18) (tptp.combb tptp.nat _let_15 tptp.nat) (tptp.div_div tptp.nat)) (tptp.hAPP tptp.nat _let_15 (tptp.hAPP _let_18 _let_18 _let_17 (tptp.minus_minus tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc _let_12)))) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) _let_6))))) (tptp.hAPP _let_15 _let_2 (tptp.hAPP _let_2 _let_16 _let_14 _let_5) _let_4))))) _let_3)) (tptp.hAPP tptp.nat _let_13 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_13) (tptp.ord_atLeastLessThan tptp.nat) _let_12) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_8 (tptp.hAPP tptp.real tptp.real tptp.sin (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_11 T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_10 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_9 _let_8 (tptp.one_one tptp.real)) (tptp.hAPP tptp.int tptp.real _let_7 _let_6))) (tptp.hAPP tptp.nat tptp.real _let_5 N_1))) tptp.pi)))) (tptp.hAPP tptp.nat tptp.real _let_5 (tptp.hAPP tptp.nat tptp.nat _let_4 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_3 N_1))))))))))))))))))))))))))))))) (forall ((B_2 $$unsorted) (K $$unsorted) (Diff $$unsorted) (H $$unsorted) (N_1 $$unsorted)) (=> (forall ((M_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 (tptp.zero_zero tptp.real)) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 T_4) H))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) T_4)))))))) (=> (= N_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc K)) (forall ((M_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) N_1))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 _let_1))) (let ((_let_5 (tptp.fact_fact tptp.nat))) (let ((_let_6 (tptp.real_1 tptp.nat))) (let ((_let_7 (tptp.power_power tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.real))) (let ((_let_9 (tptp.hAPP tptp.real _let_8 _let_7 T_4))) (let ((_let_10 (tptp.inverse_divide tptp.real))) (let ((_let_11 (tptp.fun tptp.real tptp.real))) (let ((_let_12 (tptp.times_times tptp.real))) (let ((_let_13 (tptp.hAPP tptp.real _let_11 _let_12 B_2))) (let ((_let_14 (tptp.fun tptp.nat tptp.bool))) (let ((_let_15 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_14) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) (let ((_let_16 (tptp.hAPP _let_2 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_2 _let_8) (tptp.combb tptp.nat tptp.real tptp.nat) _let_6) _let_5))) (let ((_let_17 (tptp.zero_zero tptp.real))) (let ((_let_18 (tptp.plus_plus tptp.nat))) (let ((_let_19 (tptp.fun tptp.nat _let_11))) (let ((_let_20 (tptp.hAPP _let_19 (tptp.fun _let_2 _let_19) (tptp.combb tptp.nat _let_11 tptp.nat) Diff))) (let ((_let_21 (tptp.combc tptp.nat tptp.real tptp.real))) (let ((_let_22 (tptp.fun tptp.real _let_8))) (let ((_let_23 (tptp.combb tptp.real _let_11 tptp.nat))) (let ((_let_24 (tptp.fun _let_8 _let_19))) (let ((_let_25 (tptp.fun tptp.real _let_11))) (let ((_let_26 (tptp.hAPP _let_25 _let_24 _let_23 _let_10))) (let ((_let_27 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_28 (tptp.fun _let_8 _let_8))) (let ((_let_29 (tptp.hAPP _let_25 _let_24 _let_23 _let_12))) (let ((_let_30 (tptp.big_co1399186613setsum tptp.nat tptp.real))) (let ((_let_31 (tptp.fun _let_14 tptp.real))) (let ((_let_32 (tptp.plus_plus tptp.real))) (let ((_let_33 (tptp.minus_minus tptp.real))) (let ((_let_34 (tptp.hAPP tptp.nat tptp.nat _let_3 M_2))) (let ((_let_35 (tptp.combb tptp.real _let_11 tptp.real))) (let ((_let_36 (tptp.fun _let_11 _let_25))) (let ((_let_37 (tptp.fun _let_11 _let_11))) (let ((_let_38 (tptp.fun tptp.real _let_31))) (let ((_let_39 (tptp.combs tptp.real tptp.real tptp.real))) (let ((_let_40 (tptp.fun tptp.real tptp.bool))) (let ((_let_41 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_14 (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_40 _let_41 _let_17) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_40 _let_41 T_4) H))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_40 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_40) (tptp.deriv tptp.real) (tptp.hAPP _let_11 _let_11 (tptp.hAPP _let_25 _let_37 _let_39 (tptp.hAPP _let_11 _let_25 (tptp.hAPP _let_25 _let_36 _let_35 _let_33) (tptp.hAPP tptp.nat _let_11 Diff M_2))) (tptp.hAPP _let_11 _let_11 (tptp.hAPP _let_25 _let_37 _let_39 (tptp.hAPP _let_11 _let_25 (tptp.hAPP _let_25 _let_36 _let_35 _let_32) (tptp.hAPP _let_14 _let_11 (tptp.hAPP _let_38 (tptp.fun _let_14 _let_11) (tptp.combc tptp.real _let_14 tptp.real) (tptp.hAPP _let_22 _let_38 (tptp.hAPP (tptp.fun _let_8 _let_31) (tptp.fun _let_22 _let_38) (tptp.combb _let_8 _let_31 tptp.real) _let_30) (tptp.hAPP _let_22 _let_22 (tptp.hAPP _let_28 (tptp.fun _let_22 _let_22) (tptp.combb _let_8 _let_8 tptp.real) (tptp.hAPP _let_19 _let_28 _let_27 (tptp.hAPP _let_8 _let_19 _let_29 (tptp.hAPP _let_8 _let_8 (tptp.hAPP _let_19 _let_28 _let_27 (tptp.hAPP _let_8 _let_19 _let_26 (tptp.hAPP tptp.real _let_8 (tptp.hAPP _let_19 _let_22 _let_21 (tptp.hAPP _let_2 _let_19 _let_20 (tptp.hAPP tptp.nat _let_2 _let_18 M_2))) _let_17))) _let_16)))) _let_7))) (tptp.hAPP tptp.nat _let_14 _let_15 _let_34)))) (tptp.hAPP _let_11 _let_11 (tptp.hAPP _let_11 _let_37 (tptp.combb tptp.real tptp.real tptp.real) _let_13) (tptp.hAPP tptp.real _let_11 (tptp.hAPP _let_25 _let_25 (tptp.combc tptp.real tptp.real tptp.real) (tptp.hAPP _let_11 _let_25 (tptp.hAPP _let_25 _let_36 _let_35 _let_10) (tptp.hAPP tptp.nat _let_11 (tptp.hAPP _let_22 _let_19 (tptp.combc tptp.real tptp.nat tptp.real) _let_7) _let_34))) (tptp.hAPP tptp.nat tptp.real _let_6 (tptp.hAPP tptp.nat tptp.nat _let_5 _let_34))))))) T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_11 _let_33 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_11 Diff _let_1) T_4)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_11 _let_32 (tptp.hAPP _let_14 tptp.real (tptp.hAPP _let_8 _let_31 _let_30 (tptp.hAPP _let_8 _let_8 (tptp.hAPP _let_19 _let_28 _let_27 (tptp.hAPP _let_8 _let_19 _let_29 (tptp.hAPP _let_8 _let_8 (tptp.hAPP _let_19 _let_28 _let_27 (tptp.hAPP _let_8 _let_19 _let_26 (tptp.hAPP tptp.real _let_8 (tptp.hAPP _let_19 _let_22 _let_21 (tptp.hAPP _let_2 _let_19 _let_20 (tptp.hAPP tptp.nat _let_2 _let_18 _let_1))) _let_17))) _let_16))) _let_9)) (tptp.hAPP tptp.nat _let_14 _let_15 _let_4))) (tptp.hAPP tptp.real tptp.real _let_13 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_11 _let_10 (tptp.hAPP tptp.nat tptp.real _let_9 _let_4)) (tptp.hAPP tptp.nat tptp.real _let_6 (tptp.hAPP tptp.nat tptp.nat _let_5 _let_4)))))))))))))))))))))))))))))))))))))))))))))))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (=> (not (= X_1 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.exp tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.fun tptp.nat _let_7))) (let ((_let_11 (tptp.abs_abs tptp.real))) (let ((_let_12 (tptp.hAPP tptp.real tptp.real _let_11 T_4))) (let ((_let_13 (tptp.ord_less tptp.real))) (let ((_let_14 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_14 _let_13 (tptp.zero_zero tptp.real)) _let_12)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_14 _let_13 _let_12) (tptp.hAPP tptp.real tptp.real _let_11 X_1))) (= (tptp.hAPP tptp.real tptp.real _let_5 X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_10 (tptp.hAPP (tptp.fun tptp.real _let_7) (tptp.fun _let_1 _let_10) (tptp.combb tptp.real _let_7 tptp.nat) _let_6) _let_2)) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3))) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real _let_5 T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1))))))))))))))))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted)) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.exp tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.fun tptp.real tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.fun tptp.nat _let_7))) (let ((_let_11 (tptp.abs_abs tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_11 T_4)) (tptp.hAPP tptp.real tptp.real _let_11 X_1))) (= (tptp.hAPP tptp.real tptp.real _let_5 X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_10 (tptp.hAPP (tptp.fun tptp.real _let_7) (tptp.fun _let_1 _let_10) (tptp.combb tptp.real _let_7 tptp.nat) _let_6) _let_2)) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3))) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_7 _let_6 (tptp.hAPP tptp.real tptp.real _let_5 T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1)))))))))))))))))) (forall ((K $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) F)) (=> (forall ((D_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) D_3))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat _let_1 _let_3 K))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) (tptp.hAPP tptp.nat tptp.real F (tptp.hAPP tptp.nat tptp.nat _let_4 _let_2))) (tptp.hAPP tptp.nat tptp.real F (tptp.hAPP tptp.nat tptp.nat _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_3 _let_2) (tptp.one_one tptp.nat)))))))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP _let_2 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) F) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) K))) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) F)))))))) (forall ((F $$unsorted) (J $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) H)) (exists ((B_6 $$unsorted)) (let ((_let_1 (tptp.fact_fact tptp.nat))) (let ((_let_2 (tptp.real_1 tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.hAPP tptp.real _let_3 (tptp.power_power tptp.real) H))) (let ((_let_5 (tptp.inverse_divide tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.combb tptp.real _let_6 tptp.nat))) (let ((_let_11 (tptp.fun tptp.nat _let_6))) (let ((_let_12 (tptp.fun _let_3 _let_11))) (let ((_let_13 (tptp.fun tptp.real _let_6))) (let ((_let_14 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_15 (tptp.fun _let_3 _let_3))) (= (tptp.hAPP tptp.real tptp.real F H) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_6 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_3 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_11 _let_15 _let_14 (tptp.hAPP _let_3 _let_11 (tptp.hAPP _let_13 _let_12 _let_10 _let_7) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_11 _let_15 _let_14 (tptp.hAPP _let_3 _let_11 (tptp.hAPP _let_13 _let_12 _let_10 _let_5) J)) (tptp.hAPP _let_9 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_9 _let_3) (tptp.combb tptp.nat tptp.real tptp.nat) _let_2) _let_1)))) _let_4)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_6 _let_7 B_6) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_6 _let_5 (tptp.hAPP tptp.nat tptp.real _let_4 N_1)) (tptp.hAPP tptp.nat tptp.real _let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 N_1)))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linordered_semidom X_a) (forall ((K $$unsorted) (F $$unsorted) (K_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (forall ((P_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) P_6) N_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a F P_6)) K_3)))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.zero_zero X_a)) K_3)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP _let_1 X_a (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) K)))) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.times_times X_a) (tptp.hAPP tptp.nat X_a (tptp.semiring_1_of_nat X_a) N_1)) K_3))))))))))) (forall ((N_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) F)) (=> (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) M_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real F M_2))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP _let_2 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) F) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) F)))))))) (forall ((N_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) F)) (=> (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) M_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real F M_2))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_2 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) F) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) F)))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff _let_1) F) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1)) (=> (not (= X_1 (tptp.zero_zero tptp.real))) (=> (forall ((M_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) X_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) X_2)))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.zero_zero tptp.real))) (let ((_let_11 (tptp.fun tptp.nat _let_5))) (let ((_let_12 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_13 (tptp.fun _let_1 _let_11))) (let ((_let_14 (tptp.fun tptp.real _let_5))) (let ((_let_15 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (let ((_let_17 (tptp.abs_abs tptp.real))) (let ((_let_18 (tptp.hAPP tptp.real tptp.real _let_17 T_4))) (let ((_let_19 (tptp.ord_less tptp.real))) (let ((_let_20 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_20 _let_19 _let_10) _let_18)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_20 _let_19 _let_18) (tptp.hAPP tptp.real tptp.real _let_17 X_1))) (= (tptp.hAPP tptp.real tptp.real F X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) _let_10))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1)))))))))))))))))))))))))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (and (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff _let_1) F) (forall ((M_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) X_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) X_2)))))) (not (= X_1 (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.zero_zero tptp.real))) (let ((_let_11 (tptp.fun tptp.nat _let_5))) (let ((_let_12 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_13 (tptp.fun _let_1 _let_11))) (let ((_let_14 (tptp.fun tptp.real _let_5))) (let ((_let_15 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (let ((_let_17 (tptp.abs_abs tptp.real))) (let ((_let_18 (tptp.hAPP tptp.real tptp.real _let_17 T_4))) (let ((_let_19 (tptp.ord_less tptp.real))) (let ((_let_20 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_20 _let_19 _let_10) _let_18)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_20 _let_19 _let_18) (tptp.hAPP tptp.real tptp.real _let_17 X_1))) (= (tptp.hAPP tptp.real tptp.real F X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) _let_10))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1))))))))))))))))))))))))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (=> (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff (tptp.zero_zero tptp.nat)) F) (=> (forall ((M_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.abs_abs tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_3 T_4)) (tptp.hAPP tptp.real tptp.real _let_3 X_1)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) T_4)))))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.fun tptp.nat _let_5))) (let ((_let_11 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_12 (tptp.fun _let_1 _let_10))) (let ((_let_13 (tptp.fun tptp.real _let_5))) (let ((_let_14 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_15 (tptp.fun _let_1 _let_1))) (let ((_let_16 (tptp.abs_abs tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_16 T_4)) (tptp.hAPP tptp.real tptp.real _let_16 X_1))) (= (tptp.hAPP tptp.real tptp.real F X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_1 _let_10 (tptp.hAPP _let_13 _let_12 _let_11 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_1 _let_10 (tptp.hAPP _let_13 _let_12 _let_11 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_10 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) (tptp.zero_zero tptp.real)))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1))))))))))))))))))))))))) (forall ((Diff $$unsorted) (F $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) H)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1)) (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff _let_1) F) (forall ((M_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 (tptp.zero_zero tptp.real)) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 T_4) H))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) T_4))))))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) H))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.zero_zero tptp.real))) (let ((_let_11 (tptp.fun tptp.nat _let_5))) (let ((_let_12 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_13 (tptp.fun _let_1 _let_11))) (let ((_let_14 (tptp.fun tptp.real _let_5))) (let ((_let_15 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (let ((_let_17 (tptp.ord_less tptp.real))) (let ((_let_18 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_18 _let_17 _let_10) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_18 _let_17 T_4) H)) (= (tptp.hAPP tptp.real tptp.real F H) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) _let_10))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1))))))))))))))))))))))))))) (forall ((N_1 $$unsorted) (Diff $$unsorted) (F $$unsorted) (H $$unsorted)) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) H)) (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff (tptp.zero_zero tptp.nat)) F) (forall ((M_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 (tptp.zero_zero tptp.real)) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 T_4) H))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) T_4))))))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) H))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.zero_zero tptp.real))) (let ((_let_11 (tptp.fun tptp.nat _let_5))) (let ((_let_12 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_13 (tptp.fun _let_1 _let_11))) (let ((_let_14 (tptp.fun tptp.real _let_5))) (let ((_let_15 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (let ((_let_17 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_17 (tptp.ord_less tptp.real) _let_10) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_17 (tptp.ord_less_eq tptp.real) T_4) H)) (= (tptp.hAPP tptp.real tptp.real F H) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) _let_10))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1))))))))))))))))))))))))) (forall ((Diff $$unsorted) (F $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) H) (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1)) (=> (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff _let_1) F) (=> (forall ((M_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 H) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 T_4) (tptp.zero_zero tptp.real)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) T_4)))))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) H))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.zero_zero tptp.real))) (let ((_let_11 (tptp.fun tptp.nat _let_5))) (let ((_let_12 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_13 (tptp.fun _let_1 _let_11))) (let ((_let_14 (tptp.fun tptp.real _let_5))) (let ((_let_15 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (let ((_let_17 (tptp.ord_less tptp.real))) (let ((_let_18 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_18 _let_17 H) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_18 _let_17 T_4) _let_10)) (= (tptp.hAPP tptp.real tptp.real F H) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) _let_10))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1)))))))))))))))))))))))))))))) (forall ((N_1 $$unsorted) (Diff $$unsorted) (F $$unsorted) (H $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) H)) (=> (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff (tptp.zero_zero tptp.nat)) F) (=> (forall ((M_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 (tptp.zero_zero tptp.real)) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 T_4) H))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) T_4)))))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) H))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.zero_zero tptp.real))) (let ((_let_11 (tptp.fun tptp.nat _let_5))) (let ((_let_12 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_13 (tptp.fun _let_1 _let_11))) (let ((_let_14 (tptp.fun tptp.real _let_5))) (let ((_let_15 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (let ((_let_17 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_17 (tptp.ord_less tptp.real) _let_10) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_17 (tptp.ord_less_eq tptp.real) T_4) H)) (= (tptp.hAPP tptp.real tptp.real F H) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) _let_10))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1))))))))))))))))))))))))))) (forall ((Diff $$unsorted) (F $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) H) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1)) (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff _let_1) F) (forall ((M_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 H) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 T_4) (tptp.zero_zero tptp.real)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) T_4))))))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) H))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.zero_zero tptp.real))) (let ((_let_11 (tptp.fun tptp.nat _let_5))) (let ((_let_12 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_13 (tptp.fun _let_1 _let_11))) (let ((_let_14 (tptp.fun tptp.real _let_5))) (let ((_let_15 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (let ((_let_17 (tptp.ord_less tptp.real))) (let ((_let_18 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_18 _let_17 H) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_18 _let_17 T_4) _let_10)) (= (tptp.hAPP tptp.real tptp.real F H) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) _let_10))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1))))))))))))))))))))))))))) (forall ((Diff $$unsorted) (F $$unsorted) (N_1 $$unsorted) (H $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) H)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) _let_1) N_1)) (=> (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff _let_1) F) (=> (forall ((M_2 $$unsorted) (T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 (tptp.zero_zero tptp.real)) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_3 T_4) H))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) T_4) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) T_4)))))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) H))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.zero_zero tptp.real))) (let ((_let_11 (tptp.fun tptp.nat _let_5))) (let ((_let_12 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_13 (tptp.fun _let_1 _let_11))) (let ((_let_14 (tptp.fun tptp.real _let_5))) (let ((_let_15 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_16 (tptp.fun _let_1 _let_1))) (let ((_let_17 (tptp.ord_less tptp.real))) (let ((_let_18 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_18 _let_17 _let_10) T_4)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_18 _let_17 T_4) H)) (= (tptp.hAPP tptp.real tptp.real F H) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_11 _let_16 _let_15 (tptp.hAPP _let_1 _let_11 (tptp.hAPP _let_14 _let_13 _let_12 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_11 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) _let_10))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1)))))))))))))))))))))))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (=> (and (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff (tptp.zero_zero tptp.nat)) F) (forall ((M_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) X_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) X_2))))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.fun tptp.nat _let_5))) (let ((_let_11 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_12 (tptp.fun _let_1 _let_10))) (let ((_let_13 (tptp.fun tptp.real _let_5))) (let ((_let_14 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_15 (tptp.fun _let_1 _let_1))) (let ((_let_16 (tptp.abs_abs tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_16 T_4)) (tptp.hAPP tptp.real tptp.real _let_16 X_1))) (= (tptp.hAPP tptp.real tptp.real F X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_1 _let_10 (tptp.hAPP _let_13 _let_12 _let_11 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_1 _let_10 (tptp.hAPP _let_13 _let_12 _let_11 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_10 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) (tptp.zero_zero tptp.real)))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1)))))))))))))))))))))))) (forall ((N_1 $$unsorted) (X_1 $$unsorted) (Diff $$unsorted) (F $$unsorted)) (=> (= (tptp.hAPP tptp.nat (tptp.fun tptp.real tptp.real) Diff (tptp.zero_zero tptp.nat)) F) (=> (forall ((M_2 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 Diff M_2)) X_2) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 Diff (tptp.hAPP tptp.nat tptp.nat tptp.suc M_2)) X_2)))))) (exists ((T_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (let ((_let_4 (tptp.real_1 tptp.nat))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.inverse_divide tptp.real))) (let ((_let_7 (tptp.times_times tptp.real))) (let ((_let_8 (tptp.fun tptp.nat tptp.bool))) (let ((_let_9 (tptp.fun tptp.nat tptp.nat))) (let ((_let_10 (tptp.fun tptp.nat _let_5))) (let ((_let_11 (tptp.combb tptp.real _let_5 tptp.nat))) (let ((_let_12 (tptp.fun _let_1 _let_10))) (let ((_let_13 (tptp.fun tptp.real _let_5))) (let ((_let_14 (tptp.combs tptp.nat tptp.real tptp.real))) (let ((_let_15 (tptp.fun _let_1 _let_1))) (let ((_let_16 (tptp.abs_abs tptp.real))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real _let_16 T_4)) (tptp.hAPP tptp.real tptp.real _let_16 X_1))) (= (tptp.hAPP tptp.real tptp.real F X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.hAPP _let_8 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_8 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_1 _let_10 (tptp.hAPP _let_13 _let_12 _let_11 _let_7) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_1 _let_10 (tptp.hAPP _let_13 _let_12 _let_11 _let_6) (tptp.hAPP tptp.real _let_1 (tptp.hAPP _let_10 (tptp.fun tptp.real _let_1) (tptp.combc tptp.nat tptp.real tptp.real) Diff) (tptp.zero_zero tptp.real)))) (tptp.hAPP _let_9 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_9 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) _let_4) _let_3)))) _let_2)) (tptp.hAPP tptp.nat _let_8 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_8) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_7 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_5 _let_6 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_5 Diff N_1) T_4)) (tptp.hAPP tptp.nat tptp.real _let_4 (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)))) (tptp.hAPP tptp.nat tptp.real _let_2 N_1))))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.banach X_a) (forall ((F $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat X_a) tptp.bool (tptp.summable X_a) F)) (forall ((E $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) E)) (exists ((N_3 $$unsorted)) (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_3) M_2)) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP _let_1 X_a (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) M_2) N_2)))) E))))))))))))) (forall ((F $$unsorted) (K_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (forall ((P_6 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) P_6) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real F P_6)) K_3)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_1 tptp.real (tptp.hAPP (tptp.fun tptp.nat tptp.real) (tptp.fun _let_1 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real (tptp.real_1 tptp.nat) N_1)) K_3)))))) (forall ((F $$unsorted) (X_1 $$unsorted) (F_2 $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) Ma) N_1))) (let ((_let_3 (tptp.combc tptp.nat tptp.real tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.big_co1399186613setsum tptp.nat tptp.real))) (let ((_let_9 (tptp.fun _let_1 tptp.real))) (let ((_let_10 (tptp.fun tptp.real _let_9))) (let ((_let_11 (tptp.fun tptp.real tptp.bool))) (=> (forall ((R_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less_eq tptp.nat) Ma) R_2)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_3 (tptp.ord_less tptp.nat) R_2) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) Ma) N_1)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_2) (tptp.deriv tptp.real) (tptp.hAPP tptp.nat _let_1 F R_2)) X_1) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.nat _let_1 F_2 R_2) X_1)))))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_11 (tptp.hAPP _let_6 (tptp.fun tptp.real _let_11) (tptp.deriv tptp.real) (tptp.hAPP _let_1 _let_6 (tptp.hAPP _let_10 (tptp.fun _let_1 _let_6) (tptp.combc tptp.real _let_1 tptp.real) (tptp.hAPP _let_5 _let_10 (tptp.hAPP (tptp.fun _let_4 _let_9) (tptp.fun _let_5 _let_10) (tptp.combb _let_4 _let_9 tptp.real) _let_8) (tptp.hAPP _let_7 _let_5 _let_3 F))) _let_2)) X_1) (tptp.hAPP _let_1 tptp.real (tptp.hAPP _let_4 _let_9 _let_8 (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_7 _let_5 _let_3 F_2) X_1)) _let_2)))))))))))))))) (forall ((X_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) F)) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_1 tptp.real (tptp.hAPP (tptp.fun tptp.nat tptp.real) (tptp.fun _let_1 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_2))) X_1)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) F)) X_1)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.t2_space X_a)) (forall ((F $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (=> (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_1) M_2)) (= (tptp.hAPP tptp.nat X_a F M_2) (tptp.zero_zero X_a)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 (tptp.fun X_a tptp.bool) (tptp.sums X_a) F) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_2 (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.comm_monoid_add X_b) (tptp.ordere779506340up_add X_b)) (forall ((F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) B_2) A_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) (tptp.hAPP X_a X_b F X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP _let_1 X_b _let_2 A_3)) (tptp.hAPP _let_1 X_b _let_2 B_2))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ordere216010020id_add X_b) (forall ((F $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) B_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) A_3) B_2)) (=> (forall ((B_4 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) B_4) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) B_2) A_3))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) (tptp.hAPP X_a X_b F B_4)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP _let_1 X_b _let_2 A_3)) (tptp.hAPP _let_1 X_b _let_2 B_2))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (S $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) T_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) S) T_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) T_3) S))) (= (tptp.hAPP X_a X_b F X_2) (tptp.zero_zero X_b))))) (= (tptp.hAPP _let_1 X_b _let_2 T_3) (tptp.hAPP _let_1 X_b _let_2 S)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (S $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) T_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) S) T_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) T_3) S))) (= (tptp.hAPP X_a X_b F X_2) (tptp.zero_zero X_b))))) (= (tptp.hAPP _let_1 X_b _let_2 S) (tptp.hAPP _let_1 X_b _let_2 T_3)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.ordere779506340up_add X_b) (tptp.semiring_1 X_b)) (forall ((F $$unsorted) (K_3 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F I_2)) K_3))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F) A_3)) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.times_times X_b) (tptp.hAPP tptp.nat X_b (tptp.semiring_1_of_nat X_b) (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) A_3))) K_3)))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.comm_monoid_mult X_a)) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum tptp.int X_a))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.fun tptp.int X_a))) (=> (= A_3 B_2) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set B_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (= (tptp.hAPP tptp.int X_a F X_2) (tptp.hAPP tptp.int X_a G X_2)))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 F) A_3) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 G) B_2)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (R_3 $$unsorted) (K $$unsorted) (T_3 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.finite_card X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.combb _let_2 _let_2 X_a))) (let ((_let_7 (tptp.fun X_a _let_2))) (let ((_let_8 (tptp.fun _let_7 _let_7))) (let ((_let_9 (tptp.fun X_a tptp.nat))) (let ((_let_10 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.finite_finite_1 X_a) S)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) T_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) T_3)) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 tptp.bool)) _let_3 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)) S))) (tptp.hAPP X_b _let_1 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun X_b _let_1) (tptp.combc X_a X_b tptp.bool) R_3) X_2)))) K)))))))) (= (tptp.hAPP _let_10 tptp.nat (tptp.hAPP _let_9 (tptp.fun _let_10 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) (tptp.hAPP _let_7 _let_9 (tptp.hAPP (tptp.fun _let_2 tptp.nat) (tptp.fun _let_7 _let_9) (tptp.combb _let_2 tptp.nat X_a) _let_1) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.collect X_b)) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_2 tptp.bool)) _let_3 (tptp.combc X_b _let_2 tptp.bool) (tptp.member X_b)) T_3)))) R_3)))) S) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) K) (tptp.hAPP _let_2 tptp.nat _let_1 T_3))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((I $$unsorted) (B_2 $$unsorted) (F $$unsorted) (Sa $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) Sa)) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I_2) Sa)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) (tptp.hAPP X_a X_b F I_2)))))) (=> (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F) Sa) B_2) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I) Sa)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F I)) B_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.ordered_ab_group_add X_b) (forall ((I $$unsorted) (F $$unsorted) (Sa $$unsorted)) (let ((_let_1 (tptp.zero_zero X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) Sa)) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I_2) Sa)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) (tptp.hAPP X_a X_b F I_2)))))) (=> (= (tptp.hAPP _let_2 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 X_b) (tptp.big_co1399186613setsum X_a X_b) F) Sa) _let_1) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) I) Sa)) (= (tptp.hAPP X_a X_b F I) _let_1)))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (= (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_a tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) F) A_3) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP X_a tptp.nat F X_2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.ord X_a) (tptp.comm_monoid_add X_b)) (forall ((F $$unsorted) (G $$unsorted) (B_1 $$unsorted) (D_1 $$unsorted) (A_2 $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastLessThan X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_5 (tptp.fun _let_2 X_b))) (let ((_let_6 (tptp.fun X_a X_b))) (=> (= (tptp.ti X_a A_2) (tptp.ti X_a C_1)) (=> (= (tptp.ti X_a B_1) (tptp.ti X_a D_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) C_1) X_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) X_2) D_1)) (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b G X_2)))))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_6 _let_5 _let_4 F) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 A_2) B_1)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_6 _let_5 _let_4 G) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 _let_1 C_1) D_1))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (R_3 $$unsorted) (K $$unsorted) (Ta $$unsorted) (Sa $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.nat))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.combb _let_1 _let_1 X_a))) (let ((_let_7 (tptp.fun X_a _let_1))) (let ((_let_8 (tptp.fun _let_7 _let_7))) (let ((_let_9 (tptp.fun X_a tptp.nat))) (let ((_let_10 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.finite_finite_1 X_a) Sa)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) Ta)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_1))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b (tptp.fun _let_2 tptp.bool) (tptp.member X_b) X_2) Ta)) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card X_a) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_3 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a (tptp.fun _let_1 tptp.bool)) _let_3 (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)) Sa))) (tptp.hAPP X_b _let_1 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun X_b _let_1) (tptp.combc X_a X_b tptp.bool) R_3) X_2)))) (tptp.hAPP X_b tptp.nat K X_2))))))))) (= (tptp.hAPP _let_10 tptp.nat (tptp.hAPP _let_9 (tptp.fun _let_10 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) (tptp.hAPP _let_7 _let_9 (tptp.hAPP _let_2 (tptp.fun _let_7 _let_9) (tptp.combb _let_1 tptp.nat X_a) (tptp.finite_card X_b)) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.collect X_b)) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_3 _let_8 _let_6 (tptp.hAPP _let_5 _let_3 (tptp.combs X_b tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_1 _let_5) (tptp.combb tptp.bool _let_4 X_b) tptp.fconj) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun _let_1 tptp.bool)) _let_3 (tptp.combc X_b _let_1 tptp.bool) (tptp.member X_b)) Ta)))) R_3)))) Sa) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun X_b tptp.nat) _let_2 (tptp.big_co1399186613setsum X_b tptp.nat) K) Ta)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_field X_b) (forall ((F $$unsorted) (X_1 $$unsorted) (F_2 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 X_b))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_b _let_1))) (let ((_let_7 (tptp.fun X_b X_b))) (let ((_let_8 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_a) S)) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_b tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) N_2) S)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_3 (tptp.hAPP _let_2 (tptp.fun X_b _let_3) (tptp.deriv X_b) (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun X_a _let_2) (tptp.combc X_b X_a X_b) F) N_2)) X_1) (tptp.hAPP X_a X_b (tptp.hAPP X_b _let_1 F_2 X_1) N_2))))))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_7 (tptp.fun X_b _let_8) (tptp.deriv X_b) (tptp.hAPP _let_3 _let_7 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_7) (tptp.combc X_b _let_3 X_b) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun _let_1 _let_4) (tptp.fun _let_6 _let_5) (tptp.combb _let_1 _let_4 X_b) _let_2) F)) S)) X_1) (tptp.hAPP _let_3 X_b (tptp.hAPP _let_1 _let_4 _let_2 (tptp.hAPP X_b _let_1 F_2 X_1)) S)))))))))))))))) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.nat_nat_set A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int F X_2)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP _let_1 tptp.int (tptp.hAPP (tptp.fun tptp.int tptp.int) (tptp.fun _let_1 tptp.int) (tptp.big_co1399186613setsum tptp.int tptp.int) F) A_3))))))) (forall ((X_1 $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real F N_2)))) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_1 tptp.real (tptp.hAPP (tptp.fun tptp.nat tptp.real) (tptp.fun _let_1 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_2))) X_1)))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.real) tptp.bool (tptp.summable tptp.real) F))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (= (tptp.hAPP X_a X_b G X_2) (tptp.zero_zero X_b))))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) G) A_3) (tptp.zero_zero X_b)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.comm_monoid_add X_b) (tptp.ordere779506340up_add X_b)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.zero_zero X_b)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F) A_3)) (tptp.zero_zero X_b)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.comm_monoid_add X_b) (tptp.ordere779506340up_add X_b)) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) (tptp.hAPP X_a X_b F X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.zero_zero X_b)) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F) A_3)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 X_b))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a X_b) _let_2 (tptp.big_co1399186613setsum X_a X_b) F))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 _let_1) S)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) S)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) X_2)))))) (=> (forall ((T1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) T1) S)) (forall ((T2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) T2) S)) (=> (not (= (tptp.ti _let_1 T1) (tptp.ti _let_1 T2))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 T1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_2 T2)) (= (tptp.hAPP X_a X_b F X_2) (tptp.zero_zero X_b)))))))))))))))) (= (tptp.hAPP _let_1 X_b _let_3 (tptp.hAPP _let_4 _let_1 (tptp.complete_Sup_Sup _let_1) S)) (tptp.hAPP _let_4 X_b (tptp.hAPP _let_2 (tptp.fun _let_4 X_b) (tptp.big_co1399186613setsum _let_1 X_b) _let_3) S)))))))))))) (forall ((A_2 $$unsorted) (D_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.times_times tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.hAPP tptp.int _let_3 (tptp.plus_plus tptp.int) A_2))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (let ((_let_6 (tptp.fun tptp.nat _let_3))) (let ((_let_7 (tptp.fun tptp.nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) (tptp.hAPP _let_5 tptp.int (tptp.hAPP _let_7 (tptp.fun _let_5 tptp.int) (tptp.big_co1399186613setsum tptp.nat tptp.int) (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_3 (tptp.fun _let_7 _let_7) (tptp.combb tptp.int tptp.int tptp.nat) _let_4) (tptp.hAPP tptp.int _let_7 (tptp.hAPP _let_6 (tptp.fun tptp.int _let_7) (tptp.combc tptp.nat tptp.int tptp.int) (tptp.hAPP _let_7 _let_6 (tptp.hAPP (tptp.fun tptp.int _let_3) (tptp.fun _let_7 _let_6) (tptp.combb tptp.int _let_3 tptp.nat) _let_2) _let_1)) D_1))) (tptp.hAPP tptp.nat _let_5 (tptp.ord_lessThan tptp.nat) N_1))) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 N_1)) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.one_one tptp.nat)))) D_1))))))))))))) (forall ((K_3 $$unsorted) (K $$unsorted) (F $$unsorted)) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.real F N_2))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 K) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) K_3))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.real) tptp.bool (tptp.bseq tptp.real) F)))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) K))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((I $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I) (tptp.hAPP X_a _let_1 (tptp.ord_lessThan X_a) K))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) I) K))))))) (forall ((U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) U_1)) U_1))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_lessThan X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (= (tptp.hAPP X_a _let_2 _let_1 X_1) (tptp.hAPP X_a _let_2 _let_1 Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) N_1) (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) N_1)))) (forall ((S $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) S)) (exists ((K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) S) (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) K_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_lessThan X_a))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP X_a _let_1 _let_2 X_1)) (tptp.hAPP X_a _let_1 _let_2 Y_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) X_1) Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_lessThan X_a))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less _let_1) (tptp.hAPP X_a _let_1 _let_2 Ma)) (tptp.hAPP X_a _let_1 _let_2 N_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) Ma) N_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_lessThan tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F))) (= (tptp.hAPP _let_2 X_a _let_3 (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP _let_2 X_a _let_3 (tptp.hAPP tptp.nat _let_2 _let_1 N_1))) (tptp.hAPP tptp.nat X_a F N_1))))))))) (forall ((A_2 $$unsorted) (D_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.times_times tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) A_2))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (let ((_let_5 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat)))) (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_1 (tptp.fun _let_4 tptp.nat) (tptp.big_co1399186613setsum tptp.nat tptp.nat) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.combb tptp.nat tptp.nat tptp.nat) _let_3) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_5 _let_5 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_2) D_1))) (tptp.hAPP tptp.nat _let_4 (tptp.ord_lessThan tptp.nat) N_1))) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 N_1) (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 _let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) N_1) (tptp.one_one tptp.nat))) D_1))))))))))) (forall ((U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.zero_zero tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 (tptp.ord_less_eq tptp.int) _let_3) U_1)) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.ord_atLeastLessThan tptp.int) _let_3) U_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_1 _let_2) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 U_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((A_2 $$unsorted) (D_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.plus_plus X_a))) (let ((_let_5 (tptp.hAPP X_a _let_3 _let_4 A_2))) (let ((_let_6 (tptp.fun tptp.nat tptp.bool))) (let ((_let_7 (tptp.fun tptp.nat _let_3))) (let ((_let_8 (tptp.fun tptp.nat X_a))) (let ((_let_9 (tptp.one_one X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_4 _let_9) _let_9)) (tptp.hAPP _let_6 X_a (tptp.hAPP _let_8 (tptp.fun _let_6 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) (tptp.hAPP _let_8 _let_8 (tptp.hAPP _let_3 (tptp.fun _let_8 _let_8) (tptp.combb X_a X_a tptp.nat) _let_5) (tptp.hAPP X_a _let_8 (tptp.hAPP _let_7 (tptp.fun X_a _let_8) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_8 _let_7 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_8 _let_7) (tptp.combb X_a _let_3 tptp.nat) _let_2) _let_1)) D_1))) (tptp.hAPP tptp.nat _let_6 (tptp.ord_lessThan tptp.nat) N_1))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 N_1)) (tptp.hAPP X_a X_a _let_5 (tptp.hAPP X_a X_a _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 (tptp.hAPP tptp.nat X_a _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.minus_minus tptp.nat) N_1) (tptp.one_one tptp.nat)))) D_1))))))))))))))))) (forall ((S $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) S)) (exists ((K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) S) (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) K_1))))))) (forall ((N_1 $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) N_1))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.big_co1399186613setsum tptp.nat tptp.nat))) (let ((_let_7 (tptp.fun _let_1 tptp.nat))) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) (tptp.hAPP tptp.nat tptp.nat Q_1 X_2)) (tptp.hAPP tptp.nat tptp.nat P_1 X_2)))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 (tptp.hAPP _let_1 tptp.nat (tptp.hAPP _let_4 _let_7 _let_6 P_1) _let_2)) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP _let_4 _let_7 _let_6 Q_1) _let_2)) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat tptp.nat tptp.nat) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_5) (tptp.combb tptp.nat _let_4 tptp.nat) _let_3) P_1)) Q_1)) _let_2))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (= (tptp.hAPP _let_1 tptp.real (tptp.complete_Sup_Sup tptp.real) (tptp.hAPP tptp.real _let_1 (tptp.ord_lessThan tptp.real) X_1)) X_1))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.metric_space X_a)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun _let_1 X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (= (tptp.hAPP _let_4 X_a (tptp.suminf X_a) F) (tptp.hAPP _let_4 X_a (tptp.lim X_a) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_4) (tptp.combb _let_1 X_a tptp.nat) (tptp.hAPP _let_4 _let_3 (tptp.big_co1399186613setsum tptp.nat X_a) F)) (tptp.hAPP tptp.nat _let_2 (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted) (F $$unsorted) (G $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_b) X_c))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (= (tptp.hAPP X_b X_c (tptp.hAPP X_a (tptp.fun X_b X_c) F X_2) Y_2) (tptp.hAPP _let_1 X_c G (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_2) Y_2))))) (= (tptp.hAPP (tptp.fun X_a (tptp.fun X_b X_c)) _let_1 (tptp.product_prod_case X_a X_b X_c) F) (tptp.ti _let_1 G))))) (forall ((X_a $$unsorted) (N_1 $$unsorted) (F $$unsorted) (C_1 $$unsorted) (H $$unsorted)) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat (tptp.fun X_a X_a)))) (= (tptp.hAPP tptp.nat X_a F N_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_a (tptp.fun _let_2 _let_1) (tptp.nat_rec X_a) C_1) H) N_2))))) (= (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.nat (tptp.fun X_a X_a) H N_1) (tptp.hAPP tptp.nat X_a F N_1))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (not (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.image X_a X_b) F) A_3))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.member X_a))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun _let_4 tptp.bool))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun X_a _let_8))) (and (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_7 _let_5 X_2) A_3)) (not (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_a) (tptp.hAPP _let_4 _let_4 (tptp.collect X_a) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_9 _let_6 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_4 _let_9 (tptp.hAPP (tptp.fun tptp.bool _let_8) (tptp.fun _let_4 _let_9) (tptp.combb tptp.bool _let_8 X_a) tptp.fconj) (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun X_a _let_7) _let_6 (tptp.combc X_a _let_4 tptp.bool) _let_5) A_3))) (tptp.hAPP X_b _let_4 (tptp.hAPP _let_2 (tptp.fun X_b _let_4) (tptp.combc X_a X_b tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_b _let_1 X_a) (tptp.fequal X_b)) F)) (tptp.hAPP X_a X_b F X_2))))))))))))))))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (C_1 $$unsorted) (H $$unsorted)) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat (tptp.fun X_a X_a)))) (= (tptp.hAPP tptp.nat X_a F N_2) (tptp.hAPP tptp.nat X_a (tptp.hAPP _let_2 _let_1 (tptp.hAPP X_a (tptp.fun _let_2 _let_1) (tptp.nat_rec X_a) C_1) H) N_2))))) (= (tptp.hAPP tptp.nat X_a F (tptp.zero_zero tptp.nat)) (tptp.ti X_a C_1)))) (forall ((X_a $$unsorted) (F $$unsorted) (G $$unsorted) (Ma $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a tptp.int))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.int))) (let ((_let_4 (tptp.fun X_a tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) S)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong (tptp.hAPP X_a tptp.int F X_2)) (tptp.hAPP X_a tptp.int G X_2)) Ma)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_5) tptp.zcong (tptp.hAPP _let_2 tptp.int (tptp.hAPP _let_4 _let_3 _let_1 F) S)) (tptp.hAPP _let_2 tptp.int (tptp.hAPP _let_4 _let_3 _let_1 G) S)) Ma))))))))) (forall ((P_2 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.bool tptp.bool))) (let ((_let_3 (tptp.fun tptp.int _let_2))) (let ((_let_4 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.int tptp.bool tptp.bool) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.bool _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.bool _let_2 tptp.int) tptp.fconj) (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))))) (let ((_let_5 (tptp.collect tptp.int))) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_2)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X_2))))) (= (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 P_1)) (tptp.hAPP _let_1 _let_1 _let_5 (tptp.hAPP _let_1 _let_1 _let_4 P_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (R_3 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_b _let_3))) (let ((_let_5 (tptp.fun X_b _let_1))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (let ((_let_7 (tptp.fun X_a _let_4))) (let ((_let_8 (tptp.fun X_a _let_5))) (let ((_let_9 (tptp.fun X_b tptp.bool))) (let ((_let_10 (tptp.fun _let_2 _let_9))) (let ((_let_11 (tptp.fun X_a _let_10))) (let ((_let_12 (tptp.fun X_a _let_9))) (let ((_let_13 (tptp.hAPP _let_11 (tptp.fun _let_2 _let_12) (tptp.combc X_a _let_2 _let_9) (tptp.hAPP _let_7 _let_11 (tptp.hAPP (tptp.fun _let_4 _let_10) (tptp.fun _let_7 _let_11) (tptp.combb _let_4 _let_10 X_a) (tptp.combc X_b _let_2 tptp.bool)) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combb _let_5 _let_4 X_a) (tptp.hAPP (tptp.fun _let_1 _let_3) _let_6 (tptp.combb _let_1 _let_3 X_b) (tptp.member _let_1))) (tptp.product_Pair X_a X_b)))))) (= (tptp.hBOOL (tptp.hAPP _let_12 tptp.bool (tptp.hAPP _let_12 (tptp.fun _let_12 tptp.bool) (tptp.ord_less_eq _let_12) (tptp.hAPP _let_2 _let_12 _let_13 R_3)) (tptp.hAPP _let_2 _let_12 _let_13 S))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.ord_less_eq _let_2) R_3) S))))))))))))))))) (forall ((X_a $$unsorted) (X_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) P_1) Q_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_1)))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) P_1) Q_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_1)))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (S $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.fun (tptp.product_prod X_a X_b) tptp.bool))) (= (forall ((X_2 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_2) Xa)))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 R_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 S))))))) (= (tptp.ti _let_1 R_3) (tptp.ti _let_1 S))))) (forall ((X_a $$unsorted) (R_3 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_1 _let_1) (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 _let_4 R_3)) (tptp.hAPP _let_1 _let_1 _let_4 S))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 R_3) S)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted) (P_1 $$unsorted) (Q_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) P_1) Q_1)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 P_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_1) Y_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 P_1 X_1) Y_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) P_1) Q_1)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_1) Y_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a (tptp.fun X_b tptp.bool)))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 P_1 X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_a _let_1 Q_1 X_2) Y_2))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) P_1) Q_1))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.comm_monoid_add X_b) (tptp.ordere779506340up_add X_b)) (forall ((F $$unsorted) (G $$unsorted) (K_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I_2) K_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP X_a X_b F I_2)) (tptp.hAPP X_a X_b G I_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) K_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) K_3))))))))))) (forall ((P_5 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP _let_1 tptp.int (tptp.product_snd tptp.int tptp.int) P_5))) (let ((_let_3 (tptp.hAPP _let_1 tptp.int (tptp.product_fst tptp.int tptp.int) P_5))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_4 (tptp.gcd_gcd tptp.int) _let_3) _let_2))) (let ((_let_6 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) _let_5))) (let ((_let_7 (tptp.div_div tptp.int))) (let ((_let_8 (tptp.hAPP tptp.int _let_4 _let_7 _let_2))) (let ((_let_9 (tptp.hAPP tptp.int _let_4 _let_7 _let_3))) (let ((_let_10 (tptp.product_Pair tptp.int tptp.int))) (let ((_let_11 (tptp.fun tptp.int _let_1))) (let ((_let_12 (tptp.hAPP _let_1 _let_1 tptp.normalize P_5))) (let ((_let_13 (tptp.zero_zero tptp.int))) (let ((_let_14 (= _let_2 _let_13))) (let ((_let_15 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_13) _let_2)))) (and (=> _let_15 (= _let_12 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_11 _let_10 (tptp.hAPP tptp.int tptp.int _let_9 _let_5)) (tptp.hAPP tptp.int tptp.int _let_8 _let_5)))) (=> (not _let_15) (and (=> _let_14 (= _let_12 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_11 _let_10 _let_13) (tptp.one_one tptp.int)))) (=> (not _let_14) (= _let_12 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_11 _let_10 (tptp.hAPP tptp.int tptp.int _let_9 _let_6)) (tptp.hAPP tptp.int tptp.int _let_8 _let_6))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((Q_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Q_2) (tptp.ring_1_Ints X_a))) (not (forall ((Z_2 $$unsorted)) (not (= (tptp.ti X_a Q_2) (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_2)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y)) X))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y)) Y))) (forall ((N $$unsorted) (M $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.power_power tptp.int))) (let ((_let_3 (tptp.fun tptp.nat tptp.int))) (let ((_let_4 (tptp.gcd_gcd tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 A_1) B) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_5 _let_4 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 A_1) N)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_3 _let_2 B) M)) _let_1)))))))) (forall ((X $$unsorted) (Y $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_mod tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) X) Y)) M) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) X) M) _let_1))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.gcd_gcd tptp.int))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Y)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 X) Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) X) Y))))))) (forall ((B_5 $$unsorted) (A_6 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B))) (let ((_let_4 (tptp.times_times tptp.int))) (=> (not (= _let_3 (tptp.zero_zero tptp.int))) (=> (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 A_6) _let_3)) (=> (= (tptp.ti tptp.int B) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 B_5) _let_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_6) B_5) (tptp.one_one tptp.int)))))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 X)) (tptp.hAPP tptp.nat tptp.int _let_1 Y)) (tptp.hAPP tptp.nat tptp.int _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) X) Y))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.gcd_gcd tptp.int) M))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_4) M)) N)) (tptp.hAPP tptp.int tptp.int _let_2 N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) M) N)) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 M) N))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.gcd_gcd tptp.int) M))) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) M) N)) (tptp.hAPP tptp.int tptp.int _let_2 N))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.plus_plus tptp.int) N) _let_1)) N) _let_1)))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.minus_minus tptp.int) N) _let_1)) N) _let_1)))) (forall ((E_1 $$unsorted) (B $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.gcd_gcd tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (let ((_let_4 (tptp.dvd_dvd tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 D) A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 _let_4 E_1) B)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 A_1) B) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 D) E_1) _let_1)))))))))) (forall ((N $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) D))) (=> (= (tptp.hAPP tptp.int tptp.int _let_2 A_1) _let_1) (= (tptp.hAPP tptp.int tptp.int _let_2 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) A_1) N)) _let_1))))) (forall ((M $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) M) _let_1) _let_1))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) Ma) N_1) _let_1) (and (= (tptp.ti tptp.int Ma) _let_1) (= (tptp.ti tptp.int N_1) _let_1))))) (forall ((A_1 $$unsorted) (N $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.power_power tptp.int))) (let ((_let_4 (tptp.fun tptp.nat tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 A_1) N)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 B) N)) (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int _let_4 _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B)) N))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) A_1))))) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 B))) (let ((_let_4 (tptp.hAPP tptp.int _let_2 _let_1 A_1))) (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int _let_4 C)) (tptp.hAPP tptp.int tptp.int _let_4 (tptp.hAPP tptp.int tptp.int _let_3 C)))))))) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 A_1))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 B)) C) (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 B) C))))))) (forall ((I_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) M) N))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N))))) (forall ((I_1 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) I_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) M) N))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M))))) (forall ((N $$unsorted) (K_4 $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K_4))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) M) N))))))) (forall ((K $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) Ma) N_1))) (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Ma)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 N_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.gcd_gcd tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 X) Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.div_mod tptp.int) X) Y)))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y))) (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) _let_1) _let_1))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) X) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.gcd_gcd tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 X) Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int _let_1 X)) (tptp.hAPP tptp.int tptp.int _let_1 Y))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) Y)) (tptp.hAPP tptp.int tptp.int _let_1 Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X)) Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 X) Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) X)) Y) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 X) Y))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X))) (= (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.uminus_uminus tptp.int) Y)) (tptp.hAPP tptp.int tptp.int _let_1 Y)))) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) X) Y)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X)))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) Y) X)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) Y)))) (forall ((K_4 $$unsorted) (M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.times_times tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 K_4))) (let ((_let_4 (tptp.gcd_gcd tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) K_4)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 M) N)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 (tptp.hAPP tptp.int tptp.int _let_3 M)) (tptp.hAPP tptp.int tptp.int _let_3 N)))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) Ma) N_1))) (or (not (= (tptp.ti tptp.int Ma) _let_1)) (not (= (tptp.ti tptp.int N_1) _let_1)))))) (forall ((D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) D))) (=> (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) A_1) B)) _let_1) (= (tptp.hAPP tptp.int tptp.int _let_3 B) _let_1)))))) (forall ((D $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) D))) (=> (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) A_1) B)) _let_1) (= (tptp.hAPP tptp.int tptp.int _let_3 A_1) _let_1)))))) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) D))) (=> (= (tptp.hAPP tptp.int tptp.int _let_3 A_1) _let_1) (=> (= (tptp.hAPP tptp.int tptp.int _let_3 B) _let_1) (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) A_1) B)) _let_1))))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 K_4) N) (tptp.one_one tptp.int)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) K_4) M)) N) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 M) N)))))) (forall ((D_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) D_1))) (= (= (tptp.hAPP tptp.int tptp.int _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) A_2) B_1)) _let_1) (and (= (tptp.hAPP tptp.int tptp.int _let_3 A_2) _let_1) (= (tptp.hAPP tptp.int tptp.int _let_3 B_1) _let_1))))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) (tptp.zero_zero tptp.int)) X) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.rat))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) A_1) B))) (let ((_let_4 (tptp.div_div tptp.int))) (= (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 A_1) _let_3)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 B) _let_3)) (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int _let_1 tptp.fract A_1) B))))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B))) (let ((_let_4 (tptp.div_div tptp.int))) (let ((_let_5 (tptp.zero_zero tptp.int))) (=> (or (not (= (tptp.ti tptp.int A_1) _let_5)) (not (= (tptp.ti tptp.int B) _let_5))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 A_1) _let_3)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 B) _let_3)) (tptp.one_one tptp.int))))))))) (forall ((M $$unsorted) (K_4 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K_4))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) K_4) N) (tptp.one_one tptp.int)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) M) N))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 M))))))) (forall ((Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) K))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.gcd_gcd tptp.int) K) N_1) (tptp.one_one tptp.int)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.times_times tptp.int) Ma) N_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Ma))))))) (forall ((N $$unsorted) (M $$unsorted) (R_4 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.dvd_dvd tptp.int))) (let ((_let_3 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 M) R_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 N) R_4)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.gcd_gcd tptp.int) M) N) (tptp.one_one tptp.int)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_3 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) M) N)) R_4))))))))) (forall ((P_1 $$unsorted) (Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 X_1))) (let ((_let_4 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int _let_3 Y_1))))) (let ((_let_5 (tptp.uminus_uminus tptp.int))) (let ((_let_6 (tptp.hAPP tptp.int tptp.int _let_5 Y_1))) (let ((_let_7 (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_5 X_1)))) (let ((_let_8 (tptp.zero_zero tptp.int))) (let ((_let_9 (tptp.ord_less_eq tptp.int))) (let ((_let_10 (tptp.fun tptp.int tptp.bool))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_10 _let_9 Y_1) _let_8)))) (let ((_let_12 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_10 _let_9 X_1) _let_8)))) (let ((_let_13 (tptp.hAPP tptp.int _let_10 _let_9 _let_8))) (let ((_let_14 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_13 Y_1)))) (let ((_let_15 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_13 X_1)))) (=> (=> _let_15 (=> _let_14 _let_4)) (=> (=> _let_15 (=> _let_11 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int _let_3 _let_6))))) (=> (=> _let_12 (=> _let_14 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int _let_7 Y_1))))) (=> (=> _let_12 (=> _let_11 (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int _let_7 _let_6))))) _let_4)))))))))))))))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) D_1))) (= (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) D_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 A_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 B_1)) (forall ((E $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) E))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 A_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 B_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 D_1)))))) (= (tptp.ti tptp.int D_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) A_2) B_1)))))) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y)))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) A_1) B)) B))))) (forall ((B $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) A_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) A_1) B)) A_1))))) (forall ((B_1 $$unsorted) (C_1 $$unsorted) (A_2 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int tptp.int _let_1 D_1))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int _let_1 C_1))) (let ((_let_4 (tptp.hAPP tptp.int tptp.int _let_1 B_1))) (let ((_let_5 (tptp.hAPP tptp.int tptp.int _let_1 A_2))) (let ((_let_6 (tptp.times_times tptp.int))) (let ((_let_7 (tptp.fun tptp.int tptp.int))) (let ((_let_8 (tptp.one_one tptp.int))) (let ((_let_9 (tptp.gcd_gcd tptp.int))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_9 A_2) D_1) _let_8) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_9 B_1) C_1) _let_8) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_6 _let_5) _let_3) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_7 _let_6 _let_4) _let_2)) (and (= _let_5 _let_4) (= _let_3 _let_2))))))))))))))) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.gcd_gcd tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 K) L) (tptp.hAPP tptp.int tptp.int _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.bool (tptp.fun tptp.int _let_2) (tptp.if tptp.int) (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.fequal tptp.int) L) (tptp.zero_zero tptp.int))) K) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_3 L) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 (tptp.div_mod tptp.int) (tptp.hAPP tptp.int tptp.int _let_1 K)) (tptp.hAPP tptp.int tptp.int _let_1 L)))))))))) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.one_one tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) X))) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) A_1) B) _let_1) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 A_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 B)) (= (tptp.hAPP tptp.int tptp.int (tptp.abs_abs tptp.int) X) _let_1))))))) (forall ((R_4 $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (=> (= (tptp.hAPP tptp.rat _let_1 tptp.quotient_of R_4) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) P_5) Q_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) P_5) Q_3) (tptp.one_one tptp.int))))) (forall ((R_4 $$unsorted) (P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (=> (= (tptp.hAPP _let_1 _let_1 tptp.normalize R_4) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) P_5) Q_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) P_5) Q_3) (tptp.one_one tptp.int))))) (forall ((A_2 $$unsorted) (B_1 $$unsorted)) (= (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) A_2) B_1) (tptp.one_one tptp.int)) (forall ((D_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.dvd_dvd tptp.int) D_3))) (= (and (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) D_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 A_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_2 B_1))) (= (tptp.ti tptp.int D_3) (tptp.one_one tptp.int)))))))) (forall ((Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 Y)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Y)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y))))))) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.abs_abs tptp.int))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.gcd_gcd tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 X))) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int _let_1 Y))))))) (forall ((P_5 $$unsorted) (Q_3 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.product_Pair tptp.int tptp.int) P_5) Q_3))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) Q_3)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) P_5) Q_3) (tptp.one_one tptp.int)) (= (tptp.hAPP _let_1 _let_1 tptp.normalize _let_2) _let_2)))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.product_snd tptp.int tptp.int))) (let ((_let_2 (tptp.product_fst tptp.int tptp.int))) (let ((_let_3 (tptp.product_prod tptp.int tptp.int))) (let ((_let_4 (tptp.fun tptp.int tptp.int))) (let ((_let_5 (tptp.fun _let_3 _let_4))) (let ((_let_6 (tptp.fun _let_3 tptp.int))) (let ((_let_7 (tptp.fun tptp.int tptp.bool))) (let ((_let_8 (tptp.fun _let_3 _let_7))) (let ((_let_9 (tptp.fun _let_3 tptp.bool))) (let ((_let_10 (tptp.fun tptp.bool tptp.bool))) (let ((_let_11 (tptp.fun _let_3 _let_10))) (let ((_let_12 (tptp.hAPP (tptp.fun tptp.bool _let_10) (tptp.fun _let_9 _let_11) (tptp.combb tptp.bool _let_10 _let_3) tptp.fconj))) (let ((_let_13 (tptp.combs _let_3 tptp.bool tptp.bool))) (let ((_let_14 (tptp.fun _let_9 _let_9))) (let ((_let_15 (tptp.fun tptp.int tptp.rat))) (let ((_let_16 (tptp.fun _let_3 _let_15))) (let ((_let_17 (tptp.fun _let_3 tptp.rat))) (let ((_let_18 (tptp.fun tptp.rat tptp.bool))) (= (tptp.hAPP tptp.rat _let_3 tptp.quotient_of X_1) (tptp.hAPP _let_9 _let_3 (tptp.the _let_3) (tptp.hAPP _let_9 _let_9 (tptp.hAPP _let_11 _let_14 _let_13 (tptp.hAPP _let_9 _let_11 _let_12 (tptp.hAPP _let_17 _let_9 (tptp.hAPP _let_18 (tptp.fun _let_17 _let_9) (tptp.combb tptp.rat tptp.bool _let_3) (tptp.hAPP tptp.rat _let_18 (tptp.fequal tptp.rat) X_1)) (tptp.hAPP _let_6 _let_17 (tptp.hAPP _let_16 (tptp.fun _let_6 _let_17) (tptp.combs _let_3 tptp.int tptp.rat) (tptp.hAPP _let_6 _let_16 (tptp.hAPP (tptp.fun tptp.int _let_15) (tptp.fun _let_6 _let_16) (tptp.combb tptp.int _let_15 _let_3) tptp.fract) _let_2)) _let_1)))) (tptp.hAPP _let_9 _let_9 (tptp.hAPP _let_11 _let_14 _let_13 (tptp.hAPP _let_9 _let_11 _let_12 (tptp.hAPP _let_6 _let_9 (tptp.hAPP _let_7 (tptp.fun _let_6 _let_9) (tptp.combb tptp.int tptp.bool _let_3) (tptp.hAPP tptp.int _let_7 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int))) _let_1))) (tptp.hAPP tptp.int _let_9 (tptp.hAPP _let_8 (tptp.fun tptp.int _let_9) (tptp.combc _let_3 tptp.int tptp.bool) (tptp.hAPP _let_6 _let_8 (tptp.hAPP (tptp.fun tptp.int _let_7) (tptp.fun _let_6 _let_8) (tptp.combb tptp.int _let_7 _let_3) (tptp.fequal tptp.int)) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_6 _let_6) (tptp.combs _let_3 tptp.int tptp.int) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun tptp.int _let_4) (tptp.fun _let_6 _let_5) (tptp.combb tptp.int _let_4 _let_3) (tptp.gcd_gcd tptp.int)) _let_2)) _let_1))) (tptp.one_one tptp.int))))))))))))))))))))))))) (forall ((R_4 $$unsorted)) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP _let_1 tptp.int (tptp.product_snd tptp.int tptp.int) X_2))) (let ((_let_3 (tptp.hAPP _let_1 tptp.int (tptp.product_fst tptp.int tptp.int) X_2))) (and (= R_4 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract _let_3) _let_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) _let_2)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) _let_3) _let_2) (tptp.one_one tptp.int)) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (let ((_let_2 (tptp.hAPP _let_1 tptp.int (tptp.product_snd tptp.int tptp.int) Y_2))) (let ((_let_3 (tptp.hAPP _let_1 tptp.int (tptp.product_fst tptp.int tptp.int) Y_2))) (=> (and (= R_4 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract _let_3) _let_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) _let_2)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) _let_3) _let_2) (tptp.one_one tptp.int))) (= Y_2 X_2)))))))))))) (forall ((Q_3 $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.int))) (=> (= Q_3 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_4) B_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) _let_1) B_4)) (=> (not (= (tptp.ti tptp.int A_4) _let_1)) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) A_4) B_4) (tptp.one_one tptp.int)))))))) (= Q_3 (tptp.zero_zero tptp.rat)))) (forall ((Q_3 $$unsorted)) (not (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (=> (= Q_3 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_4) B_4)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B_4)) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) A_4) B_4) (tptp.one_one tptp.int)))))))) (forall ((Q_2 $$unsorted) (P_1 $$unsorted)) (=> (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) B_4)) (=> (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) A_4) B_4) (tptp.one_one tptp.int)) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool P_1 (tptp.hAPP tptp.int tptp.rat (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.rat) tptp.fract A_4) B_4)))))) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool P_1 Q_2)))) (forall ((X_a $$unsorted) (F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I_2) A_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) (tptp.hAPP X_a tptp.int F I_2)) X_1) (tptp.one_one tptp.int))))) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) (tptp.hAPP _let_1 tptp.int (tptp.hAPP (tptp.fun X_a tptp.int) (tptp.fun _let_1 tptp.int) (tptp.big_co302546470etprod X_a tptp.int) F) A_3)) X_1) (tptp.one_one tptp.int))))) (forall ((X_a $$unsorted)) (=> (tptp.ring_1 X_a) (forall ((P_1 $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) Q_2) (tptp.ring_1_Ints X_a))) (=> (forall ((Z_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.hAPP tptp.int X_a (tptp.ring_1_of_int X_a) Z_2)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 Q_2)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (G $$unsorted) (S $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) T_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) S) T_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) T_3) S))) (= (tptp.hAPP X_a X_b G X_2) (tptp.zero_zero X_b))))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) S)) (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b G X_2))))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) S) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) T_3))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((G $$unsorted) (F $$unsorted) (S $$unsorted) (T_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) T_3)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) S) T_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_1) (tptp.minus_minus _let_1) T_3) S))) (= (tptp.hAPP X_a X_b F X_2) (tptp.zero_zero X_b))))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) S)) (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b G X_2))))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) T_3) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) S))))))))))))) (forall ((N_1 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.nat))) (let ((_let_3 (tptp.big_co1399186613setsum _let_1 tptp.nat))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun _let_4 tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 _let_1) S)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) S)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) X_2)))))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) S)) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.int) X_2) N_1))))) (= (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_2 _let_5 _let_3 (tptp.finite_card tptp.int)) S) (tptp.hAPP _let_4 tptp.nat (tptp.hAPP _let_2 _let_5 _let_3 (tptp.hAPP tptp.nat _let_2 (tptp.combk tptp.nat _let_1) N_1)) S))))))))))) (forall ((X_a $$unsorted) (F $$unsorted) (G $$unsorted) (Ma $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_a tptp.int))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.int))) (let ((_let_4 (tptp.fun X_a tptp.int))) (let ((_let_5 (tptp.fun tptp.int tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) S)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.zcong (tptp.hAPP X_a tptp.int F X_2)) (tptp.hAPP X_a tptp.int G X_2)) Ma)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_5 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_5) tptp.zcong (tptp.hAPP _let_2 tptp.int (tptp.hAPP _let_4 _let_3 _let_1 F) S)) (tptp.hAPP _let_2 tptp.int (tptp.hAPP _let_4 _let_3 _let_1 G) S)) Ma))))))))) (forall ((X_a $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.int tptp.int))) (= (tptp.hAPP tptp.int X_a (tptp.hAPP tptp.int (tptp.fun tptp.int X_a) (tptp.frac X_a) A_1) B) (tptp.hAPP _let_1 X_a (tptp.abs_Frac X_a) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) tptp.norm_frac A_1) B))))) _let_123 (forall ((X_b $$unsorted) (X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.bool tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun _let_3 _let_3))) (let ((_let_5 (tptp.fun X_b _let_3))) (let ((_let_6 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.finite_finite_1 X_a) (tptp.hAPP _let_3 _let_3 (tptp.collect X_a) P_1))) (= (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_6 _let_6 (tptp.collect X_b) (tptp.hAPP _let_5 _let_6 (tptp.hAPP (tptp.fun _let_3 tptp.bool) (tptp.fun _let_5 _let_6) (tptp.combb _let_3 tptp.bool X_b) (tptp.fEx X_a)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_5) (tptp.combb _let_3 _let_3 X_b) (tptp.hAPP _let_2 _let_4 (tptp.combs X_a tptp.bool tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.bool _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.bool _let_1 X_a) tptp.fconj) P_1))) Q_1))))) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 Y_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_1 _let_1 (tptp.collect X_b) (tptp.hAPP X_a _let_1 (tptp.hAPP (tptp.fun X_b (tptp.fun X_a tptp.bool)) (tptp.fun X_a _let_1) (tptp.combc X_b X_a tptp.bool) Q_1) Y_2)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (F $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun _let_2 _let_1))) (let ((_let_4 (tptp.fun X_b tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_3))) (let ((_let_6 (tptp.fun X_b _let_4))) (let ((_let_7 (tptp.fun X_b _let_1))) (let ((_let_8 (tptp.fun tptp.bool tptp.bool))) (let ((_let_9 (tptp.fun X_a _let_8))) (let ((_let_10 (tptp.fun _let_1 _let_9))) (let ((_let_11 (tptp.fun X_b _let_9))) (let ((_let_12 (tptp.fun _let_1 _let_1))) (let ((_let_13 (tptp.fun X_b _let_12))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) (tptp.hAPP _let_1 _let_1 (tptp.collect X_a) P_1))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_b) (tptp.hAPP _let_4 _let_4 (tptp.collect X_b) (tptp.hAPP _let_7 _let_4 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun _let_7 _let_4) (tptp.combb _let_1 tptp.bool X_b) (tptp.fEx X_a)) (tptp.hAPP _let_1 _let_7 (tptp.hAPP _let_13 (tptp.fun _let_1 _let_7) (tptp.combc X_b _let_1 _let_1) (tptp.hAPP _let_11 _let_13 (tptp.hAPP (tptp.fun _let_9 _let_12) (tptp.fun _let_11 _let_13) (tptp.combb _let_9 _let_12 X_b) (tptp.combs X_a tptp.bool tptp.bool)) (tptp.hAPP _let_7 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_7 _let_11) (tptp.combb _let_1 _let_9 X_b) (tptp.hAPP (tptp.fun tptp.bool _let_8) _let_10 (tptp.combb tptp.bool _let_8 X_a) tptp.fconj)) (tptp.hAPP _let_2 _let_7 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_7) (tptp.combc X_b _let_2 _let_1) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun _let_4 _let_3) (tptp.fun _let_6 _let_5) (tptp.combb _let_4 _let_3 X_b) (tptp.combb X_b tptp.bool X_a)) (tptp.fequal X_b))) F)))) P_1)))))))))))))))))))) (= _let_80 (tptp.hAPP _let_55 _let_55 _let_79 (tptp.hAPP _let_75 _let_55 _let_78 (tptp.hAPP _let_107 _let_75 (tptp.hAPP _let_94 (tptp.fun _let_107 _let_75) (tptp.combb _let_91 _let_15 tptp.real) _let_95) (tptp.hAPP _let_15 _let_107 (tptp.hAPP _let_119 (tptp.fun _let_15 _let_107) (tptp.combc tptp.real _let_15 _let_91) (tptp.hAPP _let_117 _let_119 (tptp.hAPP (tptp.fun _let_115 _let_118) (tptp.fun _let_117 _let_119) (tptp.combb _let_115 _let_118 tptp.real) (tptp.combc tptp.int _let_15 _let_15)) (tptp.hAPP _let_113 _let_117 (tptp.hAPP _let_116 (tptp.fun _let_113 _let_117) (tptp.combb _let_111 _let_115 tptp.real) (tptp.hAPP (tptp.fun _let_108 _let_99) _let_116 (tptp.combb _let_108 _let_99 tptp.int) _let_114)) (tptp.hAPP _let_107 _let_113 (tptp.hAPP _let_112 (tptp.fun _let_107 _let_113) (tptp.combb _let_91 _let_111 tptp.real) (tptp.hAPP _let_109 _let_112 (tptp.combb _let_15 _let_108 tptp.int) _let_110)) (tptp.hAPP _let_102 _let_107 (tptp.hAPP _let_106 (tptp.fun _let_102 _let_107) (tptp.combc tptp.real _let_102 _let_91) (tptp.hAPP _let_104 _let_106 (tptp.hAPP (tptp.fun _let_103 _let_105) (tptp.fun _let_104 _let_106) (tptp.combb _let_103 _let_105 tptp.real) (tptp.combb _let_46 _let_15 tptp.int)) (tptp.hAPP _let_57 _let_104 (tptp.hAPP (tptp.fun _let_55 _let_103) (tptp.fun _let_57 _let_104) (tptp.combb _let_55 _let_103 tptp.real) (tptp.combb tptp.real tptp.bool tptp.int)) _let_53))) (tptp.hAPP _let_46 _let_102 (tptp.hAPP _let_101 (tptp.fun _let_46 _let_102) (tptp.combc tptp.int _let_46 _let_46) (tptp.hAPP _let_45 _let_101 (tptp.hAPP (tptp.fun _let_33 _let_100) (tptp.fun _let_45 _let_101) (tptp.combb _let_33 _let_100 tptp.int) (tptp.combb tptp.real tptp.real tptp.int)) _let_47)) _let_44)))))) (tptp.hAPP _let_15 _let_15 (tptp.hAPP _let_42 _let_99 (tptp.combb tptp.bool tptp.bool tptp.int) tptp.fNot) (tptp.hAPP tptp.int _let_15 (tptp.hAPP _let_91 _let_91 _let_98 _let_88) _let_1))))))) _let_97 (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.fun tptp.nat tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (let ((_let_9 (tptp.fun _let_7 tptp.real))) (let ((_let_10 (tptp.tendsto tptp.nat tptp.real))) (let ((_let_11 (tptp.filter tptp.nat))) (let ((_let_12 (tptp.fun _let_11 tptp.bool))) (let ((_let_13 (tptp.fun tptp.real _let_12))) (=> (tptp.hBOOL (tptp.hAPP _let_11 tptp.bool (tptp.hAPP tptp.real _let_12 (tptp.hAPP _let_1 _let_13 _let_10 A_2) (tptp.zero_zero tptp.real)) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.monoseq tptp.real) A_2)) (tptp.hBOOL (tptp.hAPP _let_11 tptp.bool (tptp.hAPP tptp.real _let_12 (tptp.hAPP _let_1 _let_13 _let_10 (tptp.hAPP _let_8 _let_1 (tptp.hAPP _let_9 (tptp.fun _let_8 _let_1) (tptp.combb _let_7 tptp.real tptp.nat) (tptp.hAPP _let_1 _let_9 (tptp.big_co1399186613setsum tptp.nat tptp.real) _let_4)) (tptp.hAPP _let_5 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_5 _let_8) (tptp.combb tptp.nat _let_7 tptp.nat) (tptp.hAPP tptp.nat _let_8 (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat))) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_5 _let_6) (tptp.combb tptp.nat _let_5 tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_5 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.one_one tptp.nat))))) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) _let_4)) tptp.sequentially)))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.comm_monoid_mult X_b) (tptp.dvd X_b)) (forall ((F $$unsorted) (G $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.dvd_dvd X_b) (tptp.hAPP X_a X_b F X_2)) (tptp.hAPP X_a X_b G X_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.dvd_dvd X_b) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 F) A_3)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3))))))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.pow X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.combb _let_3 tptp.bool _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_3))) (let ((_let_7 (tptp.fun _let_6 _let_3))) (let ((_let_8 (tptp.uminus_uminus _let_2))) (let ((_let_9 (tptp.fun _let_2 _let_2))) (let ((_let_10 (tptp.fun _let_9 _let_3))) (let ((_let_11 (tptp.fun _let_2 _let_10))) (let ((_let_12 (tptp.fun tptp.bool tptp.bool))) (let ((_let_13 (tptp.fun _let_2 _let_12))) (let ((_let_14 (tptp.fun _let_3 _let_13))) (let ((_let_15 (tptp.fun _let_2 _let_13))) (let ((_let_16 (tptp.fun _let_3 _let_3))) (let ((_let_17 (tptp.fun _let_2 _let_16))) (= (tptp.hAPP _let_2 _let_3 _let_1 (tptp.hAPP _let_2 _let_2 _let_8 A_3)) (tptp.hAPP _let_3 _let_3 (tptp.collect _let_2) (tptp.hAPP _let_6 _let_3 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.fEx _let_2)) (tptp.hAPP _let_3 _let_6 (tptp.hAPP _let_17 (tptp.fun _let_3 _let_6) (tptp.combc _let_2 _let_3 _let_3) (tptp.hAPP _let_15 _let_17 (tptp.hAPP (tptp.fun _let_13 _let_16) (tptp.fun _let_15 _let_17) (tptp.combb _let_13 _let_16 _let_2) (tptp.combs _let_2 tptp.bool tptp.bool)) (tptp.hAPP _let_6 _let_15 (tptp.hAPP _let_14 (tptp.fun _let_6 _let_15) (tptp.combb _let_3 _let_13 _let_2) (tptp.hAPP (tptp.fun tptp.bool _let_12) _let_14 (tptp.combb tptp.bool _let_12 _let_2) tptp.fconj)) (tptp.hAPP _let_9 _let_6 (tptp.hAPP _let_11 (tptp.fun _let_9 _let_6) (tptp.combc _let_2 _let_9 _let_3) (tptp.hAPP _let_6 _let_11 (tptp.hAPP (tptp.fun _let_3 _let_10) (tptp.fun _let_6 _let_11) (tptp.combb _let_3 _let_10 _let_2) (tptp.combb _let_2 tptp.bool _let_2)) (tptp.fequal _let_2))) _let_8)))) (tptp.hAPP _let_6 _let_3 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP _let_2 _let_4 (tptp.member _let_2) A_3)) _let_1))))))))))))))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.ord_less_eq tptp.real) _let_1) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.ord_less tptp.real) X_1) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP tptp.real _let_2 (tptp.power_power tptp.real) X_1)) _let_1) tptp.sequentially)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.topological_space X_b) (forall ((F $$unsorted) (L $$unsorted) (A_3 $$unsorted) (A_7 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) L))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.ord_less_eq _let_1) A_3) A_7)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_7)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool _let_3 A_3)))))))))) (forall ((Y_3 $$unsorted) (Y_1 $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.tendsto tptp.nat tptp.real))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun tptp.real _let_3))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_5 _let_4 _let_1 X_3) X_1) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_5 _let_4 _let_1 Y_3) Y_1) tptp.sequentially)) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real X_3 N_2)) (tptp.hAPP tptp.nat tptp.real Y_3 N_2)))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X_1) Y_1))))))))))) (forall ((A_2 $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.real) (tptp.fun tptp.real _let_2) (tptp.tendsto tptp.nat tptp.real) X_3) X_1) tptp.sequentially)) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real X_3 N_2)) A_2))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X_1) A_2))))))) (forall ((A_2 $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.real) (tptp.fun tptp.real _let_2) (tptp.tendsto tptp.nat tptp.real) X_3) X_1) tptp.sequentially)) (=> (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) (tptp.hAPP tptp.nat tptp.real X_3 N_2)))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) X_1))))))) (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.monoseq tptp.real) A_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_2) (tptp.tendsto tptp.nat tptp.real) A_2) X_1) tptp.sequentially)) (or (and (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real A_2 N_2)) X_1))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real A_2 M_2)) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))))) (and (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) X_1) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (forall ((M_2 $$unsorted) (N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real A_2 N_2)) (tptp.hAPP tptp.nat tptp.real A_2 M_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((F $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.summable X_a) F)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP _let_3 (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) F) (tptp.zero_zero X_a)) tptp.sequentially))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.one_one tptp.real)) X_1)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_3) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_1 _let_1) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (tptp.zero_zero tptp.real)) tptp.sequentially))))))) (forall ((R_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.combb tptp.real tptp.real tptp.nat))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_7) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_4 _let_3 (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) R_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_4 _let_3 (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) tptp.suc)))) R_1) tptp.sequentially)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((Y_3 $$unsorted) (B_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.plus_plus X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.fun _let_4 _let_4))) (let ((_let_6 (tptp.fun tptp.nat _let_3))) (let ((_let_7 (tptp.tendsto tptp.nat X_a))) (let ((_let_8 (tptp.filter tptp.nat))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (let ((_let_10 (tptp.fun X_a _let_9))) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP X_a _let_9 (tptp.hAPP _let_4 _let_10 _let_7 X_3) A_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP X_a _let_9 (tptp.hAPP _let_4 _let_10 _let_7 Y_3) B_1) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP X_a _let_9 (tptp.hAPP _let_4 _let_10 _let_7 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_6 _let_5 (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_6 (tptp.hAPP (tptp.fun X_a _let_3) (tptp.fun _let_4 _let_6) (tptp.combb X_a _let_3 tptp.nat) _let_2) X_3)) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 _let_5 (tptp.combb X_a X_a tptp.nat) _let_1) Y_3))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_2) (tptp.hAPP X_a X_a _let_1 B_1))) tptp.sequentially))))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((G $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.tendsto X_a X_b))) (let ((_let_6 (tptp.filter X_a))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 F) A_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 G) B_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_b _let_2 X_a) _let_1) F)) G)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) B_1)) A_3))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((G $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.tendsto X_a X_b))) (let ((_let_6 (tptp.filter X_a))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 F) A_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 G) B_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_b _let_2 X_a) _let_1) F)) G)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) B_1)) A_3))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((B_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.tendsto tptp.nat X_a))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 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_let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 (tptp.hAPP _let_6 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_6 _let_5) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_6 (tptp.hAPP _let_7 _let_7 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) K))) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 F) A_2) tptp.sequentially))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((Y_3 $$unsorted) (B_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.tendsto tptp.nat X_a))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 X_3) A_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 Y_3) B_1) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_3)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) tptp.sequentially))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((B_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.tendsto tptp.nat X_a))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 F) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) F)) B_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) tptp.sequentially)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((K $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.tendsto tptp.nat X_a))) (let ((_let_5 (tptp.filter tptp.nat))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_a _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP X_a _let_6 (tptp.hAPP _let_3 _let_7 _let_4 F) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP X_a _let_6 (tptp.hAPP _let_3 _let_7 _let_4 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_3) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.plus_plus tptp.nat)) K))) A_2) tptp.sequentially))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((G $$unsorted) (F $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.tendsto tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 F) L_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_5) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun X_a _let_6) (tptp.fun _let_5 _let_7) (tptp.combb X_a _let_6 tptp.nat) (tptp.minus_minus X_a)) F)) G)) (tptp.zero_zero X_a)) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 G) L_2) tptp.sequentially)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((F $$unsorted) (G $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.tendsto tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.fun X_a X_a))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 G) L_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_5) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun X_a _let_6) (tptp.fun _let_5 _let_7) (tptp.combb X_a _let_6 tptp.nat) (tptp.minus_minus X_a)) F)) G)) (tptp.zero_zero X_a)) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 F) L_2) tptp.sequentially)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.tendsto tptp.nat X_a))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) Y_1)) tptp.sequentially)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_2) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_3 _let_4 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_3 _let_4) (tptp.combb X_a tptp.real tptp.nat) (tptp.norm_norm X_a)) X_3)) (tptp.zero_zero tptp.real)) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP _let_3 (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) X_3) (tptp.zero_zero X_a)) tptp.sequentially)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((Y_3 $$unsorted) (B_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.tendsto tptp.nat X_a))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 X_3) A_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 Y_3) B_1) tptp.sequentially)) (=> (not (= (tptp.ti X_a B_1) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_3)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) tptp.sequentially)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_field X_b) (forall ((G $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.tendsto X_a X_b))) (let ((_let_6 (tptp.filter X_a))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 F) A_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 G) B_1) A_3)) (=> (not (= (tptp.ti X_b B_1) (tptp.zero_zero X_b))) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_b _let_2 X_a) _let_1) F)) G)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) B_1)) A_3)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_a tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_2) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_3 _let_4 (tptp.hAPP (tptp.fun X_b tptp.real) (tptp.fun _let_3 _let_4) (tptp.combb X_b tptp.real X_a) (tptp.norm_norm X_b)) F)) (tptp.zero_zero tptp.real)) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP _let_3 (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) (tptp.zero_zero X_b)) A_3)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.real))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.filter X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_2 (tptp.fun X_b _let_4) (tptp.tendsto X_a X_b) F) (tptp.zero_zero X_b)) A_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_4) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb X_b tptp.real X_a) (tptp.norm_norm X_b)) F)) (tptp.zero_zero tptp.real)) A_3)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_a tptp.real))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_2) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_3 _let_4 (tptp.hAPP (tptp.fun X_b tptp.real) (tptp.fun _let_3 _let_4) (tptp.combb X_b tptp.real X_a) (tptp.norm_norm X_b)) F)) (tptp.zero_zero tptp.real)) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP _let_3 (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) (tptp.zero_zero X_b)) A_3)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_field X_b) (forall ((Y_1 $$unsorted) (G $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.tendsto X_a X_b))) (let ((_let_6 (tptp.filter X_a))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 G) A_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP X_b _let_4 (tptp.hAPP _let_3 (tptp.fun X_b _let_4) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_b _let_2 X_a) _let_1) G)) Y_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) Y_1)) A_3)))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.metric_space X_b) (forall ((G $$unsorted) (Ma $$unsorted) (F $$unsorted) (L $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.dist_dist X_b))) (let ((_let_2 (tptp.fun X_b tptp.real))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun X_a tptp.real))) (let ((_let_6 (tptp.filter X_a))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.tendsto X_a X_b))) (let ((_let_9 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_9 _let_8 F) L) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_9 _let_8 G) Ma) A_3)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_5 (tptp.fun tptp.real _let_7) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_5) (tptp.combs X_a X_b tptp.real) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_b _let_2 X_a) _let_1) F)) G)) (tptp.hAPP X_b tptp.real (tptp.hAPP X_b _let_2 _let_1 L) Ma)) A_3)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.real_algebra_1 X_b) (tptp.real_normed_vector X_b)) (forall ((G $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.of_real X_b))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun X_a tptp.real))) (let ((_let_4 (tptp.filter X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_5) (tptp.tendsto X_a tptp.real) G) A_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_5 (tptp.hAPP _let_2 (tptp.fun X_b _let_5) (tptp.tendsto X_a X_b) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real X_b) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real X_b X_a) _let_1) G)) (tptp.hAPP tptp.real X_b _let_1 A_2)) A_3))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_b))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.filter X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_5 (tptp.hAPP _let_3 (tptp.fun X_b _let_5) (tptp.tendsto X_a X_b) F) A_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_5) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_b tptp.real) (tptp.fun _let_3 _let_2) (tptp.combb X_b tptp.real X_a) _let_1) F)) (tptp.hAPP X_b tptp.real _let_1 A_2)) A_3))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.topological_space X_b) (forall ((K $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.filter X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_3 (tptp.hAPP _let_1 (tptp.fun X_b _let_3) (tptp.tendsto X_a X_b) (tptp.hAPP X_b _let_1 (tptp.combk X_b X_a) K)) K) A_3)))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((F $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.tendsto tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 (tptp.hAPP _let_6 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_6 _let_5) (tptp.combb tptp.nat X_a tptp.nat) F) tptp.suc)) L) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 F) L) tptp.sequentially)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((F $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.tendsto tptp.nat X_a))) (let ((_let_4 (tptp.filter tptp.nat))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_1 _let_6 _let_3 F) L) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_1 _let_6 _let_3 (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_1) (tptp.combb tptp.nat X_a tptp.nat) F) tptp.suc)) L) tptp.sequentially)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((F $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.tendsto tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.fun tptp.nat tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 (tptp.hAPP _let_6 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_6 _let_5) (tptp.combb tptp.nat X_a tptp.nat) F) tptp.suc)) L) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_5 _let_4 _let_1 F) L) tptp.sequentially)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 (tptp.fun X_a _let_3) (tptp.tendsto tptp.nat X_a) (tptp.hAPP X_a _let_1 (tptp.combk X_a tptp.nat) K)) K) tptp.sequentially)))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((K $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 (tptp.fun X_a _let_3) (tptp.tendsto tptp.nat X_a) (tptp.hAPP X_a _let_1 (tptp.combk X_a tptp.nat) K)) L) tptp.sequentially)) (= (tptp.ti X_a K) (tptp.ti X_a L))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.filter tptp.nat))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_3 (tptp.fun X_a _let_5) (tptp.tendsto tptp.nat X_a) X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_5) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_3 _let_2) (tptp.combb X_a 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(tptp.hAPP X_a _let_2 _let_1 A_2) Ma)) tptp.sequentially))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.filter tptp.nat))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_5) (tptp.tendsto tptp.nat tptp.real) X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 (tptp.fun X_a _let_5) (tptp.tendsto tptp.nat X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real X_a tptp.nat) _let_1) X_3)) (tptp.hAPP tptp.real X_a _let_1 A_2)) tptp.sequentially))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.tendsto tptp.nat X_a))) (let ((_let_4 (tptp.filter tptp.nat))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_3 X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) _let_1) X_3)) (tptp.hAPP X_a X_a _let_1 A_2)) tptp.sequentially)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.tendsto tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let 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X_b))) (let ((_let_5 (tptp.tendsto X_a X_b))) (let ((_let_6 (tptp.filter X_a))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 F) A_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 G) B_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_b _let_2 X_a) _let_1) F)) G)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) B_1)) A_3))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_algebra X_b) (forall ((Y_1 $$unsorted) (G $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.times_times X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.tendsto X_a X_b))) (let ((_let_6 (tptp.filter X_a))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 G) A_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP X_b _let_4 (tptp.hAPP _let_3 (tptp.fun X_b _let_4) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_b _let_2 X_a) _let_1) G)) Y_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_2 _let_1 A_2) Y_1)) A_3)))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_algebra X_b) (forall ((X_1 $$unsorted) (G $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.hAPP X_b _let_1 (tptp.times_times X_b) X_1))) (let 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_let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 X_3) A_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 Y_3) B_1) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_4) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_3)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) B_1)) tptp.sequentially))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.tendsto tptp.nat X_a))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (let ((_let_8 (tptp.fun X_a _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_4 _let_8 _let_5 (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 tptp.nat) _let_1) X_3)) Y_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_2) Y_1)) tptp.sequentially)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.tendsto tptp.nat X_a))) (let ((_let_5 (tptp.filter tptp.nat))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_a _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP X_a _let_6 (tptp.hAPP _let_3 _let_7 _let_4 X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP X_a _let_6 (tptp.hAPP _let_3 _let_7 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_3 _let_3) (tptp.combb X_a X_a tptp.nat) _let_2) X_3)) (tptp.hAPP X_a X_a _let_2 A_2)) tptp.sequentially))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((L $$unsorted) (X_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.tendsto tptp.nat X_a))) (let ((_let_5 (tptp.filter tptp.nat))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.fun X_a _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP X_a _let_6 (tptp.hAPP _let_3 _let_7 _let_4 X_3) X_1) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) L)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP X_a _let_6 (tptp.hAPP _let_3 _let_7 _let_4 (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_3) (tptp.combb tptp.nat X_a tptp.nat) X_3) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.times_times tptp.nat)) L))) X_1) tptp.sequentially)))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_n1866405975lgebra X_b) (forall ((F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_b))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.tendsto X_a X_b))) (let ((_let_4 (tptp.filter X_a))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_b _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_5 (tptp.hAPP _let_2 _let_6 _let_3 F) A_2) A_3)) (=> (not (= (tptp.ti X_b A_2) (tptp.zero_zero X_b))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_b _let_5 (tptp.hAPP _let_2 _let_6 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_2 _let_2) (tptp.combb X_b X_b X_a) _let_1) F)) (tptp.hAPP X_b X_b _let_1 A_2)) A_3))))))))))))) (forall ((F $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.tendsto tptp.nat tptp.real))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun tptp.real _let_4))) (let ((_let_6 (tptp.fun tptp.nat tptp.real))) (= (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_6 _let_5 _let_2 (tptp.hAPP _let_6 _let_6 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_6 _let_6) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.abs_abs tptp.real)) F)) _let_1) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_6 _let_5 _let_2 F) _let_1) tptp.sequentially)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n1866405975lgebra X_a) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.tendsto tptp.nat X_a))) (let ((_let_4 (tptp.filter tptp.nat))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_3 X_3) A_2) tptp.sequentially)) (=> (not (= (tptp.ti X_a A_2) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_2 _let_6 _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) _let_1) X_3)) (tptp.hAPP X_a X_a _let_1 A_2)) tptp.sequentially))))))))))))) (tptp.hBOOL (tptp.hAPP _let_29 tptp.bool (tptp.hAPP tptp.real _let_85 (tptp.hAPP _let_49 (tptp.fun tptp.real _let_85) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_49 _let_49 (tptp.hAPP _let_33 _let_50 _let_48 _let_84) (tptp.hAPP _let_25 _let_49 _let_83 tptp.suc))) _let_37) tptp.sequentially)) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((B_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) X_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 _let_3 A_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 _let_3 B_1) tptp.sequentially)) (= (tptp.ti X_a A_2) (tptp.ti X_a B_1)))))))))) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.one_one tptp.real)) X_1)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_4) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_1) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.hAPP tptp.real _let_2 (tptp.inverse_divide tptp.real) A_2)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) X_1))) (tptp.zero_zero tptp.real)) tptp.sequentially)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n2089651433ebra_1 X_a) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X_1)) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 (tptp.fun X_a _let_3) (tptp.tendsto tptp.nat X_a) (tptp.hAPP X_a _let_1 (tptp.power_power X_a) X_1)) (tptp.zero_zero X_a)) tptp.sequentially))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 (tptp.fun X_a _let_3) (tptp.tendsto tptp.nat X_a) X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.cauchy X_a) X_3))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n1866405975lgebra X_a) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 (tptp.fun X_a _let_3) (tptp.tendsto tptp.nat X_a) X_3) A_2) tptp.sequentially)) (=> (not (= (tptp.ti X_a A_2) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.bseq X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_1 _let_1) (tptp.combb X_a X_a tptp.nat) (tptp.inverse_inverse X_a)) X_3))))))))))) (forall ((C_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) C_1))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_1) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP tptp.real _let_2 (tptp.power_power tptp.real) _let_1)) (tptp.zero_zero tptp.real)) tptp.sequentially)))))))) (forall ((C_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) C_1)) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_3) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) C_1)) (tptp.zero_zero tptp.real)) tptp.sequentially))))))) (forall ((R_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.combb tptp.real tptp.real tptp.nat))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_7) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_4 _let_3 (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) R_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_4 _let_3 (tptp.uminus_uminus tptp.real)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_4 _let_3 (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) tptp.suc))))) R_1) tptp.sequentially)))))))))) (forall ((Sa $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.filter tptp.nat))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_1) Sa)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_6) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_4) (tptp.combc tptp.nat tptp.real tptp.real) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) tptp.powr) (tptp.real_1 tptp.nat))) (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) Sa))) _let_1) tptp.sequentially)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP _let_1 (tptp.fun X_a _let_3) (tptp.tendsto tptp.nat X_a) X_3) L_2) tptp.sequentially)) (= (tptp.hAPP _let_1 X_a (tptp.lim X_a) X_3) (tptp.ti X_a L_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun X_a (tptp.fun _let_1 tptp.bool)))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_3 X_a (tptp.lim X_a) X_3) (tptp.hAPP _let_4 X_a (tptp.the X_a) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_4) (tptp.combc X_a _let_1 tptp.bool) (tptp.hAPP _let_3 _let_2 (tptp.tendsto tptp.nat X_a) X_3)) tptp.sequentially)))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.topological_space X_a)) (forall ((F $$unsorted) (Sa $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun _let_1 X_a))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.filter tptp.nat))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 (tptp.fun X_a tptp.bool) (tptp.sums X_a) F) Sa)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP X_a _let_6 (tptp.hAPP _let_4 (tptp.fun X_a _let_6) (tptp.tendsto tptp.nat X_a) (tptp.hAPP _let_2 _let_4 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_4) (tptp.combb _let_1 X_a tptp.nat) (tptp.hAPP _let_4 _let_3 (tptp.big_co1399186613setsum tptp.nat X_a) F)) (tptp.hAPP tptp.nat _let_2 (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) Sa) tptp.sequentially)))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.comm_monoid_add X_a) (tptp.t2_space X_a)) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_2 X_a))) (let ((_let_5 (tptp.filter tptp.nat))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) F)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP X_a _let_6 (tptp.hAPP _let_1 (tptp.fun X_a _let_6) (tptp.tendsto tptp.nat X_a) (tptp.hAPP _let_3 _let_1 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_1) (tptp.combb _let_2 X_a tptp.nat) (tptp.hAPP _let_1 _let_4 (tptp.big_co1399186613setsum tptp.nat X_a) F)) (tptp.hAPP tptp.nat _let_3 (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) (tptp.hAPP _let_1 X_a (tptp.suminf X_a) F)) tptp.sequentially)))))))))))) (forall ((R_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.combb tptp.real tptp.real tptp.nat))) (let ((_let_4 (tptp.fun _let_1 _let_1))) (let ((_let_5 (tptp.fun tptp.real tptp.real))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_7) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_4 _let_3 (tptp.hAPP tptp.real _let_5 (tptp.times_times tptp.real) R_1)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_4 _let_3 (tptp.hAPP tptp.real _let_5 (tptp.plus_plus tptp.real) (tptp.one_one tptp.real))) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_4 _let_3 (tptp.uminus_uminus tptp.real)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 _let_4 _let_3 (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_1) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) tptp.suc)))))) R_1) tptp.sequentially)))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.filter tptp.nat))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_5) (tptp.tendsto tptp.nat tptp.real) A_2) (tptp.zero_zero tptp.real)) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.monoseq tptp.real) A_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.combc tptp.nat tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb tptp.nat _let_2 tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 _let_1 (tptp.times_times tptp.nat)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.one_one tptp.nat)))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (let ((_let_6 (tptp.combb tptp.nat tptp.real tptp.nat))) (let ((_let_7 (tptp.fun _let_2 _let_5))) (let ((_let_8 (tptp.one_one tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun _let_5 _let_5))) (let ((_let_11 (tptp.fun tptp.nat _let_9))) (let ((_let_12 (tptp.filter tptp.nat))) (let ((_let_13 (tptp.fun _let_12 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) X_1)) _let_8)) (tptp.hBOOL (tptp.hAPP _let_12 tptp.bool (tptp.hAPP tptp.real _let_13 (tptp.hAPP _let_5 (tptp.fun tptp.real _let_13) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_11 _let_10 (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_5 _let_11 (tptp.hAPP (tptp.fun tptp.real _let_9) (tptp.fun _let_5 _let_11) (tptp.combb tptp.real _let_9 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_9 _let_10 (tptp.combb tptp.real tptp.real tptp.nat) (tptp.hAPP tptp.real _let_9 (tptp.inverse_divide tptp.real) _let_8)) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_5 _let_7 _let_6 (tptp.real_1 tptp.nat)) _let_4)))) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_5 _let_7 _let_6 (tptp.hAPP tptp.real _let_5 (tptp.power_power tptp.real) X_1)) _let_4))) (tptp.zero_zero tptp.real)) tptp.sequentially))))))))))))))))) (= _let_80 (tptp.hAPP _let_55 _let_55 _let_79 (tptp.hAPP _let_75 _let_55 _let_78 (tptp.hAPP _let_61 _let_75 (tptp.hAPP _let_73 (tptp.fun _let_61 _let_75) (tptp.combb _let_58 _let_15 tptp.real) (tptp.hAPP _let_74 _let_73 (tptp.combb _let_22 tptp.bool tptp.int) (tptp.fEx tptp.nat))) (tptp.hAPP _let_22 _let_61 (tptp.hAPP _let_72 (tptp.fun _let_22 _let_61) (tptp.combc tptp.real _let_22 _let_58) (tptp.hAPP _let_70 _let_72 (tptp.hAPP (tptp.fun _let_68 _let_71) (tptp.fun _let_70 _let_72) (tptp.combb _let_68 _let_71 tptp.real) (tptp.combc tptp.int _let_22 _let_22)) (tptp.hAPP _let_67 _let_70 (tptp.hAPP _let_69 (tptp.fun _let_67 _let_70) (tptp.combb _let_65 _let_68 tptp.real) (tptp.hAPP (tptp.fun _let_62 _let_41) _let_69 (tptp.combb _let_62 _let_41 tptp.int) (tptp.combs tptp.nat tptp.bool tptp.bool))) (tptp.hAPP _let_61 _let_67 (tptp.hAPP _let_66 (tptp.fun _let_61 _let_67) (tptp.combb _let_58 _let_65 tptp.real) (tptp.hAPP _let_63 _let_66 (tptp.combb _let_22 _let_62 tptp.int) (tptp.hAPP _let_64 _let_63 (tptp.combb tptp.bool _let_42 tptp.nat) tptp.fconj))) (tptp.hAPP _let_52 _let_61 (tptp.hAPP _let_60 (tptp.fun _let_52 _let_61) (tptp.combc tptp.real _let_52 _let_58) (tptp.hAPP _let_56 _let_60 (tptp.hAPP (tptp.fun _let_54 _let_59) (tptp.fun _let_56 _let_60) (tptp.combb _let_54 _let_59 tptp.real) (tptp.combb _let_49 _let_22 tptp.int)) (tptp.hAPP _let_57 _let_56 (tptp.hAPP (tptp.fun _let_55 _let_54) (tptp.fun _let_57 _let_56) (tptp.combb _let_55 _let_54 tptp.real) (tptp.combb tptp.real tptp.bool tptp.nat)) _let_53))) (tptp.hAPP _let_49 _let_52 (tptp.hAPP _let_51 (tptp.fun _let_49 _let_52) (tptp.combc tptp.int _let_49 _let_49) (tptp.hAPP _let_45 _let_51 (tptp.hAPP (tptp.fun _let_33 _let_50) (tptp.fun _let_45 _let_51) (tptp.combb _let_33 _let_50 tptp.int) _let_48) _let_47)) _let_43)))))) (tptp.hAPP _let_22 _let_22 (tptp.hAPP _let_42 _let_41 (tptp.combb tptp.bool tptp.bool tptp.nat) tptp.fNot) (tptp.hAPP tptp.nat _let_22 _let_24 _let_40))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat tptp.bool))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.fun _let_6 tptp.real))) (let ((_let_9 (tptp.tendsto tptp.nat tptp.real))) (let ((_let_10 (tptp.filter tptp.nat))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (let ((_let_12 (tptp.fun tptp.real _let_11))) (=> (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.real _let_11 (tptp.hAPP _let_1 _let_12 _let_9 A_2) (tptp.zero_zero tptp.real)) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.monoseq tptp.real) A_2)) (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.real _let_11 (tptp.hAPP _let_1 _let_12 _let_9 (tptp.hAPP _let_7 _let_1 (tptp.hAPP _let_8 (tptp.fun _let_7 _let_1) (tptp.combb _let_6 tptp.real tptp.nat) (tptp.hAPP _let_1 _let_8 (tptp.big_co1399186613setsum tptp.nat tptp.real) _let_4)) (tptp.hAPP _let_5 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_7) (tptp.combb tptp.nat _let_6 tptp.nat) (tptp.hAPP tptp.nat _let_7 (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat))) (tptp.hAPP tptp.nat _let_5 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) _let_4)) tptp.sequentially))))))))))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.fun tptp.nat tptp.bool))) (let ((_let_8 (tptp.fun tptp.nat _let_7))) (let ((_let_9 (tptp.fun _let_7 tptp.real))) (let ((_let_10 (tptp.tendsto tptp.nat tptp.real))) (let ((_let_11 (tptp.filter tptp.nat))) (let ((_let_12 (tptp.fun _let_11 tptp.bool))) (let ((_let_13 (tptp.fun tptp.real _let_12))) (=> (tptp.hBOOL (tptp.hAPP _let_11 tptp.bool (tptp.hAPP tptp.real _let_12 (tptp.hAPP _let_1 _let_13 _let_10 A_2) (tptp.zero_zero tptp.real)) tptp.sequentially)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real A_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (tptp.hBOOL (tptp.hAPP _let_11 tptp.bool (tptp.hAPP tptp.real _let_12 (tptp.hAPP _let_1 _let_13 _let_10 (tptp.hAPP _let_8 _let_1 (tptp.hAPP _let_9 (tptp.fun _let_8 _let_1) (tptp.combb _let_7 tptp.real tptp.nat) (tptp.hAPP _let_1 _let_9 (tptp.big_co1399186613setsum tptp.nat tptp.real) _let_4)) (tptp.hAPP _let_5 _let_8 (tptp.hAPP _let_8 (tptp.fun _let_5 _let_8) (tptp.combb tptp.nat _let_7 tptp.nat) (tptp.hAPP tptp.nat _let_8 (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat))) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.hAPP _let_5 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_5 _let_6) (tptp.combb tptp.nat _let_5 tptp.nat) (tptp.plus_plus tptp.nat)) (tptp.hAPP tptp.nat _let_5 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))))) (tptp.one_one tptp.nat))))) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) _let_4)) tptp.sequentially))))))))))))))))))) (forall ((N_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_3 _let_3) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_3 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_3 _let_5) (tptp.combb tptp.real _let_4 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_3 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2))) (let ((_let_7 (tptp.filter tptp.nat))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP tptp.real _let_8 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_8) (tptp.tendsto tptp.nat tptp.real) A_2) (tptp.zero_zero tptp.real)) tptp.sequentially)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real A_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_3 tptp.real (tptp.suminf tptp.real) _let_6)) (tptp.hAPP _let_2 tptp.real (tptp.hAPP _let_3 (tptp.fun _let_2 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) _let_6) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N_1)) (tptp.one_one tptp.nat)))))))))))))))))) (forall ((X_a $$unsorted) (G $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (Net $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.complex))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a tptp.real))) (let ((_let_4 (tptp.fun X_a tptp.complex))) (let ((_let_5 (tptp.filter X_a))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.tendsto X_a tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_3 _let_8 _let_7 F) A_2) Net)) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_3 _let_8 _let_7 G) B_1) Net)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.complex _let_6 (tptp.hAPP _let_4 (tptp.fun tptp.complex _let_6) (tptp.tendsto X_a tptp.complex) (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_4) (tptp.combs X_a tptp.real tptp.complex) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real _let_1 X_a) tptp.complex_1) F)) G)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 A_2) B_1)) Net))))))))))))) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.complex))) (let ((_let_2 (tptp.tendsto tptp.nat tptp.complex))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun tptp.complex _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.complex _let_4 (tptp.hAPP _let_1 _let_5 _let_2 X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.complex _let_4 (tptp.hAPP _let_1 _let_5 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun _let_1 _let_1) (tptp.combb tptp.complex tptp.complex tptp.nat) tptp.cnj) X_3)) (tptp.hAPP tptp.complex tptp.complex tptp.cnj A_2)) tptp.sequentially))))))))) (forall ((X_a $$unsorted) (G $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.complex))) (let ((_let_2 (tptp.tendsto X_a tptp.complex))) (let ((_let_3 (tptp.filter X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (let ((_let_5 (tptp.fun tptp.complex _let_4))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.complex _let_4 (tptp.hAPP _let_1 _let_5 _let_2 G) A_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.complex _let_4 (tptp.hAPP _let_1 _let_5 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun _let_1 _let_1) (tptp.combb tptp.complex tptp.complex X_a) tptp.cnj) G)) (tptp.hAPP tptp.complex tptp.complex tptp.cnj A_2)) A_3))))))))) (forall ((X_a $$unsorted) (G $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.real))) (let ((_let_2 (tptp.fun X_a tptp.complex))) (let ((_let_3 (tptp.filter X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.complex _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.complex _let_4) (tptp.tendsto X_a tptp.complex) G) A_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_4) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real X_a) tptp.im) G)) (tptp.hAPP tptp.complex tptp.real tptp.im A_2)) A_3)))))))) (forall ((X_a $$unsorted) (G $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.real))) (let ((_let_2 (tptp.fun X_a tptp.complex))) (let ((_let_3 (tptp.filter X_a))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.complex _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.complex _let_4) (tptp.tendsto X_a tptp.complex) G) A_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_4) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real X_a) tptp.re) G)) (tptp.hAPP tptp.complex tptp.real tptp.re A_2)) A_3)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.ord_less_eq _let_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.ord_less _let_1) A_3) B_2)) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 A_3) B_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 B_2) A_3))))))))) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.complex _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.complex _let_4) (tptp.tendsto tptp.nat tptp.complex) X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_4) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.re) X_3)) (tptp.hAPP tptp.complex tptp.real tptp.re A_2)) tptp.sequentially)))))))) (forall ((X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.complex))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.complex _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.complex _let_4) (tptp.tendsto tptp.nat tptp.complex) X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_4) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb tptp.complex tptp.real tptp.nat) tptp.im) X_3)) (tptp.hAPP tptp.complex tptp.real tptp.im A_2)) tptp.sequentially)))))))) (forall ((Y_3 $$unsorted) (B_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.complex))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.nat tptp.complex))) (let ((_let_5 (tptp.filter tptp.nat))) (let ((_let_6 (tptp.fun _let_5 tptp.bool))) (let ((_let_7 (tptp.tendsto tptp.nat tptp.real))) (let ((_let_8 (tptp.fun tptp.real _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_3 _let_8 _let_7 X_3) A_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_3 _let_8 _let_7 Y_3) B_1) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP tptp.complex _let_6 (tptp.hAPP _let_4 (tptp.fun tptp.complex _let_6) (tptp.tendsto tptp.nat tptp.complex) (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_4) (tptp.combs tptp.nat tptp.real tptp.complex) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real _let_1 tptp.nat) tptp.complex_1) X_3)) Y_3)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_1 tptp.complex_1 A_2) B_1)) tptp.sequentially))))))))))))) (forall ((P_1 $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1))) (let ((_let_5 (tptp.combb _let_1 tptp.real tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat tptp.real))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun _let_1 tptp.real))) (let ((_let_9 (tptp.fun tptp.real tptp.real))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.filter tptp.nat))) (let ((_let_12 (tptp.fun _let_11 tptp.bool))) (let ((_let_13 (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) A_2) B_1)))) (=> _let_13 (=> _let_13 (=> _let_13 (=> (tptp.hBOOL (tptp.hAPP _let_11 tptp.bool (tptp.hAPP tptp.real _let_12 (tptp.hAPP _let_6 (tptp.fun tptp.real _let_12) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_10 (tptp.fun _let_6 _let_6) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_6 _let_10 (tptp.hAPP (tptp.fun tptp.real _let_9) (tptp.fun _let_6 _let_10) (tptp.combb tptp.real _let_9 tptp.nat) (tptp.minus_minus tptp.real)) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_8 _let_7 _let_5 (tptp.product_fst tptp.real tptp.real)) _let_4))) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_8 _let_7 _let_5 (tptp.product_snd tptp.real tptp.real)) _let_4))) (tptp.zero_zero tptp.real)) tptp.sequentially)) (exists ((L_3 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1))) (let ((_let_5 (tptp.combb _let_1 tptp.real tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat tptp.real))) (let ((_let_7 (tptp.fun _let_2 _let_6))) (let ((_let_8 (tptp.fun _let_1 tptp.real))) (let ((_let_9 (tptp.tendsto tptp.nat tptp.real))) (let ((_let_10 (tptp.filter tptp.nat))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (let ((_let_12 (tptp.fun tptp.real _let_11))) (and (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_1 tptp.real (tptp.product_fst tptp.real tptp.real) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1) N_2))) L_3)))))) (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.real _let_11 (tptp.hAPP _let_6 _let_12 _let_9 (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_8 _let_7 _let_5 (tptp.product_fst tptp.real tptp.real)) _let_4)) L_3) tptp.sequentially)) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.product_prod tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) L_3) (tptp.hAPP _let_1 tptp.real (tptp.product_snd tptp.real tptp.real) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.real _let_2 (tptp.hAPP tptp.real _let_3 (tptp.hAPP (tptp.fun _let_1 tptp.bool) (tptp.fun tptp.real _let_3) tptp.bolzano_bisect P_1) A_2) B_1) N_2)))))))) (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.real _let_11 (tptp.hAPP _let_6 _let_12 _let_9 (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_8 _let_7 _let_5 (tptp.product_snd tptp.real tptp.real)) _let_4)) L_3) tptp.sequentially)))))))))))))))))))))))))))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat tptp.bool))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.fun _let_6 tptp.real))) (let ((_let_9 (tptp.tendsto tptp.nat tptp.real))) (let ((_let_10 (tptp.filter tptp.nat))) (let ((_let_11 (tptp.fun _let_10 tptp.bool))) (let ((_let_12 (tptp.fun tptp.real _let_11))) (=> (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.real _let_11 (tptp.hAPP _let_1 _let_12 _let_9 A_2) (tptp.zero_zero tptp.real)) tptp.sequentially)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real A_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.real _let_11 (tptp.hAPP _let_1 _let_12 _let_9 (tptp.hAPP _let_7 _let_1 (tptp.hAPP _let_8 (tptp.fun _let_7 _let_1) (tptp.combb _let_6 tptp.real tptp.nat) (tptp.hAPP _let_1 _let_8 (tptp.big_co1399186613setsum tptp.nat tptp.real) _let_4)) (tptp.hAPP _let_5 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_7) (tptp.combb tptp.nat _let_6 tptp.nat) (tptp.hAPP tptp.nat _let_7 (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat))) (tptp.hAPP tptp.nat _let_5 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls))))))) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) _let_4)) tptp.sequentially)))))))))))))))))) (forall ((N_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_7) (tptp.tendsto tptp.nat tptp.real) A_2) (tptp.zero_zero tptp.real)) tptp.sequentially)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real A_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP _let_5 tptp.real (tptp.hAPP _let_1 (tptp.fun _let_5 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) _let_4) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_5) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N_1)))) (tptp.hAPP _let_1 tptp.real (tptp.suminf tptp.real) _let_4)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) X_3) L_2) tptp.sequentially)) (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (exists ((No $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) No)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) No) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) L_2)) R_2)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) X_3) L_2) tptp.sequentially)) (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (exists ((No $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) No) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) L_2))) R_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_1 $$unsorted) (X_3 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) X_3) L_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_1)) (exists ((No $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) No) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) L_2))) R_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) X_3) L_2) tptp.sequentially)) (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (exists ((No $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) No) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) L_2)) R_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((R_1 $$unsorted) (X_3 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) X_3) L_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_1)) (exists ((No $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) No) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) L_2)) R_1)))))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.tendsto tptp.nat tptp.real) A_2) _let_1) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.monoseq tptp.real) A_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.nat tptp.real A_2 (tptp.zero_zero tptp.nat))) _let_1)) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N_2))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_3) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_5) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun tptp.real _let_6) (tptp.fun _let_5 _let_7) (tptp.combb tptp.real _let_6 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_5 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2))) (let ((_let_9 (tptp.hAPP _let_5 (tptp.fun _let_3 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) _let_8))) (let ((_let_10 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_10 tptp.bool) (tptp.member tptp.real) (tptp.hAPP _let_5 tptp.real (tptp.suminf tptp.real) _let_8)) (tptp.hAPP tptp.real _let_10 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_10) (tptp.ord_atLeastAtMost tptp.real) (tptp.hAPP _let_3 tptp.real _let_9 (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) _let_2) (tptp.one_one tptp.nat))))) (tptp.hAPP _let_3 tptp.real _let_9 (tptp.hAPP tptp.nat _let_3 _let_4 _let_2)))))))))))))))))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.real))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.tendsto tptp.nat tptp.real) A_2) _let_1) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.monoseq tptp.real) A_2)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) _let_1) (tptp.hAPP tptp.nat tptp.real A_2 (tptp.zero_zero tptp.nat)))) (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.times_times tptp.nat) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) (tptp.hAPP tptp.int tptp.int tptp.bit0 (tptp.hAPP tptp.int tptp.int tptp.bit1 tptp.pls)))) N_2))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (let ((_let_4 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_3) (tptp.ord_atLeastLessThan tptp.nat) (tptp.zero_zero tptp.nat)))) (let ((_let_5 (tptp.fun tptp.nat tptp.real))) (let ((_let_6 (tptp.fun tptp.real tptp.real))) (let ((_let_7 (tptp.fun tptp.nat _let_6))) (let ((_let_8 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_5) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun tptp.real _let_6) (tptp.fun _let_5 _let_7) (tptp.combb tptp.real _let_6 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_5 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2))) (let ((_let_9 (tptp.hAPP _let_5 (tptp.fun _let_3 tptp.real) (tptp.big_co1399186613setsum tptp.nat tptp.real) _let_8))) (let ((_let_10 (tptp.fun tptp.real tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_10 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_10 tptp.bool) (tptp.member tptp.real) (tptp.hAPP _let_5 tptp.real (tptp.suminf tptp.real) _let_8)) (tptp.hAPP tptp.real _let_10 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_10) (tptp.ord_atLeastAtMost tptp.real) (tptp.hAPP _let_3 tptp.real _let_9 (tptp.hAPP tptp.nat _let_3 _let_4 _let_2))) (tptp.hAPP _let_3 tptp.real _let_9 (tptp.hAPP tptp.nat _let_3 _let_4 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) _let_2) (tptp.one_one tptp.nat)))))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.ord_atLeastAtMost X_a))) (let ((_let_4 (tptp.fun X_a _let_2))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 A_2) B_1)) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_4 _let_3 C_1) D_1))) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) D_1)))))))))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) Y_1) X_1)) (= (tptp.hAPP _let_1 tptp.real (tptp.complete_Sup_Sup tptp.real) (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.ord_atLeastAtMost tptp.real) Y_1) X_1)) X_1)))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.ord_atLeastAtMost X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun X_a _let_3))) (= (tptp.hAPP _let_3 _let_3 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun _let_3 _let_3) (tptp.image X_a X_a) _let_1) (tptp.hAPP X_a _let_3 (tptp.hAPP X_a _let_4 _let_2 X_1) Y_1)) (tptp.hAPP X_a _let_3 (tptp.hAPP X_a _let_4 _let_2 (tptp.hAPP X_a X_a _let_1 Y_1)) (tptp.hAPP X_a X_a _let_1 X_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 C_1))) (let ((_let_4 (tptp.ord_less X_a))) (let ((_let_5 (tptp.ord_atLeastAtMost X_a))) (let ((_let_6 (tptp.fun X_a _let_2))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less _let_2) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_6 _let_5 A_2) B_1)) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_6 _let_5 C_1) D_1))) (and (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_2) B_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) D_1)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 C_1) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_4 B_1) D_1))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_3 D_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 (tptp.ord_atLeastLessThan X_a) A_2) B_1)) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 (tptp.ord_atLeastAtMost X_a) C_1) D_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) A_2) B_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) D_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.ord_less_eq X_a))) (let ((_let_3 (tptp.fun X_a _let_1))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a _let_3 (tptp.ord_atLeastAtMost X_a) A_2) B_1)) (tptp.hAPP X_a _let_1 (tptp.hAPP X_a _let_3 (tptp.ord_atLeastLessThan X_a) C_1) D_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 A_2) B_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 _let_2 C_1) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less X_a) B_1) D_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.dense_linorder X_a) (forall ((A_2 $$unsorted) (B_1 $$unsorted) (C_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun X_a _let_2))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 (tptp.fun _let_2 tptp.bool) (tptp.ord_less_eq _let_2) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 (tptp.ord_gr676655987ssThan X_a) A_2) B_1)) (tptp.hAPP X_a _let_2 (tptp.hAPP X_a _let_3 (tptp.ord_atLeastAtMost X_a) C_1) D_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 (tptp.ord_less X_a) A_2) B_1)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 C_1) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B_1) D_1))))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.filter tptp.nat))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_5) (tptp.tendsto tptp.nat tptp.real) A_2) (tptp.zero_zero tptp.real)) tptp.sequentially)) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real A_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))) (tptp.hAPP tptp.nat tptp.real A_2 N_2)))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat tptp.real tptp.real) (tptp.hAPP _let_1 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_1 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) (tptp.times_times tptp.real)) (tptp.hAPP tptp.real _let_1 (tptp.power_power tptp.real) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)))) A_2)))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X_1 $$unsorted) (C_1 $$unsorted) (K_3 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (let ((_let_2 (tptp.filter X_a))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat _let_3))) (let ((_let_5 (tptp.power_power X_a))) (let ((_let_6 (tptp.fun tptp.nat X_a))) (let ((_let_7 (tptp.hAPP X_a _let_6 _let_5 X_1))) (let ((_let_8 (tptp.fun X_a X_a))) (let ((_let_9 (tptp.combb X_a _let_8 tptp.nat))) (let ((_let_10 (tptp.fun tptp.nat _let_8))) (let ((_let_11 (tptp.fun _let_6 _let_10))) (let ((_let_12 (tptp.fun X_a _let_8))) (let ((_let_13 (tptp.hAPP _let_12 _let_11 _let_9 (tptp.times_times X_a)))) (let ((_let_14 (tptp.combs tptp.nat X_a X_a))) (let ((_let_15 (tptp.fun _let_6 _let_6))) (let ((_let_16 (tptp.fun X_a _let_6))) (let ((_let_17 (tptp.fun _let_8 _let_16))) (let ((_let_18 (tptp.combb _let_6 _let_10 X_a))) (let ((_let_19 (tptp.fun X_a _let_10))) (let ((_let_20 (tptp.fun _let_16 _let_19))) (let ((_let_21 (tptp.hAPP _let_11 _let_20 _let_18 (tptp.hAPP _let_12 _let_11 _let_9 (tptp.minus_minus X_a))))) (let ((_let_22 (tptp.fun X_a _let_15))) (let ((_let_23 (tptp.hAPP (tptp.fun _let_10 _let_15) (tptp.fun _let_19 _let_22) (tptp.combb _let_10 _let_15 X_a) _let_14))) (let ((_let_24 (tptp.combc X_a _let_6 _let_6))) (let ((_let_25 (tptp.fun _let_6 _let_16))) (let ((_let_26 (tptp.fun X_a _let_16))) (let ((_let_27 (tptp.fun _let_2 tptp.bool))) (let ((_let_28 (tptp.norm_norm X_a))) (let ((_let_29 (tptp.diffs X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.summable X_a) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_6 _let_10 _let_13 (tptp.hAPP _let_6 _let_6 _let_29 (tptp.hAPP _let_6 _let_6 _let_29 C_1)))) (tptp.hAPP X_a _let_6 _let_5 K_3)))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real _let_28 X_1)) (tptp.hAPP X_a tptp.real _let_28 K_3))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_27 (tptp.hAPP _let_8 (tptp.fun X_a _let_27) (tptp.tendsto X_a X_a) (tptp.hAPP _let_16 _let_8 (tptp.hAPP (tptp.fun _let_6 X_a) (tptp.fun _let_16 _let_8) (tptp.combb _let_6 X_a X_a) (tptp.suminf X_a)) (tptp.hAPP _let_16 _let_16 (tptp.hAPP _let_15 (tptp.fun _let_16 _let_16) (tptp.combb _let_6 _let_6 X_a) (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_6 _let_10 _let_13 C_1))) (tptp.hAPP _let_6 _let_16 (tptp.hAPP _let_22 _let_25 _let_24 (tptp.hAPP _let_19 _let_22 _let_23 (tptp.hAPP _let_16 _let_19 _let_21 (tptp.hAPP _let_8 _let_16 (tptp.hAPP _let_26 _let_17 (tptp.combs X_a X_a _let_6) (tptp.hAPP _let_19 _let_26 (tptp.hAPP (tptp.fun _let_10 _let_16) (tptp.fun _let_19 _let_26) (tptp.combb _let_10 _let_16 X_a) (tptp.combc tptp.nat X_a X_a)) (tptp.hAPP _let_16 _let_19 (tptp.hAPP _let_11 _let_20 _let_18 (tptp.hAPP _let_12 _let_11 _let_9 (tptp.inverse_divide X_a))) (tptp.hAPP _let_6 _let_16 (tptp.hAPP _let_22 _let_25 _let_24 (tptp.hAPP _let_19 _let_22 _let_23 (tptp.hAPP _let_16 _let_19 _let_21 (tptp.hAPP _let_8 _let_16 (tptp.hAPP _let_16 _let_17 (tptp.combb X_a _let_6 X_a) _let_5) (tptp.hAPP X_a _let_8 (tptp.plus_plus X_a) X_1))))) _let_7)))) (tptp.combi X_a))))) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_10 _let_15 _let_14 (tptp.hAPP _let_6 _let_10 _let_13 (tptp.semiring_1_of_nat X_a))) (tptp.hAPP _let_3 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_3 _let_6) (tptp.combb tptp.nat X_a tptp.nat) _let_7) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_4 _let_4 (tptp.combc tptp.nat tptp.nat tptp.nat) (tptp.minus_minus tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.zero_zero tptp.nat))))))))) _let_1) (tptp.hAPP X_a _let_2 (tptp.at X_a) _let_1))))))))))))))))))))))))))))))))))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) L) U_1))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.int) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) L) U_1))))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.nat_nat_set (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) X_1) Y_1)))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted)) (= (forall ((M_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 M_2)))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 X_2))))))) (forall ((P_1 $$unsorted) (N_1 $$unsorted)) (= (exists ((M_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) M_2) N_1)) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 M_2)))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) X_2) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) (tptp.zero_zero tptp.nat)) N_1))) (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool P_1 X_2))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.semiring_1_of_nat tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_3) (tptp.ord_atLeastAtMost tptp.nat) Ma) N_1) (tptp.hAPP _let_2 _let_3 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_3) (tptp.image tptp.int tptp.nat) tptp.nat_1) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.ord_atLeastAtMost tptp.int) (tptp.hAPP tptp.nat tptp.int _let_1 Ma)) (tptp.hAPP tptp.nat tptp.int _let_1 N_1)))))))) (forall ((I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.ord_atLeastAtMost tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.nat) (tptp.fun _let_2 _let_2) (tptp.image tptp.nat tptp.nat) tptp.suc) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 I) J)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc I)) (tptp.hAPP tptp.nat tptp.nat tptp.suc J))))))) (forall ((K $$unsorted) (I $$unsorted) (J $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.ord_atLeastAtMost tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun tptp.nat _let_2))) (= (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_4 _let_4) (tptp.image tptp.nat tptp.nat) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_1) K)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat _let_5 _let_3 I) J)) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP tptp.nat _let_5 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 I) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 J) K)))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.fact_fact tptp.nat) N_1) (tptp.hAPP _let_1 tptp.nat (tptp.hAPP (tptp.fun tptp.nat tptp.nat) (tptp.fun _let_1 tptp.nat) (tptp.big_co302546470etprod tptp.nat tptp.nat) (tptp.combi tptp.nat)) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) (tptp.one_one tptp.nat)) N_1))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (= (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.ord_atLeastLessThan tptp.nat) L) (tptp.hAPP tptp.nat tptp.nat tptp.suc U_1)) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat _let_2 (tptp.ord_atLeastAtMost tptp.nat) L) U_1))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (Ma $$unsorted) (K $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastAtMost tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.plus_plus tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.fun tptp.nat X_a))) (let ((_let_8 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_9 (tptp.fun _let_2 X_a))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_7 _let_9 _let_8 F) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 Ma) K)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_5 _let_4 N_1) K))) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_7 _let_9 _let_8 (tptp.hAPP _let_5 _let_7 (tptp.hAPP _let_7 (tptp.fun _let_5 _let_7) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_5 (tptp.hAPP _let_6 _let_6 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_4) K))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 Ma) N_1))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastAtMost tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_7 (tptp.fun _let_2 X_a))) (= (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_7 _let_6 F) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_7 _let_6 (tptp.hAPP _let_5 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_4) (tptp.combb tptp.nat X_a tptp.nat) F) tptp.suc)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 Ma) N_1))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.topological_space X_b)) (forall ((K_3 $$unsorted) (F $$unsorted) (L_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) X_1))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_3) (tptp.tendsto X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 _let_4 L_2) _let_2)) (=> (= (tptp.ti X_b K_3) (tptp.ti X_b L_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 _let_4 K_3) _let_2))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.metric_space X_b) (tptp.real_n2089651433ebra_1 X_a)) (forall ((M_1 $$unsorted) (F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_3) (tptp.tendsto X_a X_b) F))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 _let_4 L_2) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 _let_4 M_1) _let_2)) (= (tptp.ti X_b L_2) (tptp.ti X_b M_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_n1866405975lgebra X_a) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.inverse_inverse X_a))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (not (= (tptp.ti X_a A_2) (tptp.zero_zero X_a))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_3 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun X_a _let_3) (tptp.tendsto X_a X_a) _let_2) (tptp.hAPP X_a X_a _let_2 A_2)) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_algebra X_b)) (forall ((G $$unsorted) (M_1 $$unsorted) (F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.times_times X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.tendsto X_a X_b))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 F) L_2) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 G) M_1) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_6 _let_6) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun _let_6 _let_5) (tptp.combb X_b _let_4 X_a) _let_3) F)) G)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 L_2) M_1)) _let_2)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_algebra X_b)) (forall ((Y_1 $$unsorted) (G $$unsorted) (L $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.times_times X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.tendsto X_a X_b))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 G) L) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 (tptp.hAPP X_b _let_6 (tptp.hAPP _let_5 (tptp.fun X_b _let_6) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun _let_6 _let_5) (tptp.combb X_b _let_4 X_a) _let_3) G)) Y_1)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 L) Y_1)) _let_2))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_algebra X_b)) (forall ((X_1 $$unsorted) (G $$unsorted) (L $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.hAPP X_b _let_3 (tptp.times_times X_b) X_1))) (let ((_let_5 (tptp.fun X_a X_b))) (let ((_let_6 (tptp.tendsto X_a X_b))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 _let_8 _let_6 G) L) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 _let_8 _let_6 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_3 (tptp.fun _let_5 _let_5) (tptp.combb X_b X_b X_a) _let_4) G)) (tptp.hAPP X_b X_b _let_4 L)) _let_2)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.times_times X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_5 (tptp.hAPP _let_3 (tptp.fun X_a _let_5) (tptp.tendsto X_a X_a) (tptp.hAPP X_a _let_3 (tptp.hAPP _let_4 _let_4 (tptp.combc X_a X_a X_a) _let_2) Y_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_3 _let_2 A_2) Y_1)) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.times_times X_a) X_1))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_2 (tptp.fun X_a _let_4) (tptp.tendsto X_a X_a) _let_3) (tptp.hAPP X_a X_a _let_3 A_2)) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((F $$unsorted) (L $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.abs_abs tptp.real))) (let ((_let_4 (tptp.fun X_a tptp.real))) (let ((_let_5 (tptp.tendsto X_a tptp.real))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun tptp.real _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_4 _let_7 _let_5 F) L) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_6 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_4 _let_4) (tptp.combb tptp.real tptp.real X_a) _let_3) F)) (tptp.hAPP tptp.real tptp.real _let_3 L)) _let_2))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.uminus_uminus X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.tendsto X_a X_b))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun X_b _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 (tptp.hAPP _let_4 _let_7 _let_5 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_let_1 (tptp.at X_a) X_1))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.real_n2089651433ebra_1 X_b) (tptp.zero X_a) (tptp.metric_space X_a)) (forall ((A_2 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.filter X_b))) (let ((_let_2 (tptp.zero_zero X_a))) (let ((_let_3 (tptp.fun X_b X_a))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (=> (not (= (tptp.ti X_a K) _let_2)) (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_3 (tptp.fun X_a _let_4) (tptp.tendsto X_b X_a) (tptp.hAPP X_a _let_3 (tptp.combk X_a X_b) K)) _let_2) (tptp.hAPP X_b _let_1 (tptp.at X_b) A_2)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_field X_b)) (forall ((Y_1 $$unsorted) (G $$unsorted) (L $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.inverse_divide X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 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(tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 G) M_1) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_6 _let_6) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun _let_6 _let_5) (tptp.combb X_b _let_4 X_a) _let_3) F)) G)) (tptp.hAPP X_b X_b (tptp.hAPP X_b _let_4 _let_3 L_2) M_1)) _let_2)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((G $$unsorted) (Ma $$unsorted) (F $$unsorted) (L $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) X_1))) (let ((_let_3 (tptp.minus_minus X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.tendsto X_a X_b))) (let ((_let_8 (tptp.fun 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(tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun tptp.complex _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.complex _let_5 (tptp.hAPP _let_3 _let_6 _let_4 G) L) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.complex _let_5 (tptp.hAPP _let_3 _let_6 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun _let_3 _let_3) (tptp.combb tptp.complex tptp.complex X_a) tptp.cnj) G)) (tptp.hAPP tptp.complex tptp.complex tptp.cnj L)) _let_2)))))))))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.complex))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun tptp.real _let_2) (tptp.tendsto tptp.complex tptp.real) tptp.re) (tptp.hAPP tptp.complex tptp.real tptp.re A_2)) (tptp.hAPP tptp.complex _let_1 (tptp.at tptp.complex) A_2)))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.complex))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun tptp.real _let_2) (tptp.tendsto tptp.complex tptp.real) tptp.im) (tptp.hAPP tptp.complex tptp.real tptp.im A_2)) (tptp.hAPP tptp.complex _let_1 (tptp.at tptp.complex) A_2)))))) (forall ((A_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.complex))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.complex _let_2 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun tptp.complex _let_2) (tptp.tendsto tptp.complex tptp.complex) tptp.cnj) (tptp.hAPP tptp.complex tptp.complex tptp.cnj A_2)) (tptp.hAPP tptp.complex _let_1 (tptp.at tptp.complex) A_2)))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun 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(tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_a X_b))) (let ((_let_6 (tptp.tendsto X_a X_b))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 _let_8 _let_6 F) _let_3) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 _let_8 _let_6 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_5) (tptp.combb X_b X_b X_a) (tptp.hAPP X_b _let_4 (tptp.times_times X_b) C_1)) F)) _let_3) _let_2)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_algebra X_b)) (forall ((X_1 $$unsorted) (G $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.zero_zero X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_a X_b))) (let ((_let_6 (tptp.tendsto X_a X_b))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 _let_8 _let_6 G) _let_3) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 _let_8 _let_6 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_4 (tptp.fun _let_5 _let_5) (tptp.combb X_b X_b X_a) (tptp.hAPP X_b _let_4 (tptp.times_times X_b) X_1)) G)) _let_3) _let_2)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_algebra X_b)) (forall ((C_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.zero_zero X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.tendsto X_a X_b))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (=> (tptp.hBOOL 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tptp.bool))) (let ((_let_8 (tptp.fun X_b _let_7))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 _let_8 _let_6 F) _let_3) (tptp.hAPP X_a _let_2 _let_1 A_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 _let_8 _let_6 (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_5) (tptp.combb X_a X_b X_a) F) (tptp.hAPP X_a _let_4 (tptp.plus_plus X_a) A_2))) _let_3) (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((G $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.zero_zero X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.tendsto X_a X_b))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 F) _let_3) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 G) _let_3) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_6 _let_9 _let_7 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_6 _let_6) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun X_b _let_4) (tptp.fun _let_6 _let_5) (tptp.combb X_b _let_4 X_a) (tptp.plus_plus X_b)) F)) G)) _let_3) _let_2)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_vector X_a) (tptp.topological_space X_b)) (forall ((F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.at X_a))) (let ((_let_2 (tptp.filter X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.tendsto X_a X_b))) (let ((_let_6 (tptp.fun _let_2 tptp.bool))) (let ((_let_7 (tptp.fun X_b _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_6 (tptp.hAPP _let_4 _let_7 _let_5 F) L_2) (tptp.hAPP X_a _let_2 _let_1 A_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_6 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_4) (tptp.combb X_a X_b X_a) F) (tptp.hAPP X_a _let_3 (tptp.plus_plus X_a) A_2))) L_2) (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_vector X_a) (tptp.topological_space X_b)) (forall ((F $$unsorted) (A_2 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.at X_a))) (let ((_let_2 (tptp.filter X_a))) (let ((_let_3 (tptp.tendsto X_a X_b))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP 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tptp.complex tptp.real) (tptp.fun _let_4 _let_3) (tptp.combb tptp.complex tptp.real X_a) tptp.im) G)) (tptp.hAPP tptp.complex tptp.real tptp.im L)) _let_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_atLeastAtMost tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) Ma) N_1)) (= (tptp.hAPP _let_2 X_a _let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 Ma) N_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a F Ma)) (tptp.hAPP _let_2 X_a _let_4 (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc Ma)) N_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((G $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.zero_zero tptp.complex))) (let ((_let_4 (tptp.fun X_a tptp.complex))) (let ((_let_5 (tptp.tendsto X_a tptp.complex))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun tptp.complex _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.complex _let_6 (tptp.hAPP _let_4 _let_7 _let_5 G) _let_3) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.complex _let_6 (tptp.hAPP _let_4 _let_7 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP (tptp.fun tptp.complex tptp.complex) (tptp.fun _let_4 _let_4) (tptp.combb tptp.complex tptp.complex X_a) tptp.cnj) G)) _let_3) _let_2))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.metric_space X_a) (tptp.real_normed_vector X_b)) (forall ((L $$unsorted) (F $$unsorted) (G $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.tendsto X_a X_b))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.fun _let_6 _let_6))) (let ((_let_8 (tptp.fun X_b X_b))) (let ((_let_9 (tptp.fun X_a _let_8))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_9 _let_7 (tptp.combs X_a X_b X_b) (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun X_b _let_8) (tptp.fun _let_6 _let_9) (tptp.combb X_b _let_8 X_a) (tptp.plus_plus X_b)) F)) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_8 _let_7 (tptp.combb X_b X_b X_a) (tptp.uminus_uminus X_b)) G))) (tptp.zero_zero X_b)) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 G) L) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 F) L) _let_2)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.minus_minus X_a))) (let ((_let_3 (tptp.combc X_a X_a X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.combb X_a _let_4 X_a))) (let ((_let_7 (tptp.fun _let_4 _let_5))) (let ((_let_8 (tptp.fun _let_1 tptp.bool))) (let ((_let_9 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_9 (tptp.hAPP _let_4 (tptp.fun X_a _let_9) (tptp.deriv X_a) F) X_1) D_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_8 (tptp.hAPP _let_4 (tptp.fun X_a _let_8) (tptp.tendsto X_a X_a) (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_4) (tptp.combs X_a X_a X_a) (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_5 _let_7 _let_6 (tptp.inverse_divide X_a)) (tptp.hAPP X_a _let_4 (tptp.hAPP _let_5 _let_5 _let_3 (tptp.hAPP _let_4 _let_5 (tptp.hAPP _let_5 _let_7 _let_6 _let_2) F)) (tptp.hAPP X_a X_a F X_1)))) (tptp.hAPP X_a _let_4 (tptp.hAPP _let_5 _let_5 _let_3 _let_2) X_1))) D_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) X_1)))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.metric_space X_a) (tptp.topological_space X_b) (tptp.topological_space X_c)) (forall ((G $$unsorted) (C_1 $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun X_a X_c))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun X_b X_c))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.filter X_b))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 (tptp.hAPP _let_4 (tptp.fun X_b _let_6) (tptp.tendsto X_a X_b) F) B_1) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP X_c _let_8 (tptp.hAPP _let_5 (tptp.fun X_c _let_8) (tptp.tendsto X_b X_c) G) C_1) (tptp.hAPP X_b _let_7 (tptp.at X_b) B_1))) (=> (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((X_2 $$unsorted)) (=> (and (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_2) A_2)) D_3))) (not (= (tptp.hAPP X_a X_b F X_2) (tptp.ti X_b B_1))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c _let_6 (tptp.hAPP _let_3 (tptp.fun X_c _let_6) (tptp.tendsto X_a X_c) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.combb X_b X_c X_a) G) F)) C_1) _let_2)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastAtMost tptp.nat) Ma))) (let ((_let_4 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_2 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F))) (let ((_let_5 (tptp.hAPP _let_2 X_a _let_4 (tptp.hAPP tptp.nat _let_2 _let_3 _let_1)))) (let ((_let_6 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less tptp.nat) _let_1) Ma)))) (and (=> _let_6 (= _let_5 (tptp.zero_zero X_a))) (=> (not _let_6) (= _let_5 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP _let_2 X_a _let_4 (tptp.hAPP tptp.nat _let_2 _let_3 N_1))) (tptp.hAPP tptp.nat X_a F _let_1)))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (P_4 $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.plus_plus tptp.nat) N_1))) (let ((_let_2 (tptp.hAPP tptp.nat tptp.nat _let_1 P_4))) (let ((_let_3 (tptp.hAPP tptp.nat tptp.nat _let_1 (tptp.one_one tptp.nat)))) (let ((_let_4 (tptp.ord_atLeastAtMost tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_5 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) F))) (let ((_let_8 (tptp.hAPP tptp.nat _let_6 _let_4 Ma))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_5 (tptp.ord_less_eq tptp.nat) Ma) _let_3)) (= (tptp.hAPP _let_5 X_a _let_7 (tptp.hAPP tptp.nat _let_5 _let_8 _let_2)) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP _let_5 X_a _let_7 (tptp.hAPP tptp.nat _let_5 _let_8 N_1))) (tptp.hAPP _let_5 X_a _let_7 (tptp.hAPP tptp.nat _let_5 (tptp.hAPP tptp.nat _let_6 _let_4 _let_3) _let_2)))))))))))))))) (forall ((L $$unsorted) (U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (= (tptp.hAPP _let_2 tptp.nat (tptp.finite_card tptp.int) (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.ord_atLeastAtMost tptp.int) L) U_1)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.plus_plus tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) U_1) L)) (tptp.one_one tptp.int))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) Ma))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_6 (tptp.fun _let_1 X_a))) (let ((_let_7 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (let ((_let_8 (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 _let_6 _let_5 F) (tptp.hAPP tptp.nat _let_1 _let_2 _let_7)))) (let ((_let_9 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less tptp.nat) _let_7) Ma)))) (and (=> _let_9 (= _let_8 (tptp.zero_zero X_a))) (=> (not _let_9) (= _let_8 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.plus_plus X_a) (tptp.hAPP tptp.nat X_a F Ma)) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_3 _let_6 _let_5 (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_4 _let_3) (tptp.combb tptp.nat X_a tptp.nat) F) tptp.suc)) (tptp.hAPP tptp.nat _let_1 _let_2 N_1)))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.inverse X_a) (tptp.real_normed_vector X_a)) (forall ((F $$unsorted) (A_2 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.at X_a))) (let ((_let_2 (tptp.filter X_a))) (let ((_let_3 (tptp.minus_minus X_a))) (let ((_let_4 (tptp.combc X_a X_a X_a))) (let ((_let_5 (tptp.fun X_a X_a))) (let ((_let_6 (tptp.fun X_a _let_5))) (let ((_let_7 (tptp.hAPP X_a X_a F A_2))) (let ((_let_8 (tptp.combb X_a _let_5 X_a))) (let ((_let_9 (tptp.fun _let_5 _let_6))) (let ((_let_10 (tptp.hAPP _let_6 _let_9 _let_8 _let_3))) (let ((_let_11 (tptp.hAPP _let_6 _let_9 _let_8 (tptp.inverse_divide X_a)))) (let ((_let_12 (tptp.combs X_a X_a X_a))) (let ((_let_13 (tptp.fun _let_5 _let_5))) (let ((_let_14 (tptp.tendsto X_a X_a))) (let ((_let_15 (tptp.fun _let_2 tptp.bool))) (let ((_let_16 (tptp.fun X_a _let_15))) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_15 (tptp.hAPP _let_5 _let_16 _let_14 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_6 _let_13 _let_12 (tptp.hAPP _let_5 _let_6 _let_11 (tptp.hAPP X_a _let_5 (tptp.hAPP _let_6 _let_6 _let_4 (tptp.hAPP _let_5 _let_6 _let_10 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_5 _let_13 (tptp.combb X_a X_a X_a) F) (tptp.hAPP X_a _let_5 (tptp.plus_plus X_a) A_2)))) _let_7))) (tptp.combi X_a))) D_2) (tptp.hAPP X_a _let_2 _let_1 (tptp.zero_zero X_a)))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a _let_15 (tptp.hAPP _let_5 _let_16 _let_14 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_6 _let_13 _let_12 (tptp.hAPP _let_5 _let_6 _let_11 (tptp.hAPP X_a _let_5 (tptp.hAPP _let_6 _let_6 _let_4 (tptp.hAPP _let_5 _let_6 _let_10 F)) _let_7))) (tptp.hAPP X_a _let_5 (tptp.hAPP _let_6 _let_6 _let_4 _let_3) A_2))) D_2) (tptp.hAPP X_a _let_2 _let_1 A_2))))))))))))))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_vector X_a) (tptp.topological_space X_b) (tptp.topological_space X_c)) (forall ((G $$unsorted) (C_1 $$unsorted) (F $$unsorted) (B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun X_a X_c))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun X_b X_c))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.filter X_b))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 (tptp.hAPP _let_4 (tptp.fun X_b _let_6) (tptp.tendsto X_a X_b) F) B_1) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP X_c _let_8 (tptp.hAPP _let_5 (tptp.fun X_c _let_8) (tptp.tendsto X_b X_c) G) C_1) (tptp.hAPP X_b _let_7 (tptp.at X_b) B_1))) (=> (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((X_2 $$unsorted)) (=> (and (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X_2) A_2))) D_3))) (not (= (tptp.hAPP X_a X_b F X_2) (tptp.ti X_b B_1))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c _let_6 (tptp.hAPP _let_3 (tptp.fun X_c _let_6) (tptp.tendsto X_a X_c) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.combb X_b X_c X_a) G) F)) C_1) _let_2)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun X_a tptp.real))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_5 (tptp.fun tptp.real _let_3) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_4 _let_5 (tptp.hAPP (tptp.fun X_b tptp.real) (tptp.fun _let_4 _let_5) (tptp.combb X_b tptp.real X_a) (tptp.norm_norm X_b)) F)) (tptp.zero_zero tptp.real)) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.hAPP _let_4 (tptp.fun X_b _let_3) (tptp.tendsto X_a X_b) F) (tptp.zero_zero X_b)) _let_2))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun X_a tptp.real))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_5 (tptp.hAPP _let_4 (tptp.fun X_b _let_5) (tptp.tendsto X_a X_b) F) (tptp.zero_zero X_b)) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_5) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun X_b tptp.real) (tptp.fun _let_4 _let_3) (tptp.combb X_b tptp.real X_a) (tptp.norm_norm X_b)) F)) (tptp.zero_zero tptp.real)) _let_2))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun X_a tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_5 (tptp.fun tptp.real _let_3) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_4 _let_5 (tptp.hAPP (tptp.fun X_b tptp.real) (tptp.fun _let_4 _let_5) (tptp.combb X_b tptp.real X_a) (tptp.norm_norm X_b)) F)) (tptp.zero_zero tptp.real)) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.hAPP _let_4 (tptp.fun X_b _let_3) (tptp.tendsto X_a X_b) F) (tptp.zero_zero X_b)) _let_2))))))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fact_fact tptp.nat))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 (tptp.ord_less_eq tptp.nat) N_1) Ma)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.div_div tptp.nat) (tptp.hAPP tptp.nat tptp.nat _let_3 Ma)) (tptp.hAPP tptp.nat tptp.nat _let_3 N_1)) (tptp.hAPP _let_2 tptp.nat (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.nat) (tptp.big_co302546470etprod tptp.nat tptp.nat) (tptp.combi tptp.nat)) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_2) (tptp.ord_atLeastAtMost tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) N_1) (tptp.one_one tptp.nat))) Ma)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_algebra_1 X_b) (tptp.real_normed_vector X_b)) (forall ((G $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_a tptp.real))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_5) (tptp.tendsto X_a tptp.real) G) (tptp.zero_zero tptp.real)) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_5 (tptp.hAPP _let_3 (tptp.fun X_b _let_5) (tptp.tendsto X_a X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.real X_b) (tptp.fun _let_4 _let_3) (tptp.combb tptp.real X_b X_a) (tptp.of_real X_b)) G)) (tptp.zero_zero X_b)) _let_2))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) N_1)) (= (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) N_1) (tptp.hAPP _let_1 tptp.int (tptp.hAPP (tptp.fun tptp.int tptp.int) (tptp.fun _let_1 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) (tptp.combi tptp.int)) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) N_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((G $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun X_a tptp.real))) (let ((_let_4 (tptp.fun X_a tptp.complex))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.complex _let_5 (tptp.hAPP _let_4 (tptp.fun tptp.complex _let_5) (tptp.tendsto X_a tptp.complex) G) (tptp.zero_zero tptp.complex)) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_5) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_4 _let_3) (tptp.combb tptp.complex tptp.real X_a) tptp.re) G)) (tptp.zero_zero tptp.real)) _let_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((G $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun X_a tptp.real))) (let ((_let_4 (tptp.fun X_a tptp.complex))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.complex _let_5 (tptp.hAPP _let_4 (tptp.fun tptp.complex _let_5) (tptp.tendsto X_a tptp.complex) G) (tptp.zero_zero tptp.complex)) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_3 (tptp.fun tptp.real _let_5) (tptp.tendsto X_a tptp.real) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.complex tptp.real) (tptp.fun _let_4 _let_3) (tptp.combb tptp.complex tptp.real X_a) tptp.im) G)) (tptp.zero_zero tptp.real)) _let_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_semiring_1 X_a) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.one_one X_a))) (let ((_let_2 (tptp.semiring_1_of_nat X_a))) (let ((_let_3 (tptp.hAPP tptp.nat X_a _let_2 N_1))) (let ((_let_4 (tptp.plus_plus X_a))) (let ((_let_5 (tptp.fun X_a X_a))) (let ((_let_6 (tptp.times_times X_a))) (let ((_let_7 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_6 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 _let_1) _let_1)) (tptp.hAPP _let_7 X_a (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun _let_7 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) _let_2) (tptp.hAPP tptp.nat _let_7 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_7) (tptp.ord_atLeastAtMost tptp.nat) (tptp.one_one tptp.nat)) N_1))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_6 _let_3) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_5 _let_4 _let_3) _let_1))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ab_group_add X_a) (forall ((F $$unsorted) (Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.one_one tptp.nat))) (let ((_let_3 (tptp.plus_plus tptp.nat))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun tptp.nat X_a))) (let ((_let_7 (tptp.minus_minus X_a))) (let ((_let_8 (tptp.fun X_a X_a))) (let ((_let_9 (tptp.fun tptp.nat _let_8))) (let ((_let_10 (tptp.hAPP _let_1 X_a (tptp.hAPP _let_6 (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_9 (tptp.fun _let_6 _let_6) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_6 _let_9 (tptp.hAPP (tptp.fun X_a _let_8) (tptp.fun _let_6 _let_9) (tptp.combb X_a _let_8 tptp.nat) _let_7) F)) (tptp.hAPP _let_4 _let_6 (tptp.hAPP _let_6 (tptp.fun _let_4 _let_6) (tptp.combb tptp.nat X_a tptp.nat) F) (tptp.hAPP tptp.nat _let_4 (tptp.hAPP _let_5 _let_5 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_3) _let_2)))) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) Ma) N_1)))) (let ((_let_11 (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_1 (tptp.ord_less_eq tptp.nat) Ma) N_1)))) (and (=> _let_11 (= _let_10 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_8 _let_7 (tptp.hAPP tptp.nat X_a F Ma)) (tptp.hAPP tptp.nat X_a F (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_4 _let_3 N_1) _let_2))))) (=> (not _let_11) (= _let_10 (tptp.zero_zero X_a)))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.combb X_a _let_2 X_a))) (let ((_let_5 (tptp.fun X_a _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_8 (tptp.hAPP _let_2 (tptp.fun X_a _let_8) (tptp.deriv X_a) F) X_1) D_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_2 (tptp.fun X_a _let_7) (tptp.tendsto X_a X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_3 (tptp.combs X_a X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_5 _let_6 _let_4 (tptp.inverse_divide X_a)) (tptp.hAPP X_a _let_2 (tptp.hAPP _let_5 _let_5 (tptp.combc X_a X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_5 _let_6 _let_4 (tptp.minus_minus X_a)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.combb X_a X_a X_a) F) (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) X_1)))) (tptp.hAPP X_a X_a F X_1)))) (tptp.combi X_a))) D_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) (tptp.zero_zero X_a)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.combb X_a _let_2 X_a))) (let ((_let_5 (tptp.fun X_a _let_2))) (let ((_let_6 (tptp.fun _let_2 _let_5))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (let ((_let_8 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_8 (tptp.hAPP _let_2 (tptp.fun X_a _let_8) (tptp.deriv X_a) F) X_1) D_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_2 (tptp.fun X_a _let_7) (tptp.tendsto X_a X_a) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_5 _let_3 (tptp.combs X_a X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_5 _let_6 _let_4 (tptp.inverse_divide X_a)) (tptp.hAPP X_a _let_2 (tptp.hAPP _let_5 _let_5 (tptp.combc X_a X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_5 _let_6 _let_4 (tptp.minus_minus X_a)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.combb X_a X_a X_a) F) (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) X_1)))) (tptp.hAPP X_a X_a F X_1)))) (tptp.combi X_a))) D_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) (tptp.zero_zero X_a)))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_algebra X_a) (tptp.banach X_a)) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.fun tptp.nat tptp.nat))) (let ((_let_5 (tptp.fun _let_4 _let_3))) (let ((_let_6 (tptp.fun tptp.nat _let_3))) (let ((_let_7 (tptp.fun tptp.nat _let_4))) (let ((_let_8 (tptp.times_times X_a))) (let ((_let_9 (tptp.fun X_a X_a))) (let ((_let_10 (tptp.fun tptp.nat _let_9))) (let ((_let_11 (tptp.fun _let_3 _let_3))) (let ((_let_12 (tptp.fun _let_1 X_a))) (let ((_let_13 (tptp.fun tptp.nat _let_12))) (let ((_let_14 (tptp.suminf X_a))) (let ((_let_15 (tptp.fun tptp.nat tptp.real))) (let ((_let_16 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_3 _let_15) (tptp.combb X_a tptp.real tptp.nat) (tptp.norm_norm X_a)))) (let ((_let_17 (tptp.summable tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_15 tptp.bool _let_17 (tptp.hAPP _let_3 _let_15 _let_16 A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_15 tptp.bool _let_17 (tptp.hAPP _let_3 _let_15 _let_16 B_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_9 _let_8 (tptp.hAPP _let_3 X_a _let_14 A_2)) (tptp.hAPP _let_3 X_a _let_14 B_1)) (tptp.hAPP _let_3 X_a _let_14 (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_13 (tptp.fun _let_2 _let_3) (tptp.combs tptp.nat _let_1 X_a) (tptp.hAPP _let_6 _let_13 (tptp.hAPP (tptp.fun _let_3 _let_12) (tptp.fun _let_6 _let_13) (tptp.combb _let_3 _let_12 tptp.nat) (tptp.big_co1399186613setsum tptp.nat X_a)) (tptp.hAPP _let_6 _let_6 (tptp.hAPP _let_11 (tptp.fun _let_6 _let_6) (tptp.combb _let_3 _let_3 tptp.nat) (tptp.hAPP _let_10 _let_11 (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_10 (tptp.hAPP (tptp.fun X_a _let_9) (tptp.fun _let_3 _let_10) (tptp.combb X_a _let_9 tptp.nat) _let_8) A_2))) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_5 (tptp.fun _let_7 _let_6) (tptp.combb _let_4 _let_3 tptp.nat) (tptp.hAPP _let_3 _let_5 (tptp.combb tptp.nat X_a tptp.nat) B_1)) (tptp.minus_minus tptp.nat))))) (tptp.hAPP tptp.nat _let_2 (tptp.ord_atLeastAtMost tptp.nat) (tptp.zero_zero tptp.nat))))))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((F $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (let ((_let_5 (tptp.fun tptp.nat tptp.nat))) (let ((_let_6 (tptp.fun _let_5 _let_4))) (let ((_let_7 (tptp.fun tptp.nat _let_4))) (let ((_let_8 (tptp.fun tptp.nat _let_5))) (let ((_let_9 (tptp.big_co1399186613setsum tptp.nat X_a))) (let ((_let_10 (tptp.fun _let_2 X_a))) (let ((_let_11 (tptp.fun tptp.nat _let_10))) (let ((_let_12 (tptp.fun _let_5 _let_3))) (let ((_let_13 (tptp.fun tptp.nat _let_3))) (let ((_let_14 (tptp.product_prod tptp.nat tptp.nat))) (let ((_let_15 (tptp.fun _let_14 tptp.bool))) (let ((_let_16 (tptp.fun _let_14 X_a))) (= (tptp.hAPP _let_15 X_a (tptp.hAPP _let_16 (tptp.fun _let_15 X_a) (tptp.big_co1399186613setsum _let_14 X_a) (tptp.hAPP _let_7 _let_16 (tptp.product_prod_case tptp.nat tptp.nat X_a) F)) (tptp.hAPP _let_15 _let_15 (tptp.collect _let_14) (tptp.hAPP _let_3 _let_15 (tptp.product_prod_case tptp.nat tptp.nat tptp.bool) (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_13 _let_13 (tptp.combc tptp.nat tptp.nat _let_2) (tptp.hAPP _let_13 _let_13 (tptp.hAPP (tptp.fun _let_3 _let_3) (tptp.fun _let_13 _let_13) (tptp.combb _let_3 _let_3 tptp.nat) (tptp.combc tptp.nat tptp.nat tptp.bool)) (tptp.hAPP _let_8 _let_13 (tptp.hAPP _let_12 (tptp.fun _let_8 _let_13) (tptp.combb _let_5 _let_3 tptp.nat) (tptp.hAPP _let_3 _let_12 (tptp.combb tptp.nat _let_2 tptp.nat) (tptp.ord_less tptp.nat))) (tptp.plus_plus tptp.nat)))) N_1)))) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_10 _let_9 (tptp.hAPP _let_3 _let_4 (tptp.hAPP _let_11 (tptp.fun _let_3 _let_4) (tptp.combs tptp.nat _let_2 X_a) (tptp.hAPP _let_7 _let_11 (tptp.hAPP (tptp.fun _let_4 _let_10) (tptp.fun _let_7 _let_11) (tptp.combb _let_4 _let_10 tptp.nat) _let_9) (tptp.hAPP _let_8 _let_7 (tptp.hAPP _let_6 (tptp.fun _let_8 _let_7) (tptp.combb _let_5 _let_4 tptp.nat) (tptp.hAPP _let_7 _let_6 (tptp.combs tptp.nat tptp.nat X_a) F)) (tptp.minus_minus tptp.nat)))) (tptp.hAPP tptp.nat _let_3 (tptp.ord_atLeastAtMost tptp.nat) _let_1))) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.ord_atLeastLessThan tptp.nat) _let_1) N_1)))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_algebra X_a) (tptp.banach X_a)) (forall ((B_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.suminf X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.times_times X_a))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun tptp.nat tptp.bool))) (let ((_let_6 (tptp.fun tptp.nat _let_5))) (let ((_let_7 (tptp.fun tptp.nat tptp.nat))) (let ((_let_8 (tptp.fun _let_7 _let_2))) (let ((_let_9 (tptp.fun tptp.nat _let_2))) (let ((_let_10 (tptp.fun tptp.nat _let_7))) (let ((_let_11 (tptp.fun tptp.nat _let_4))) (let ((_let_12 (tptp.fun _let_2 _let_2))) (let ((_let_13 (tptp.fun _let_5 X_a))) (let ((_let_14 (tptp.fun tptp.nat _let_13))) (let ((_let_15 (tptp.fun tptp.nat tptp.real))) (let ((_let_16 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_2 _let_15) (tptp.combb X_a tptp.real tptp.nat) (tptp.norm_norm X_a)))) (let ((_let_17 (tptp.summable tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_15 tptp.bool _let_17 (tptp.hAPP _let_2 _let_15 _let_16 A_2))) (=> (tptp.hBOOL (tptp.hAPP _let_15 tptp.bool _let_17 (tptp.hAPP _let_2 _let_15 _let_16 B_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 (tptp.fun X_a tptp.bool) (tptp.sums X_a) (tptp.hAPP _let_6 _let_2 (tptp.hAPP _let_14 (tptp.fun _let_6 _let_2) (tptp.combs tptp.nat _let_5 X_a) (tptp.hAPP _let_9 _let_14 (tptp.hAPP (tptp.fun _let_2 _let_13) (tptp.fun _let_9 _let_14) (tptp.combb _let_2 _let_13 tptp.nat) (tptp.big_co1399186613setsum tptp.nat X_a)) (tptp.hAPP _let_9 _let_9 (tptp.hAPP _let_12 (tptp.fun _let_9 _let_9) (tptp.combb _let_2 _let_2 tptp.nat) (tptp.hAPP _let_11 _let_12 (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_2 _let_11 (tptp.hAPP (tptp.fun X_a _let_4) (tptp.fun _let_2 _let_11) (tptp.combb X_a _let_4 tptp.nat) _let_3) A_2))) (tptp.hAPP _let_10 _let_9 (tptp.hAPP _let_8 (tptp.fun _let_10 _let_9) (tptp.combb _let_7 _let_2 tptp.nat) (tptp.hAPP _let_2 _let_8 (tptp.combb tptp.nat X_a tptp.nat) B_1)) (tptp.minus_minus tptp.nat))))) (tptp.hAPP tptp.nat _let_6 (tptp.ord_atLeastAtMost tptp.nat) (tptp.zero_zero tptp.nat)))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP _let_2 X_a _let_1 A_2)) (tptp.hAPP _let_2 X_a _let_1 B_1)))))))))))))))))))))))))) (tptp.hBOOL (tptp.hAPP _let_36 tptp.bool (tptp.hAPP tptp.real _let_39 (tptp.hAPP _let_33 (tptp.fun tptp.real _let_39) (tptp.tendsto tptp.real tptp.real) (tptp.hAPP _let_33 _let_33 (tptp.hAPP _let_38 (tptp.fun _let_33 _let_33) (tptp.combs tptp.real tptp.real tptp.real) (tptp.hAPP _let_33 _let_38 (tptp.hAPP _let_38 (tptp.fun _let_33 _let_38) (tptp.combb tptp.real _let_33 tptp.real) _let_32) tptp.cos)) tptp.sin)) _let_37) (tptp.hAPP tptp.real _let_36 (tptp.at tptp.real) _let_35))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_b)) (forall ((G $$unsorted) (F $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun tptp.nat X_b))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_a _let_2))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.real) tptp.bool (tptp.summable tptp.real) F)) (=> (forall ((H_1 $$unsorted) (N_2 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) H_1))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (not (= (tptp.ti X_a H_1) (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_1) K)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP tptp.nat X_b (tptp.hAPP X_a (tptp.fun tptp.nat X_b) G H_1) N_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.nat tptp.real F N_2)) _let_1)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_5 (tptp.hAPP _let_3 (tptp.fun X_b _let_5) (tptp.tendsto X_a X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun _let_2 X_b) (tptp.fun _let_4 _let_3) (tptp.combb _let_2 X_b X_a) (tptp.suminf X_b)) G)) (tptp.zero_zero X_b)) (tptp.hAPP X_a _let_1 (tptp.at X_a) (tptp.zero_zero X_a))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (K_3 $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K)) (=> (forall ((H_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) H_1))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (not (= (tptp.ti X_a H_1) (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) _let_1) K)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less_eq tptp.real) (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_a X_b F H_1))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) K_3) _let_1)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) (tptp.zero_zero X_b)) (tptp.hAPP X_a _let_1 (tptp.at X_a) (tptp.zero_zero X_a))))))))))) (forall ((F $$unsorted) (L $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.filter tptp.real))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_2) (tptp.tendsto tptp.real tptp.real) F) L) (tptp.hAPP tptp.real _let_1 (tptp.at tptp.real) C_1))) (=> (not (= L (tptp.zero_zero tptp.real))) (exists ((R_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (forall ((X_2 $$unsorted)) (=> (and (not (= X_2 C_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) C_1) X_2))) R_2))) (not (= (tptp.hAPP tptp.real tptp.real F X_2) (tptp.zero_zero tptp.real)))))))))))) (forall ((F $$unsorted) (L $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.filter tptp.real))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_2) (tptp.tendsto tptp.real tptp.real) F) L) (tptp.hAPP tptp.real _let_1 (tptp.at tptp.real) C_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) L)) (exists ((R_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= X_2 C_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) C_1) X_2))) R_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real F X_2)))))))))))))) (forall ((F $$unsorted) (L $$unsorted) (C_1 $$unsorted)) (let ((_let_1 (tptp.filter tptp.real))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_2) (tptp.tendsto tptp.real tptp.real) F) L) (tptp.hAPP tptp.real _let_1 (tptp.at tptp.real) C_1))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) L) (tptp.zero_zero tptp.real))) (exists ((R_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= X_2 C_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) C_1) X_2))) R_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real F X_2)) (tptp.zero_zero tptp.real)))))))))))))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Ta) (tptp.one_one tptp.int))) A_3)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) A_3)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X_2) Ta)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) D_2)) Ta))))))))))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Ta))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) A_3)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) D_2))))))))) (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) B_2)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X_2) Ta)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_2) D_2)) Ta))))))))) (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Ta) (tptp.one_one tptp.int))) B_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) Ta))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) B_2)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_2) D_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.real))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (forall ((S_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (and (forall ((N_2 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.real S_2 N_2) A_2))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.tendsto tptp.nat tptp.real) S_2) A_2) tptp.sequentially))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_1 (tptp.fun X_a _let_4) (tptp.tendsto tptp.nat X_a) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun _let_2 _let_1) (tptp.combb tptp.real X_a tptp.nat) X_3) S_2)) L_2) tptp.sequentially)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.real X_a) X_3) L_2) (tptp.hAPP tptp.real _let_1 (tptp.at tptp.real) A_2))))))))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Ta))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) A_3)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) D_2))))))))) (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) B_2)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X_2) Ta)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_2) D_2)) Ta))))))))) (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Ta) (tptp.one_one tptp.int))) B_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int Ta))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) B_2)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xb) Xa))))))))) (=> (= (tptp.ti tptp.int X_2) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_2) D_2) _let_1))))))))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Ta) (tptp.one_one tptp.int))) A_3)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int Ta))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) A_3)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xb) Xa))))))))) (=> (= (tptp.ti tptp.int X_2) _let_1) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) D_2) _let_1))))))))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Ta) A_3)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int Ta))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) A_3)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xb) Xa))))))))) (=> (not (= (tptp.ti tptp.int X_2) _let_1)) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) D_2) _let_1)))))))))) (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Ta) B_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ti tptp.int Ta))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) B_2)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xb) Xa))))))))) (=> (not (= (tptp.ti tptp.int X_2) _let_1)) (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_2) D_2) _let_1)))))))))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Ta) A_3)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) A_3)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 X_2) Ta)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) D_2)) Ta))))))))))) (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Ta) B_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Ta))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) B_2)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_2) D_2))))))))))) (forall ((P_1 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_1)) (=> (forall ((X_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_1) D_1))))))) (= (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X1))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_2) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_1))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_vector X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) L_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (exists ((S_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) S_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X_2) A_2))) S_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP X_a X_b F X_2)) L_2))) R_2)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_vector X_a) (tptp.real_normed_vector X_b)) (forall ((R_1 $$unsorted) (F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) L_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_1)) (exists ((S_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) S_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X_2) A_2))) S_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP X_a X_b F X_2)) L_2))) R_1))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_vector X_a) (tptp.topological_space X_b)) (forall ((L $$unsorted) (F $$unsorted) (G $$unsorted) (A_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.tendsto X_a X_b))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_3)) (=> (forall ((X_2 $$unsorted)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X_2) A_2))) R_3)) (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b G X_2))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 G) L) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 F) L) _let_2)))))))))))))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_1 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D_1) D_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 X_2))) (let ((_let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D_1))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) A_3)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xb) Xa))))))))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 (tptp.hAPP tptp.int tptp.int _let_3 Ta)))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 D_2)) Ta))))))))))))) (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_1 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D_1) D_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D_1))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) B_2)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xb) Xa))))))))) (=> (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 X_2) Ta)))) (not (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) D_2)) Ta)))))))))))) (forall ((Ta $$unsorted) (B_2 $$unsorted) (D_1 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D_1) D_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (let ((_let_2 (tptp.plus_plus tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D_1))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) B_2)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 X_2) Ta))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 _let_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) D_2)) Ta))))))))))) (forall ((Ta $$unsorted) (A_3 $$unsorted) (D_1 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D_1) D_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.plus_plus tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int _let_2 _let_1 X_2))) (let ((_let_4 (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.dvd_dvd tptp.int) D_1))) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) A_3)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 (tptp.hAPP tptp.int tptp.int _let_3 Ta))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool _let_4 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 (tptp.hAPP tptp.int tptp.int _let_3 D_2)) Ta)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.metric_space X_a) (tptp.metric_space X_b)) (forall ((R_1 $$unsorted) (F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) L_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_1)) (exists ((S_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) S_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_2) A_2)) S_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_b tptp.real (tptp.hAPP X_b (tptp.fun X_b tptp.real) (tptp.dist_dist X_b) (tptp.hAPP X_a X_b F X_2)) L_2)) R_1))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.metric_space X_a) (tptp.topological_space X_b)) (forall ((L $$unsorted) (F $$unsorted) (G $$unsorted) (A_2 $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.tendsto X_a X_b))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_3)) (=> (forall ((X_2 $$unsorted)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_2) A_2)) R_3)) (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b G X_2))))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 G) L) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 F) L) _let_2)))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.metric_space X_a) (tptp.metric_space X_b)) (forall ((F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) L_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (exists ((S_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) S_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_2) A_2)) S_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_b tptp.real (tptp.hAPP X_b (tptp.fun X_b tptp.real) (tptp.dist_dist X_b) (tptp.hAPP X_a X_b F X_2)) L_2)) R_2)))))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_c) (tptp.real_normed_vector X_b)) (forall ((G $$unsorted) (Ma $$unsorted) (F $$unsorted) (L $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_3) (tptp.tendsto X_a X_b) F) L) _let_2)) (=> (forall ((X_2 $$unsorted)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_c tptp.real (tptp.norm_norm X_c) (tptp.hAPP X_c X_c (tptp.hAPP X_c (tptp.fun X_c X_c) (tptp.minus_minus X_c) (tptp.hAPP X_a X_c G X_2)) Ma))) (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP X_a X_b F X_2)) L)))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_a X_c) (tptp.fun X_c _let_3) (tptp.tendsto X_a X_c) G) Ma) _let_2)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.metric_space X_a) (tptp.metric_space X_b)) (forall ((X_3 $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) X_3) L_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (forall ((S_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_b))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (and (forall ((N_2 $$unsorted)) (not (= (tptp.hAPP tptp.nat X_a S_2 N_2) (tptp.ti X_a A_2)))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_2 (tptp.fun X_a _let_4) (tptp.tendsto tptp.nat X_a) S_2) A_2) tptp.sequentially))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_1 (tptp.fun X_b _let_4) (tptp.tendsto tptp.nat X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_2 _let_1) (tptp.combb X_a X_b tptp.nat) X_3) S_2)) L_2) tptp.sequentially)))))))))))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.metric_space X_c) (tptp.metric_space X_b)) (forall ((G $$unsorted) (Ma $$unsorted) (F $$unsorted) (L $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_3 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_3) (tptp.tendsto X_a X_b) F) L) _let_2)) (=> (forall ((X_2 $$unsorted)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_c tptp.real (tptp.hAPP X_c (tptp.fun X_c tptp.real) (tptp.dist_dist X_c) (tptp.hAPP X_a X_c G X_2)) Ma)) (tptp.hAPP X_b tptp.real (tptp.hAPP X_b (tptp.fun X_b tptp.real) (tptp.dist_dist X_b) (tptp.hAPP X_a X_b F X_2)) L))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c _let_3 (tptp.hAPP (tptp.fun X_a X_c) (tptp.fun X_c _let_3) (tptp.tendsto X_a X_c) G) Ma) _let_2)))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (and (tptp.real_normed_algebra X_b) (tptp.comm_ring_1 X_b)) (forall ((X_3 $$unsorted) (L_2 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun tptp.nat X_b))) (let ((_let_7 (tptp.fun tptp.nat _let_3))) (let ((_let_8 (tptp.filter tptp.nat))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_b))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) N_2) S)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_3 (tptp.hAPP _let_1 (tptp.fun X_b _let_3) (tptp.tendsto tptp.nat X_b) (tptp.hAPP X_a _let_1 X_3 N_2)) (tptp.hAPP X_a X_b L_2 N_2)) tptp.sequentially)))))))) (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP X_b _let_9 (tptp.hAPP _let_6 (tptp.fun X_b _let_9) (tptp.tendsto tptp.nat X_b) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_7 (tptp.fun _let_2 _let_6) (tptp.combc tptp.nat _let_2 X_b) (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun _let_4 _let_3) (tptp.fun _let_5 _let_7) (tptp.combb _let_4 _let_3 tptp.nat) _let_1) (tptp.hAPP (tptp.fun X_a _let_6) _let_5 (tptp.combc X_a tptp.nat X_b) X_3))) S)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 L_2) S)) tptp.sequentially))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((X_3 $$unsorted) (L_2 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun tptp.nat X_b))) (let ((_let_7 (tptp.fun tptp.nat _let_3))) (let ((_let_8 (tptp.filter tptp.nat))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (=> (forall ((N_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_b))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) N_2) S)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_3 (tptp.hAPP _let_1 (tptp.fun X_b _let_3) (tptp.tendsto tptp.nat X_b) (tptp.hAPP X_a _let_1 X_3 N_2)) (tptp.hAPP X_a X_b L_2 N_2)) tptp.sequentially)))))))) (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP X_b _let_9 (tptp.hAPP _let_6 (tptp.fun X_b _let_9) (tptp.tendsto tptp.nat X_b) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_7 (tptp.fun _let_2 _let_6) (tptp.combc tptp.nat _let_2 X_b) (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun _let_4 _let_3) (tptp.fun _let_5 _let_7) (tptp.combb _let_4 _let_3 tptp.nat) _let_1) (tptp.hAPP (tptp.fun X_a _let_6) _let_5 (tptp.combc X_a tptp.nat X_b) X_3))) S)) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 L_2) S)) tptp.sequentially))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_3 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (exists ((No $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) No) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) L_2))) R_2))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) X_3) L_2) tptp.sequentially)))))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.real))) (let ((_let_2 (tptp.filter tptp.nat))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (forall ((R_2 $$unsorted)) (exists ((N_3 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) N_3) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) R_2) (tptp.hAPP tptp.nat tptp.real X_3 N_2))))))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.real _let_3 (tptp.hAPP _let_1 (tptp.fun tptp.real _let_3) (tptp.tendsto tptp.nat tptp.real) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_1 _let_1) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) X_3)) (tptp.zero_zero tptp.real)) tptp.sequentially))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.real))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((S_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.filter tptp.nat))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (and (forall ((N_2 $$unsorted)) (not (= (tptp.hAPP tptp.nat tptp.real S_2 N_2) A_2))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP tptp.real _let_4 (tptp.hAPP _let_2 (tptp.fun tptp.real _let_4) (tptp.tendsto tptp.nat tptp.real) S_2) A_2) tptp.sequentially))) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP X_a _let_4 (tptp.hAPP _let_1 (tptp.fun X_a _let_4) (tptp.tendsto tptp.nat X_a) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun _let_2 _let_1) (tptp.combb tptp.real X_a tptp.nat) X_3) S_2)) L_2) tptp.sequentially)))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.real X_a) X_3) L_2) (tptp.hAPP tptp.real _let_1 (tptp.at tptp.real) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.metric_space X_a) (forall ((X_3 $$unsorted) (L_2 $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (exists ((No $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) No) N_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) (tptp.hAPP tptp.nat X_a X_3 N_2)) L_2)) R_2))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_2 (tptp.hAPP (tptp.fun tptp.nat X_a) (tptp.fun X_a _let_2) (tptp.tendsto tptp.nat X_a) X_3) L_2) tptp.sequentially)))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_vector X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (exists ((S_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) S_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.minus_minus X_a) X_2) A_2))) S_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_b tptp.real (tptp.norm_norm X_b) (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.minus_minus X_b) (tptp.hAPP X_a X_b F X_2)) L_2))) R_2)))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) L_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_field X_a) (forall ((N_1 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.hAPP tptp.nat _let_2 (tptp.minus_minus tptp.nat) N_1))) (let ((_let_4 (tptp.power_power X_a))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.fact_fact tptp.nat))) (let ((_let_7 (tptp.real_1 tptp.nat))) (let ((_let_8 (tptp.fun tptp.nat tptp.real))) (let ((_let_9 (tptp.hAPP _let_8 (tptp.fun _let_2 _let_8) (tptp.combb tptp.nat tptp.real tptp.nat) _let_7))) (let ((_let_10 (tptp.inverse_inverse tptp.real))) (let ((_let_11 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_8 _let_8) (tptp.combb tptp.real tptp.real tptp.nat) _let_10))) (let ((_let_12 (tptp.scaleR_scaleR X_a))) (let ((_let_13 (tptp.fun X_a X_a))) (let ((_let_14 (tptp.fun tptp.nat _let_13))) (let ((_let_15 (tptp.hAPP (tptp.fun tptp.real _let_13) (tptp.fun _let_8 _let_14) (tptp.combb tptp.real _let_13 tptp.nat) _let_12))) (let ((_let_16 (tptp.combs tptp.nat X_a X_a))) (let ((_let_17 (tptp.fun _let_5 _let_5))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_13 _let_12 (tptp.hAPP tptp.real tptp.real _let_10 (tptp.hAPP tptp.nat tptp.real _let_7 (tptp.hAPP tptp.nat tptp.nat _let_6 N_1)))) (tptp.hAPP tptp.nat X_a (tptp.hAPP X_a _let_5 _let_4 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_13 (tptp.plus_plus X_a) X_1) Y_1)) N_1)) (tptp.hAPP _let_1 X_a (tptp.hAPP _let_5 (tptp.fun _let_1 X_a) (tptp.big_co1399186613setsum tptp.nat X_a) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_14 _let_17 _let_16 (tptp.hAPP _let_5 _let_14 (tptp.hAPP (tptp.fun X_a _let_13) (tptp.fun _let_5 _let_14) (tptp.combb X_a _let_13 tptp.nat) (tptp.times_times X_a)) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_14 _let_17 _let_16 (tptp.hAPP _let_8 _let_14 _let_15 (tptp.hAPP _let_8 _let_8 _let_11 (tptp.hAPP _let_2 _let_8 _let_9 _let_6)))) (tptp.hAPP X_a _let_5 _let_4 X_1)))) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_14 _let_17 _let_16 (tptp.hAPP _let_8 _let_14 _let_15 (tptp.hAPP _let_8 _let_8 _let_11 (tptp.hAPP _let_2 _let_8 _let_9 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_2 _let_2) (tptp.combb tptp.nat tptp.nat tptp.nat) _let_6) _let_3))))) (tptp.hAPP _let_2 _let_5 (tptp.hAPP _let_5 (tptp.fun _let_2 _let_5) (tptp.combb tptp.nat X_a tptp.nat) (tptp.hAPP X_a _let_5 _let_4 Y_1)) _let_3)))) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) (tptp.zero_zero tptp.nat)) N_1))))))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (= (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_1) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) A_1)) (tptp.hAPP X_a tptp.real _let_1 X))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_4 (tptp.fun tptp.real tptp.bool) (tptp.sums tptp.real) X_3) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_5 (tptp.fun X_a tptp.bool) (tptp.sums X_a) (tptp.hAPP X_a _let_5 (tptp.hAPP _let_3 (tptp.fun X_a _let_5) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) _let_1) X_3)) X_1)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_1)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) R_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.sums X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 X_3) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_3 _let_3) (tptp.combb X_a X_a tptp.nat) _let_2) X_3)) (tptp.hAPP X_a X_a _let_2 A_2)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.cauchy X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 X_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) R_1)) X_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) R_1))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (let ((_let_4 (tptp.suminf X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.summable X_a) X_3)) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP _let_3 X_a _let_4 X_3)) (tptp.hAPP _let_3 X_a _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_3 _let_3) (tptp.combb X_a X_a tptp.nat) _let_2) X_3))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.summable X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 X_3)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool _let_3 (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_2) (tptp.combb X_a X_a tptp.nat) (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) R_1)) X_3)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.summable tptp.real) X_3)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.summable X_a) (tptp.hAPP X_a _let_4 (tptp.hAPP _let_2 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real _let_1 tptp.nat) (tptp.scaleR_scaleR X_a)) X_3)) X_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_1) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 B) X)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) A_1) B)) X))))))) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (= (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR tptp.real) A_1) X) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_1 (tptp.times_times tptp.real) A_1) X)))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((A_1 $$unsorted) (R_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) A_1))) (let ((_let_3 (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) R_4))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_3 B)) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_2 B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra X_a) (forall ((X $$unsorted) (A_1 $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X))) (let ((_let_3 (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) A_1))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_3 Y)) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_2 Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Xa_1 $$unsorted) (R_4 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.times_times X_a) Xa_1))) (let ((_let_3 (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) R_4))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_3 X)) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_2 X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra X_a) (forall ((A_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 (tptp.scaleR_scaleR X_a) A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X)) Y) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((R_4 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 (tptp.scaleR_scaleR X_a) R_4))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 A_1)) B) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((R_4 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 (tptp.scaleR_scaleR X_a) R_4))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X)) Y) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((R_4 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) R_4) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.times_times X_a) (tptp.hAPP tptp.real X_a (tptp.of_real X_a) R_4)) X)))))) (forall ((R_4 $$unsorted) (X $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.complex tptp.complex) (tptp.scaleR_scaleR tptp.complex) R_4) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_4) (tptp.hAPP tptp.complex tptp.real tptp.im X)))) (forall ((R_4 $$unsorted) (X $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.complex tptp.complex) (tptp.scaleR_scaleR tptp.complex) R_4) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_4) (tptp.hAPP tptp.complex tptp.real tptp.re X)))) (forall ((R_4 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_4))) (let ((_let_2 (tptp.fun tptp.real tptp.complex))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.complex tptp.complex) (tptp.scaleR_scaleR tptp.complex) R_4) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.complex_1 A_1) B)) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real _let_2 tptp.complex_1 (tptp.hAPP tptp.real tptp.real _let_1 A_1)) (tptp.hAPP tptp.real tptp.real _let_1 B)))))) (forall ((X_a $$unsorted)) (=> (and (tptp.divisi14063676e_zero X_a) (tptp.real_div_algebra X_a)) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.scaleR_scaleR X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_3 _let_2 A_1) X)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) A_1)) (tptp.hAPP X_a X_a _let_1 X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) A_1)) B) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) A_1)) X) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_1) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((X $$unsorted) (Xa_1 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.uminus_uminus tptp.real) X)) Xa_1) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 X) Xa_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_1))) (let ((_let_2 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 X)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_1))) (let ((_let_2 (tptp.uminus_uminus X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a _let_1 B)))))))) (forall ((R_4 $$unsorted) (X $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.re (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.complex tptp.complex) (tptp.scaleR_scaleR tptp.complex) R_4) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.scaleR_scaleR tptp.real) R_4) (tptp.hAPP tptp.complex tptp.real tptp.re X)))) (forall ((R_4 $$unsorted) (X $$unsorted)) (= (tptp.hAPP tptp.complex tptp.real tptp.im (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.complex tptp.complex) (tptp.scaleR_scaleR tptp.complex) R_4) X)) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.scaleR_scaleR tptp.real) R_4) (tptp.hAPP tptp.complex tptp.real tptp.im X)))) (forall ((R_4 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.complex tptp.complex) (tptp.scaleR_scaleR tptp.complex) R_4))) (= (tptp.hAPP tptp.complex tptp.complex tptp.cnj (tptp.hAPP tptp.complex tptp.complex _let_1 X)) (tptp.hAPP tptp.complex tptp.complex _let_1 (tptp.hAPP tptp.complex tptp.complex tptp.cnj X))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((R_4 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.of_real X_a))) (= (tptp.hAPP tptp.real X_a _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.scaleR_scaleR tptp.real) R_4) X)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) R_4) (tptp.hAPP tptp.real X_a _let_1 X))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 A_1))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 _let_1 B))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 X)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (R_4 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 A_1))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 _let_1 R_4))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 B)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((Ra $$unsorted) (R_4 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 _let_1 Ra))) (let ((_let_4 (tptp.hAPP tptp.real _let_2 _let_1 R_4))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 X)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 X)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_4 $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.scaleR_scaleR tptp.real) R_4) A_1)) B) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 R_4) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_4 $$unsorted) (X $$unsorted) (Xa_1 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.scaleR_scaleR tptp.real) R_4) X)) Xa_1) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 R_4) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 X) Xa_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_algebra_1 X_a) (forall ((R_4 $$unsorted)) (= (tptp.hAPP tptp.real X_a (tptp.of_real X_a) R_4) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) R_4) (tptp.one_one X_a)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_2 $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_2))) (= (= (tptp.hAPP X_a X_a _let_1 X_1) (tptp.hAPP X_a X_a _let_1 Y_1)) (or (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)) (= A_2 (tptp.zero_zero tptp.real)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((X $$unsorted) (Y $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_1))) (=> (not (= A_1 (tptp.zero_zero tptp.real))) (=> (= (tptp.hAPP X_a X_a _let_1 X) (tptp.hAPP X_a X_a _let_1 Y)) (= (tptp.ti X_a X) (tptp.ti X_a Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_1) _let_1) _let_1))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_2 $$unsorted) (X_1 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_1) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 B_1) X_1)) (or (= A_2 B_1) (= (tptp.ti X_a X_1) (tptp.zero_zero X_a))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (not (= (tptp.ti X_a X) (tptp.zero_zero X_a))) (=> (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_1) X) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 B) X)) (= A_1 B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) (tptp.one_one tptp.real)) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((R_4 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.inverse_divide X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP tptp.real _let_2 (tptp.scaleR_scaleR X_a) R_4))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 X)) Y) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_2 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.zero_zero X_a))) (= (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_2) X_1) _let_1) (or (= A_2 (tptp.zero_zero tptp.real)) (= (tptp.ti X_a X_1) _let_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) (tptp.zero_zero tptp.real)) X) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((B $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) (tptp.zero_zero tptp.real)) B) (tptp.zero_zero X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) A_1) B)) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_1) X)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 B) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (A_6 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) A_1) A_6)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_6) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((X $$unsorted) (Y $$unsorted) (Xa_1 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.plus_plus tptp.real) X) Y)) Xa_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 X) Xa_1)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 Y) Xa_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) A_1) B)) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_1) X)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 B) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (A_6 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) A_1) A_6)) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_6) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((X $$unsorted) (Y $$unsorted) (Xa_1 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) Y)) Xa_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.minus_minus X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 X) Xa_1)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 Y) Xa_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (B_5 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) A_1))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 B) B_5)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 B_5))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) A_1))) (let ((_let_3 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 X)) (tptp.hAPP X_a X_a _let_2 Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (B_5 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) A_1))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 B) B_5)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 B)) (tptp.hAPP X_a X_a _let_2 B_5))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((A_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP tptp.real _let_1 (tptp.scaleR_scaleR X_a) A_1))) (let ((_let_3 (tptp.minus_minus X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 X)) (tptp.hAPP X_a X_a _let_2 Y))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_4 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.sgn_sgn X_a))) (let ((_let_2 (tptp.scaleR_scaleR X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_3 _let_2 R_4) X)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.sgn_sgn tptp.real) R_4)) (tptp.hAPP X_a X_a _let_1 X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted) (Y $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) B))) (let ((_let_4 (tptp.scaleR_scaleR X_a))) (let ((_let_5 (tptp.hAPP tptp.real _let_2 _let_4 A_1))) (let ((_let_6 (tptp.hAPP tptp.real _let_2 _let_4 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) X) A_1)))) (let ((_let_7 (tptp.plus_plus X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_4 X) Y)) (tptp.hAPP X_a X_a _let_5 B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_7 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_7 (tptp.hAPP X_a X_a _let_6 _let_3)) (tptp.hAPP X_a X_a _let_6 B))) (tptp.hAPP X_a X_a _let_5 _let_3))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.real))) (let ((_let_4 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.cauchy tptp.real) X_3)) (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.cauchy X_a) (tptp.hAPP X_a _let_4 (tptp.hAPP _let_2 (tptp.fun X_a _let_4) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real _let_1 tptp.nat) (tptp.scaleR_scaleR X_a)) X_3)) X_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_vector X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) X) (tptp.hAPP X_a X_a (tptp.uminus_uminus X_a) X))))) (forall ((X_a $$unsorted)) (=> (tptp.sgn_div_norm X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.sgn_sgn X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) X))) X))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((G $$unsorted) (B_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a tptp.real))) (let ((_let_5 (tptp.fun X_a X_b))) (let ((_let_6 (tptp.tendsto X_a X_b))) (let ((_let_7 (tptp.filter X_a))) (let ((_let_8 (tptp.fun _let_7 tptp.bool))) (let ((_let_9 (tptp.fun X_b _let_8))) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP tptp.real _let_8 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_8) (tptp.tendsto X_a tptp.real) F) A_2) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_5 _let_9 _let_6 G) B_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP X_b _let_8 (tptp.hAPP _let_5 _let_9 _let_6 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_3 (tptp.fun _let_5 _let_5) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.real _let_2 X_a) _let_1) F)) G)) (tptp.hAPP X_b X_b (tptp.hAPP tptp.real _let_2 _let_1 A_2) B_1)) A_3)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((X_1 $$unsorted) (G $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_b))) (let ((_let_2 (tptp.fun X_b X_b))) (let ((_let_3 (tptp.fun X_a _let_2))) (let ((_let_4 (tptp.fun X_a tptp.real))) (let ((_let_5 (tptp.fun X_a X_b))) (let ((_let_6 (tptp.filter X_a))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_7) (tptp.tendsto X_a tptp.real) G) A_2) A_3)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_5 (tptp.fun X_b _let_7) (tptp.tendsto X_a X_b) (tptp.hAPP X_b _let_5 (tptp.hAPP _let_3 (tptp.fun X_b _let_5) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.real _let_2 X_a) _let_1) G)) X_1)) (tptp.hAPP X_b X_b (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_1)) A_3))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.real_normed_vector X_b) (forall ((R_1 $$unsorted) (G $$unsorted) (A_2 $$unsorted) (A_3 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_let_4 (tptp.fun tptp.real _let_8) (tptp.tendsto tptp.nat tptp.real) X_3) A_2) tptp.sequentially)) (=> (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP X_a _let_8 (tptp.hAPP _let_5 _let_9 _let_6 Y_3) B_1) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_7 tptp.bool (tptp.hAPP X_a _let_8 (tptp.hAPP _let_5 _let_9 _let_6 (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_3 (tptp.fun _let_5 _let_5) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) _let_1) X_3)) Y_3)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_2) B_1)) tptp.sequentially)))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (let ((_let_6 (tptp.filter tptp.nat))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_4 (tptp.fun tptp.real _let_7) (tptp.tendsto tptp.nat tptp.real) X_3) A_2) tptp.sequentially)) (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_a _let_7 (tptp.hAPP _let_5 (tptp.fun X_a _let_7) (tptp.tendsto tptp.nat X_a) (tptp.hAPP X_a _let_5 (tptp.hAPP _let_3 (tptp.fun X_a _let_5) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) _let_1) X_3)) X_1)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_1)) tptp.sequentially))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X_1 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.scaleR_scaleR X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun tptp.nat tptp.real))) (let ((_let_5 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.summable tptp.real) X_3)) (= (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP _let_4 tptp.real (tptp.suminf tptp.real) X_3)) X_1) (tptp.hAPP _let_5 X_a (tptp.suminf X_a) (tptp.hAPP X_a _let_5 (tptp.hAPP _let_3 (tptp.fun X_a _let_5) (tptp.combc tptp.nat X_a X_a) (tptp.hAPP _let_4 _let_3 (tptp.hAPP (tptp.fun tptp.real _let_2) (tptp.fun _let_4 _let_3) (tptp.combb tptp.real _let_2 tptp.nat) _let_1) X_3)) X_1)))))))))))) (forall ((X $$unsorted)) (= (tptp.hAPP tptp.complex tptp.complex (tptp.sgn_sgn tptp.complex) X) (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.complex tptp.complex) (tptp.scaleR_scaleR tptp.complex) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) (tptp.hAPP tptp.complex tptp.real (tptp.norm_norm tptp.complex) X))) X))) (forall ((X_a $$unsorted)) (=> (tptp.real_div_algebra X_a) (forall ((X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.inverse_inverse X_a))) (let ((_let_2 (tptp.scaleR_scaleR X_a))) (let ((_let_3 (tptp.fun X_a X_a))) (=> (not (= A_1 (tptp.zero_zero tptp.real))) (=> (not (= (tptp.ti X_a X) (tptp.zero_zero X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_3 _let_2 A_1) X)) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) A_1)) (tptp.hAPP X_a X_a _let_1 X))))))))))) (forall ((R_4 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) R_4))) (= (tptp.hAPP tptp.complex tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.complex tptp.complex) (tptp.scaleR_scaleR tptp.complex) R_4) X) (tptp.hAPP tptp.real tptp.complex (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.complex) tptp.complex_1 (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.complex tptp.real tptp.re X))) (tptp.hAPP tptp.real tptp.real _let_1 (tptp.hAPP tptp.complex tptp.real tptp.im X)))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.metric_space X_a) (tptp.real_normed_vector X_b)) (forall ((G $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.zero_zero X_b))) (let ((_let_4 (tptp.fun X_b X_b))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun X_a tptp.real))) (let ((_let_7 (tptp.fun X_a X_b))) (let ((_let_8 (tptp.tendsto X_a X_b))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (let ((_let_10 (tptp.fun X_b _let_9))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_9 (tptp.hAPP _let_6 (tptp.fun tptp.real _let_9) (tptp.tendsto X_a tptp.real) F) (tptp.zero_zero tptp.real)) _let_2)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_9 (tptp.hAPP _let_7 _let_10 _let_8 G) _let_3) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_9 (tptp.hAPP _let_7 _let_10 _let_8 (tptp.hAPP _let_7 _let_7 (tptp.hAPP _let_5 (tptp.fun _let_7 _let_7) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_6 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_6 _let_5) (tptp.combb tptp.real _let_4 X_a) (tptp.scaleR_scaleR X_b)) F)) G)) _let_3) _let_2))))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((X_1 $$unsorted) (G $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun X_a tptp.real))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_5 (tptp.fun tptp.real _let_7) (tptp.tendsto X_a tptp.real) G) (tptp.zero_zero tptp.real)) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_6 (tptp.fun X_b _let_7) (tptp.tendsto X_a X_b) (tptp.hAPP X_b _let_6 (tptp.hAPP _let_4 (tptp.fun X_b _let_6) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_5 _let_4 (tptp.hAPP (tptp.fun tptp.real _let_3) (tptp.fun _let_5 _let_4) (tptp.combb tptp.real _let_3 X_a) (tptp.scaleR_scaleR X_b)) G)) X_1)) (tptp.zero_zero X_b)) _let_2))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((C_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.fun X_b X_b))) (let ((_let_4 (tptp.fun X_a _let_3))) (let ((_let_5 (tptp.fun X_a tptp.real))) (let ((_let_6 (tptp.fun X_a X_b))) (let ((_let_7 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_7 (tptp.hAPP _let_5 (tptp.fun tptp.real _let_7) (tptp.tendsto X_a tptp.real) F) (tptp.zero_zero tptp.real)) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_7 (tptp.hAPP _let_6 (tptp.fun X_b _let_7) (tptp.tendsto X_a X_b) (tptp.hAPP X_b _let_6 (tptp.hAPP _let_4 (tptp.fun X_b _let_6) (tptp.combc X_a X_b X_b) (tptp.hAPP _let_5 _let_4 (tptp.hAPP (tptp.fun tptp.real _let_3) (tptp.fun _let_5 _let_4) (tptp.combb tptp.real _let_3 X_a) (tptp.scaleR_scaleR X_b)) F)) C_1)) (tptp.zero_zero X_b)) _let_2))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_n2089651433ebra_1 X_a) (tptp.banach X_a)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.summable X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.real _let_4 tptp.nat) (tptp.scaleR_scaleR X_a)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_2 _let_2) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) (tptp.fact_fact tptp.nat))))) (tptp.hAPP X_a _let_1 (tptp.power_power X_a) X_1)))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_n2089651433ebra_1 X_a) (tptp.banach X_a)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.summable tptp.real) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun X_a tptp.real) (tptp.fun _let_1 _let_2) (tptp.combb X_a tptp.real tptp.nat) (tptp.norm_norm X_a)) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.real _let_4 tptp.nat) (tptp.scaleR_scaleR X_a)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_2 _let_2) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) (tptp.fact_fact tptp.nat))))) (tptp.hAPP X_a _let_1 (tptp.power_power X_a) X_1))))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (= (tptp.hAPP X_a X_a (tptp.exp X_a) X_2) (tptp.hAPP _let_1 X_a (tptp.suminf X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.real _let_4 tptp.nat) (tptp.scaleR_scaleR X_a)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_2 _let_2) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) (tptp.fact_fact tptp.nat))))) (tptp.hAPP X_a _let_1 (tptp.power_power X_a) X_2)))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (= (tptp.hAPP X_a X_a (tptp.exp X_a) X_1) (tptp.hAPP _let_1 X_a (tptp.suminf X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.real _let_4 tptp.nat) (tptp.scaleR_scaleR X_a)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_2 _let_2) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) (tptp.fact_fact tptp.nat))))) (tptp.hAPP X_a _let_1 (tptp.power_power X_a) X_1)))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (let ((_let_2 (tptp.fun tptp.nat tptp.real))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.fun X_a X_a))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.sums X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP _let_5 (tptp.fun _let_1 _let_1) (tptp.combs tptp.nat X_a X_a) (tptp.hAPP _let_2 _let_5 (tptp.hAPP (tptp.fun tptp.real _let_4) (tptp.fun _let_2 _let_5) (tptp.combb tptp.real _let_4 tptp.nat) (tptp.scaleR_scaleR X_a)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_2 _let_2) (tptp.combb tptp.real tptp.real tptp.nat) (tptp.inverse_inverse tptp.real)) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_2) (tptp.combb tptp.nat tptp.real tptp.nat) (tptp.real_1 tptp.nat)) (tptp.fact_fact tptp.nat))))) (tptp.hAPP X_a _let_1 (tptp.power_power X_a) X_1))) (tptp.hAPP X_a X_a (tptp.exp X_a) X_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) X_2) X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) X_2)) K_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_4) B_4))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) A_4)) (tptp.hAPP X_a tptp.real _let_1 B_4))) K_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_4) B_4))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) A_4)) (tptp.hAPP X_a tptp.real _let_1 B_4))) K_2))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) X_2) X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) X_2)) K_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_4 $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) R_4) X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((X $$unsorted)) (exists ((K_2 $$unsorted)) (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real (tptp.norm_norm X_a) (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) X_2) X))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) X_2)) K_2)))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (exists ((K_2 $$unsorted)) (forall ((A_4 $$unsorted) (B_4 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (let ((_let_2 (tptp.times_times tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) A_4) B_4))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_3 _let_2 (tptp.hAPP tptp.real tptp.real (tptp.norm_norm tptp.real) A_4)) (tptp.hAPP X_a tptp.real _let_1 B_4))) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_4 $$unsorted)) (exists ((K_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) K_2)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) R_4) X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_vector X_a) (forall ((R_4 $$unsorted)) (exists ((K_2 $$unsorted)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.norm_norm X_a))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real _let_1 (tptp.hAPP X_a X_a (tptp.hAPP tptp.real (tptp.fun X_a X_a) (tptp.scaleR_scaleR X_a) R_4) X_2))) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.times_times tptp.real) (tptp.hAPP X_a tptp.real _let_1 X_2)) K_2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.topological_space X_b)) (forall ((L $$unsorted) (Ma $$unsorted) (F $$unsorted) (G $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.at X_a))) (let ((_let_2 (tptp.filter X_a))) (let ((_let_3 (tptp.tendsto X_a X_b))) (let ((_let_4 (tptp.fun _let_2 tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (=> (= (tptp.ti X_a A_2) (tptp.ti X_a B_1)) (=> (forall ((X_2 $$unsorted)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a B_1))) (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b G X_2)))) (=> (= (tptp.ti X_b L) (tptp.ti X_b Ma)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 F) L) (tptp.hAPP X_a _let_2 _let_1 A_2))) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 G) Ma) (tptp.hAPP X_a _let_2 _let_1 B_1)))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted) (X_c $$unsorted)) (=> (tptp.real_normed_vector X_c) (forall ((F $$unsorted) (A_2 $$unsorted) (A_3 $$unsorted) (S $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a X_c))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_a X_c))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_b X_c))) (let ((_let_7 (tptp.fun X_b _let_3))) (let ((_let_8 (tptp.filter X_b))) (let ((_let_9 (tptp.fun _let_8 tptp.bool))) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.filter X_b))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP X_a (tptp.fun _let_4 tptp.bool) (tptp.member X_a) I_2) S)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_c _let_3 (tptp.hAPP _let_1 (tptp.fun X_c _let_3) (tptp.tendsto X_b X_c) (tptp.hAPP X_a _let_1 F I_2)) (tptp.hAPP X_a X_c A_2 I_2)) A_3)))))))) (tptp.hBOOL (tptp.hAPP _let_8 tptp.bool (tptp.hAPP X_c _let_9 (tptp.hAPP _let_6 (tptp.fun X_c _let_9) (tptp.tendsto X_b X_c) (tptp.hAPP _let_2 _let_6 (tptp.hAPP _let_7 (tptp.fun _let_2 _let_6) (tptp.combc X_b _let_2 X_c) (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun _let_4 _let_3) (tptp.fun _let_5 _let_7) (tptp.combb _let_4 _let_3 X_b) _let_1) (tptp.hAPP (tptp.fun X_a _let_6) _let_5 (tptp.combc X_a X_b X_c) F))) S)) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 A_2) S)) A_3))))))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.metric_space X_a) (tptp.metric_space X_b)) (forall ((F $$unsorted) (L_2 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) R_2)) (exists ((S_1 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) S_1)) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_2) A_2)) S_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 (tptp.hAPP X_b tptp.real (tptp.hAPP X_b (tptp.fun X_b tptp.real) (tptp.dist_dist X_b) (tptp.hAPP X_a X_b F X_2)) L_2)) R_2)))))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F) L_2) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))))))))) (not (tptp.hBOOL (tptp.hAPP _let_29 tptp.bool (tptp.trivial_limit tptp.nat) tptp.sequentially))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.topological_space X_b)) (forall ((L $$unsorted) (F $$unsorted) (G $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.tendsto X_a X_b))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (let ((_let_5 (tptp.fun X_b _let_4))) (let ((_let_6 (tptp.fun X_a X_b))) (=> (forall ((X_2 $$unsorted)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b G X_2)))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 F) L) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_6 _let_5 _let_3 G) L) _let_2))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.t2_space X_b) (forall ((L_1 $$unsorted) (F $$unsorted) (L $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (let ((_let_3 (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun X_b _let_2) (tptp.tendsto X_a X_b) F))) (=> (not (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.trivial_limit X_a) A_3))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 _let_3 L) A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_2 _let_3 L_1) A_3)) (= (tptp.ti X_b L) (tptp.ti X_b L_1))))))))))) _let_28 (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (= (tptp.hAPP X_a X_b G X_2) (tptp.hAPP X_a X_b H X_2))))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 H) A_3))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_c $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 (tptp.hAPP _let_1 X_a (tptp.hAPP (tptp.fun X_b (tptp.fun X_c X_a)) (tptp.fun _let_1 X_a) (tptp.product_prod_case X_b X_c X_a) P_1) Z))) (not (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.product_prod X_b X_c))) (=> (= (tptp.ti _let_1 Z) (tptp.hAPP X_c _let_1 (tptp.hAPP X_b (tptp.fun X_c _let_1) (tptp.product_Pair X_b X_c) X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 (tptp.hAPP X_c X_a (tptp.hAPP X_b (tptp.fun X_c X_a) P_1 X_2) Y_2))))))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted) (P_4 $$unsorted) (F $$unsorted) (G $$unsorted) (Q_2 $$unsorted)) (let ((_let_1 (tptp.product_prod_case X_a X_b X_c))) (let ((_let_2 (tptp.product_prod X_a X_b))) (let ((_let_3 (tptp.fun _let_2 X_c))) (let ((_let_4 (tptp.fun X_a (tptp.fun X_b X_c)))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.product_prod X_a X_b))) (=> (= (tptp.hAPP X_b _let_2 (tptp.hAPP X_a (tptp.fun X_b _let_2) (tptp.product_Pair X_a X_b) X_2) Y_2) (tptp.ti _let_2 Q_2)) (= (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 F X_2) Y_2) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 G X_2) Y_2)))))) (=> (= (tptp.ti _let_2 P_4) (tptp.ti _let_2 Q_2)) (= (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 F) P_4) (tptp.hAPP _let_2 X_c (tptp.hAPP _let_4 _let_3 _let_1 G) Q_2))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_mult X_b) (forall ((F $$unsorted) (F_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) F_1)) (= (tptp.hAPP X_a X_b F X_2) (tptp.one_one X_b))))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co302546470etprod X_a X_b) F) F_1) (tptp.one_one X_b))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_semiring_1 X_b) (forall ((D_1 $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((I_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.dvd_dvd X_b) D_1) (tptp.hAPP X_a X_b F I_2)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.dvd_dvd X_b) D_1) (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F) A_3)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((G $$unsorted) (H $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_b))) (let ((_let_4 (tptp.fun X_a X_b))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (= (tptp.hAPP X_a X_b G X_2) (tptp.hAPP X_a X_b H X_2))))) (= (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 G) A_3) (tptp.hAPP _let_2 X_b (tptp.hAPP _let_4 _let_3 _let_1 H) A_3))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted)) (=> (tptp.comm_monoid_add X_b) (forall ((F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (= (tptp.hAPP X_a X_b F X_2) (tptp.zero_zero X_b))))) (= (tptp.hAPP _let_1 X_b (tptp.hAPP (tptp.fun X_a X_b) (tptp.fun _let_1 X_b) (tptp.big_co1399186613setsum X_a X_b) F) A_3) (tptp.zero_zero X_b))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((G $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2))) (let ((_let_3 (tptp.zero_zero tptp.real))) (let ((_let_4 (tptp.tendsto X_a tptp.real))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun tptp.real _let_5))) (let ((_let_7 (tptp.fun X_a tptp.real))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_7 _let_6 _let_4 F) _let_3) _let_2)) (=> (forall ((X_2 $$unsorted)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP X_a tptp.real G X_2))))) (=> (forall ((X_2 $$unsorted)) (=> (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP X_a tptp.real G X_2)) (tptp.hAPP X_a tptp.real F X_2))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real _let_5 (tptp.hAPP _let_7 _let_6 _let_4 G) _let_3) _let_2))))))))))))))) (forall ((A_1 $$unsorted) (B $$unsorted)) (=> (not (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) A_1) B) (tptp.zero_zero tptp.int))) (exists ((A_5 $$unsorted) (B_3 $$unsorted)) (let ((_let_1 (tptp.gcd_gcd tptp.int))) (let ((_let_2 (tptp.fun tptp.int tptp.int))) (let ((_let_3 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_1) B))) (let ((_let_4 (tptp.times_times tptp.int))) (and (= (tptp.ti tptp.int A_1) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 A_5) _let_3)) (= (tptp.ti tptp.int B) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_4 B_3) _let_3)) (= (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_2 _let_1 A_5) B_3) (tptp.one_one tptp.int)))))))))) (forall ((X_a $$unsorted) (C_1 $$unsorted) (P_1 $$unsorted)) (=> (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X1))) (=> (= (tptp.ti X_a C_1) (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.hilbert_Eps X_a) P_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 C_1))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.comm_monoid_mult X_a) (forall ((H $$unsorted) (G $$unsorted) (S $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.big_co302546470etprod X_b X_a))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.one_one X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 R_3 _let_6) _let_6)) (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.times_times X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 R_3 X1) X2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 R_3 Y1) Y2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 R_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X1) Y1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X2) Y2)))))))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) S)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) S)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) R_3 (tptp.hAPP X_b X_a H X_2)) (tptp.hAPP X_b X_a G X_2)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 R_3 (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 H) S)) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 G) S)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (let ((_let_4 (tptp.fun tptp.bool tptp.bool))) (let ((_let_5 (tptp.fun X_a _let_4))) (let ((_let_6 (tptp.fun _let_2 _let_2))) (let ((_let_7 (tptp.fun X_a _let_6))) (let ((_let_8 (tptp.fun X_a _let_2))) (let ((_let_9 (tptp.fun _let_1 tptp.bool))) (= (tptp.hAPP _let_9 _let_1 (tptp.hilbert_Eps _let_1) (tptp.hAPP _let_8 _let_9 (tptp.product_prod_case X_a X_b tptp.bool) (tptp.hAPP _let_2 _let_8 (tptp.hAPP _let_7 (tptp.fun _let_2 _let_8) (tptp.combc X_a _let_2 _let_2) (tptp.hAPP _let_5 _let_7 (tptp.hAPP (tptp.fun _let_4 _let_6) (tptp.fun _let_5 _let_7) (tptp.combb _let_4 _let_6 X_a) (tptp.combb tptp.bool tptp.bool X_b)) (tptp.hAPP _let_3 _let_5 (tptp.hAPP (tptp.fun tptp.bool _let_4) (tptp.fun _let_3 _let_5) (tptp.combb tptp.bool _let_4 X_a) tptp.fconj) (tptp.hAPP X_a _let_3 (tptp.fequal X_a) X_1)))) (tptp.hAPP X_b _let_2 (tptp.fequal X_b) Y_1)))) (tptp.hAPP X_b _let_1 (tptp.hAPP X_a (tptp.fun X_b _let_1) (tptp.product_Pair X_a X_b) X_1) Y_1)))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun X_b _let_1))) (let ((_let_4 (tptp.fun _let_3 _let_2))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.fun X_a _let_2))) (let ((_let_7 (tptp.fun X_a _let_3))) (let ((_let_8 (tptp.hilbert_Eps _let_1))) (= (tptp.hAPP _let_5 _let_1 _let_8 P_1) (tptp.hAPP _let_5 _let_1 _let_8 (tptp.hAPP _let_6 _let_5 (tptp.product_prod_case X_a X_b tptp.bool) (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_4 (tptp.fun _let_7 _let_6) (tptp.combb _let_3 _let_2 X_a) (tptp.hAPP _let_5 _let_4 (tptp.combb _let_1 tptp.bool X_b) P_1)) (tptp.product_Pair X_a X_b)))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.product_prod X_a X_b))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_1 X_a))) (let ((_let_5 (tptp.fun X_a _let_2))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (let ((_let_7 (tptp.fun _let_1 X_b))) (let ((_let_8 (tptp.hilbert_Eps _let_1))) (= (tptp.hAPP _let_6 _let_1 _let_8 (tptp.hAPP _let_5 _let_6 (tptp.product_prod_case X_a X_b tptp.bool) P_1)) (tptp.hAPP _let_6 _let_1 _let_8 (tptp.hAPP _let_7 _let_6 (tptp.hAPP _let_3 (tptp.fun _let_7 _let_6) (tptp.combs _let_1 X_b tptp.bool) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.combb X_a _let_2 _let_1) P_1) (tptp.product_fst X_a X_b))) (tptp.product_snd X_a X_b))))))))))))) (forall ((X_a $$unsorted) (P_3 $$unsorted) (X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_3 X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_3 (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.hilbert_Eps X_a) P_3))))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (X_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.hilbert_Eps X_a) P_1))))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (=> (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.hilbert_Eps X_a) P_1))))) (forall ((X_a $$unsorted) (P_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.hilbert_Eps X_a) P_1))) (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X1))))) (forall ((X_a $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a _let_1))) (= (tptp.hAPP _let_1 X_a (tptp.hilbert_Eps X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_a X_a tptp.bool) (tptp.fequal X_a)) X_1)) (tptp.ti X_a X_1))))) (forall ((X_a $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hAPP _let_1 X_a (tptp.hilbert_Eps X_a) (tptp.hAPP X_a _let_1 (tptp.fequal X_a) X_1)) (tptp.ti X_a X_1)))) (forall ((X_a $$unsorted) (P_1 $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 A_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2)) (= (tptp.ti X_a X_2) (tptp.ti X_a A_2)))) (= (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.hilbert_Eps X_a) P_1) (tptp.ti X_a A_2))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun tptp.nat _let_5))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun tptp.nat _let_7))) (let ((_let_10 (tptp.fun tptp.nat _let_4))) (let ((_let_11 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_11 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_11 tptp.bool) (tptp.strict_mono tptp.nat X_a) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_10 _let_6 (tptp.combs tptp.nat _let_2 _let_2) (tptp.hAPP _let_9 _let_10 (tptp.hAPP (tptp.fun _let_7 _let_4) (tptp.fun _let_9 _let_10) (tptp.combb _let_7 _let_4 tptp.nat) (tptp.combs tptp.nat tptp.bool tptp.bool)) (tptp.hAPP _let_3 _let_9 (tptp.hAPP _let_8 (tptp.fun _let_3 _let_9) (tptp.combb _let_2 _let_7 tptp.nat) (tptp.hAPP (tptp.fun tptp.bool _let_5) _let_8 (tptp.combb tptp.bool _let_5 tptp.nat) tptp.fconj)) _let_1))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_4 _let_6 (tptp.combb _let_2 _let_2 tptp.nat) (tptp.hAPP _let_5 _let_4 (tptp.combb tptp.bool tptp.bool tptp.nat) tptp.fNot)) (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.bool) _let_1)))) F)) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_1) X_1)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F X_1)) (tptp.hAPP tptp.nat X_a F Y_1))))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((F $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.fun tptp.bool tptp.bool))) (let ((_let_6 (tptp.fun _let_3 _let_3))) (let ((_let_7 (tptp.fun tptp.nat _let_5))) (let ((_let_8 (tptp.fun _let_2 _let_7))) (let ((_let_9 (tptp.fun tptp.nat _let_7))) (let ((_let_10 (tptp.fun tptp.nat _let_4))) (let ((_let_11 (tptp.fun tptp.nat X_a))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_2) Y_2)) (not (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 Y_2) X_2)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) (tptp.hAPP tptp.nat X_a F X_2)) (tptp.hAPP tptp.nat X_a F Y_2))))))) (tptp.hBOOL (tptp.hAPP _let_11 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_11 tptp.bool) (tptp.strict_mono tptp.nat X_a) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_10 _let_6 (tptp.combs tptp.nat _let_2 _let_2) (tptp.hAPP _let_9 _let_10 (tptp.hAPP (tptp.fun _let_7 _let_4) (tptp.fun _let_9 _let_10) (tptp.combb _let_7 _let_4 tptp.nat) (tptp.combs tptp.nat tptp.bool tptp.bool)) (tptp.hAPP _let_3 _let_9 (tptp.hAPP _let_8 (tptp.fun _let_3 _let_9) (tptp.combb _let_2 _let_7 tptp.nat) (tptp.hAPP (tptp.fun tptp.bool _let_5) _let_8 (tptp.combb tptp.bool _let_5 tptp.nat) tptp.fconj)) _let_1))) (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_4 _let_6 (tptp.combb _let_2 _let_2 tptp.nat) (tptp.hAPP _let_5 _let_4 (tptp.combb tptp.bool tptp.bool tptp.nat) tptp.fNot)) (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.bool) _let_1)))) F))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((F $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat X_a))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (let ((_let_4 (tptp.fun tptp.nat tptp.bool))) (let ((_let_5 (tptp.fun tptp.nat _let_4))) (let ((_let_6 (tptp.fun _let_4 _let_4))) (let ((_let_7 (tptp.fun tptp.bool tptp.bool))) (let ((_let_8 (tptp.fun _let_5 _let_5))) (let ((_let_9 (tptp.fun tptp.nat _let_7))) (let ((_let_10 (tptp.fun _let_4 _let_9))) (let ((_let_11 (tptp.fun tptp.nat _let_9))) (let ((_let_12 (tptp.fun tptp.nat _let_6))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_5 _let_3 (tptp.strict_mono tptp.nat X_a) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_12 _let_8 (tptp.combs tptp.nat _let_4 _let_4) (tptp.hAPP _let_11 _let_12 (tptp.hAPP (tptp.fun _let_9 _let_6) (tptp.fun _let_11 _let_12) (tptp.combb _let_9 _let_6 tptp.nat) (tptp.combs tptp.nat tptp.bool tptp.bool)) (tptp.hAPP _let_5 _let_11 (tptp.hAPP _let_10 (tptp.fun _let_5 _let_11) (tptp.combb _let_4 _let_9 tptp.nat) (tptp.hAPP (tptp.fun tptp.bool _let_7) _let_10 (tptp.combb tptp.bool _let_7 tptp.nat) tptp.fconj)) _let_1))) (tptp.hAPP _let_5 _let_5 (tptp.hAPP _let_6 _let_8 (tptp.combb _let_4 _let_4 tptp.nat) (tptp.hAPP _let_7 _let_6 (tptp.combb tptp.bool tptp.bool tptp.nat) tptp.fNot)) (tptp.hAPP _let_5 _let_5 (tptp.combc tptp.nat tptp.nat tptp.bool) _let_1)))) F)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_5 _let_3 (tptp.mono tptp.nat X_a) _let_1) F)))))))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.dvd_dvd tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (let ((_let_3 (tptp.fun tptp.nat X_a))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP (tptp.fun tptp.nat _let_2) (tptp.fun _let_3 tptp.bool) (tptp.mono tptp.nat X_a) _let_1) F)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat _let_2 _let_1 X_1) Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a F X_1)) (tptp.hAPP tptp.nat X_a F Y_1))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((F $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_a))) (=> (forall ((X_2 $$unsorted) (Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.dvd_dvd tptp.nat) X_2) Y_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP tptp.nat X_a F X_2)) (tptp.hAPP tptp.nat X_a F Y_2))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP (tptp.fun tptp.nat (tptp.fun tptp.nat tptp.bool)) (tptp.fun _let_1 tptp.bool) (tptp.mono tptp.nat X_a) (tptp.dvd_dvd tptp.nat)) F))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (tptp.comm_monoid_add X_a) (forall ((H $$unsorted) (G $$unsorted) (S $$unsorted) (R_3 $$unsorted)) (let ((_let_1 (tptp.big_co1399186613setsum X_b X_a))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.fun _let_2 X_a))) (let ((_let_4 (tptp.fun X_b X_a))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (let ((_let_6 (tptp.zero_zero X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 R_3 _let_6) _let_6)) (=> (forall ((X1 $$unsorted) (Y1 $$unsorted) (X2 $$unsorted) (Y2 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 R_3 X1) X2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 R_3 Y1) Y2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_3 R_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X1) Y1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X2) Y2)))))))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.finite_finite_1 X_b) S)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b (tptp.fun _let_1 tptp.bool) (tptp.member X_b) X_2) S)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) R_3 (tptp.hAPP X_b X_a H X_2)) (tptp.hAPP X_b X_a G X_2)))))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_5 R_3 (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 H) S)) (tptp.hAPP _let_2 X_a (tptp.hAPP _let_4 _let_3 _let_1 G) S)))))))))))))))) (forall ((N_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.ord_min tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.bool (tptp.fun tptp.nat _let_3) (tptp.if tptp.nat) (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 N_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1))))))))) (forall ((V_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.ord_min tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.bool (tptp.fun tptp.nat _let_3) (tptp.if tptp.nat) (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)) (tptp.zero_zero tptp.nat)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)) N_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X_1) Y_1)) Z)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Z))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X_1) Y_1))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) X) (tptp.ti X_a X))))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((M $$unsorted) (I_1 $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_min tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.minus_minus tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 M) I_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 N) I_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_3 (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)) I_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) N) _let_1) _let_1))) (forall ((N $$unsorted)) (let ((_let_1 (tptp.zero_zero tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_min tptp.nat) _let_1) N) _let_1))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_min tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) Z_1) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Y))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Z_1)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 C)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 Y))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) A_1) (tptp.ti X_a A_1))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B))) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Z_1 $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Z_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) Y) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y) (tptp.ti X_a Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) A_1) B)) X)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) Y_1) Z))) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Z)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) Y_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X_1) Y_1) (tptp.ti X_a X_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y)) Y))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Y)) X))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X_1) Y_1)) Z)) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) Z))))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ord X_b)) (forall ((U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b))) (let ((_let_2 (tptp.hAPP tptp.int X_b _let_1 V))) (let ((_let_3 (tptp.hAPP tptp.int X_b _let_1 U))) (let ((_let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_min X_b) _let_3) _let_2))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) _let_3) _let_2)))) (and (=> _let_5 (= _let_4 _let_3)) (=> (not _let_5) (= _let_4 _let_2))))))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_min tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Ma) (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_4 (tptp.nat_case tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 (tptp.combb tptp.nat tptp.nat tptp.nat) tptp.suc) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_1) N_1))) Ma))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_min tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1)) Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.nat_case tptp.nat) (tptp.zero_zero tptp.nat)) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.combb tptp.nat tptp.nat tptp.nat) tptp.suc) (tptp.hAPP tptp.nat _let_2 _let_1 N_1))) Ma)))))) (forall ((X_a $$unsorted)) (let ((_let_1 (tptp.fun X_a (tptp.fun X_a tptp.bool)))) (=> (tptp.linorder X_a) (= (tptp.hAPP _let_1 (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.max X_a) (tptp.hAPP _let_1 _let_1 (tptp.combc X_a X_a tptp.bool) (tptp.ord_less_eq X_a))) (tptp.ord_min X_a))))) (forall ((X_a $$unsorted)) (=> (tptp.order X_a) (forall ((X $$unsorted) (Least $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Least) X_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) X) Least) (tptp.ti X_a Least)))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((X $$unsorted) (Least $$unsorted)) (=> (forall ((X_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Least) X_2))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_min X_a) Least) X) (tptp.ti X_a Least)))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (= (tptp.ord_min X_a) (tptp.hAPP (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.min X_a) (tptp.ord_less_eq X_a))))) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.rat tptp.rat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.rat))) (=> (exists ((A_4 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.zero_zero tptp.rat)) A_4)) (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.hAPP tptp.rat tptp.rat (tptp.abs_abs tptp.rat) (tptp.hAPP tptp.nat tptp.rat X_3 N_2))) A_4))))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool tptp.vanishes Y_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool tptp.vanishes (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs tptp.nat tptp.rat tptp.rat) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.rat _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.rat _let_1 tptp.nat) (tptp.times_times tptp.rat)) X_3)) Y_3))))))))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat Ma)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat N_1)) (= (tptp.hAPP tptp.int _let_2 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_2) (tptp.ord_atLeastAtMost tptp.int) Ma) N_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun tptp.nat tptp.int) (tptp.fun _let_1 _let_2) (tptp.image tptp.nat tptp.int) (tptp.semiring_1_of_nat tptp.int)) (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 Ma)) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 N_1))))))))) (forall ((X_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) X_1)))) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.rat tptp.rat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.rat))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool tptp.vanishes X_3)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool tptp.vanishes Y_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool tptp.vanishes (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs tptp.nat tptp.rat tptp.rat) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.rat _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.rat _let_1 tptp.nat) (tptp.minus_minus tptp.rat)) X_3)) Y_3))))))))) (forall ((Y_3 $$unsorted) (X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.rat tptp.rat))) (let ((_let_2 (tptp.fun tptp.nat _let_1))) (let ((_let_3 (tptp.fun tptp.nat tptp.rat))) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool tptp.vanishes X_3)) (=> (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool tptp.vanishes Y_3)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool tptp.vanishes (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs tptp.nat tptp.rat tptp.rat) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.rat _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.rat _let_1 tptp.nat) (tptp.plus_plus tptp.rat)) X_3)) Y_3))))))))) (forall ((C_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.rat))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.vanishes (tptp.hAPP tptp.rat _let_1 (tptp.combk tptp.rat tptp.nat) C_1))) (= C_1 (tptp.zero_zero tptp.rat))))) (forall ((X_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.rat))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.vanishes X_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.vanishes (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.rat tptp.rat) (tptp.fun _let_1 _let_1) (tptp.combb tptp.rat tptp.rat tptp.nat) (tptp.uminus_uminus tptp.rat)) X_3)))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.times_times tptp.int) X) Y)))))) (forall ((N $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat (tptp.hAPP tptp.nat tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.nat tptp.int) (tptp.power_power tptp.int) X) N))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_mod tptp.int) X) Y)))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.div_div tptp.int) X) Y)))))) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) tptp.nat_tsub X) Y)))))) (forall ((X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.nat_nat_set A_3)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_1) A_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X_1)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat _let_1)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat _let_2)) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X) Y)))))) (forall ((Z_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) Z_1)))) (forall ((Y_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool tptp.nat_nat_set (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) X_1) Y_1)))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat _let_21)) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat Y)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.gcd_gcd tptp.int) X) Y)))))) (forall ((X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less_eq tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.int tptp.int (tptp.fact_fact tptp.int) X))))) (forall ((A_3 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (let ((_let_2 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat X_1)) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool tptp.nat_nat_set A_3)) (= (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_2 tptp.bool) (tptp.member tptp.int) X_1) A_3)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.nat (tptp.fun _let_1 tptp.bool) (tptp.member tptp.nat) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 X_1)) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.image tptp.int tptp.nat) tptp.nat_1) A_3))))))))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat _let_19)) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.nat))) (let ((_let_2 (tptp.fun X_a tptp.int))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat (tptp.hAPP X_a tptp.int F X_2)))))) (= (tptp.hAPP _let_3 tptp.int (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.int) (tptp.big_co302546470etprod X_a tptp.int) F) A_3) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP _let_3 tptp.nat (tptp.hAPP _let_1 (tptp.fun _let_3 tptp.nat) (tptp.big_co302546470etprod X_a tptp.nat) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.combb tptp.int tptp.nat X_a) tptp.nat_1) F)) A_3)))))))) (forall ((X_a $$unsorted) (F $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.nat))) (let ((_let_2 (tptp.fun X_a tptp.int))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool tptp.nat_is_nat (tptp.hAPP X_a tptp.int F X_2)))))) (= (tptp.hAPP _let_3 tptp.int (tptp.hAPP _let_2 (tptp.fun _let_3 tptp.int) (tptp.big_co1399186613setsum X_a tptp.int) F) A_3) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) (tptp.hAPP _let_3 tptp.nat (tptp.hAPP _let_1 (tptp.fun _let_3 tptp.nat) (tptp.big_co1399186613setsum X_a tptp.nat) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_2 _let_1) (tptp.combb tptp.int tptp.nat X_a) tptp.nat_1) F)) A_3)))))))) (forall ((X_3 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.rat) tptp.bool tptp.vanishes X_3)) (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.zero_zero tptp.rat)) R_2)) (exists ((K_1 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) N_2)) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.hAPP tptp.rat tptp.rat (tptp.abs_abs tptp.rat) (tptp.hAPP tptp.nat tptp.rat X_3 N_2))) R_2))))))))) (forall ((R_1 $$unsorted) (X_3 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.rat) tptp.bool tptp.vanishes X_3)) (=> (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.zero_zero tptp.rat)) R_1)) (exists ((K_1 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) N_2)) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.hAPP tptp.rat tptp.rat (tptp.abs_abs tptp.rat) (tptp.hAPP tptp.nat tptp.rat X_3 N_2))) R_1)))))))) (forall ((X_3 $$unsorted)) (=> (forall ((R_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.zero_zero tptp.rat)) R_2)) (exists ((K_1 $$unsorted)) (forall ((N_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less_eq tptp.nat) K_1) N_2)) (tptp.hBOOL (tptp.hAPP tptp.rat tptp.bool (tptp.hAPP tptp.rat (tptp.fun tptp.rat tptp.bool) (tptp.ord_less tptp.rat) (tptp.hAPP tptp.rat tptp.rat (tptp.abs_abs tptp.rat) (tptp.hAPP tptp.nat tptp.rat X_3 N_2))) R_2))))))) (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.rat) tptp.bool tptp.vanishes X_3)))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.hilbert_Eps X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.hAPP _let_2 X_a _let_1 Q_1))) (let ((_let_4 (tptp.hAPP _let_2 X_a _let_1 P_1))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 _let_4)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 _let_3)) (=> (= _let_4 _let_3) (exists ((A_4 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 A_4)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 A_4)))))))))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted) (A_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 A_2)) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.hilbert_Eps X_a) P_1)))))) (forall ((X_a $$unsorted) (A_2 $$unsorted) (P_1 $$unsorted)) (=> (exists ((X_2 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2)) (forall ((Y_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 Y_2)) (= (tptp.ti X_a Y_2) (tptp.ti X_a X_2)))))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 A_2)) (= (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.hilbert_Eps X_a) P_1) (tptp.ti X_a A_2))))) (forall ((X_a $$unsorted) (Q_1 $$unsorted) (P_1 $$unsorted)) (=> (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X1))) (=> (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 X_2)))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool Q_1 (tptp.hAPP (tptp.fun X_a tptp.bool) X_a (tptp.hilbert_Eps X_a) P_1)))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted)) (let ((_let_1 (tptp.powp X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.fun _let_2 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.ord_less_eq _let_2) A_3) B_2)) (tptp.hBOOL (tptp.hAPP _let_3 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_3 tptp.bool) (tptp.ord_less_eq _let_3) (tptp.hAPP _let_2 _let_3 _let_1 A_3)) (tptp.hAPP _let_2 _let_3 _let_1 B_2)))))))) (forall ((X_a $$unsorted) (A_3 $$unsorted) (X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.powp X_a) (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_a _let_2) (tptp.fun _let_1 _let_1) (tptp.combc X_a _let_1 tptp.bool) (tptp.member X_a)) A_3)) X_2)) (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_2 tptp.bool) (tptp.member _let_1) X_2) (tptp.hAPP _let_1 _let_2 (tptp.pow X_a) A_3))))))) (forall ((Ma $$unsorted) (X_2 $$unsorted) (Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.int _let_1))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcongm Ma) X_2) Xa)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_2 tptp.zcong X_2) Xa) Ma)))))) (forall ((B_2 $$unsorted) (P_2 $$unsorted) (P_1 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) X_2) Z_2)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X_2)))))) (=> (forall ((X_2 $$unsorted)) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) B_2)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) X_2) D_2)))))) (=> (forall ((X_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_1) D_2))))))) (= (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X1))) (or (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_2) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X_2))))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_2) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (exists ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) B_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) Xa) X_2)))))))))))))))) (forall ((A_3 $$unsorted) (B_2 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.hAPP (tptp.fun tptp.int tptp.int) (tptp.fun _let_1 tptp.int) (tptp.big_co302546470etprod tptp.int tptp.int) (tptp.combi tptp.int)))) (let ((_let_3 (tptp.fun tptp.int _let_1))) (let ((_let_4 (tptp.product_prod _let_1 _let_1))) (let ((_let_5 (tptp.fun _let_4 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_5 tptp.bool (tptp.hAPP _let_4 (tptp.fun _let_5 tptp.bool) (tptp.member _let_4) (tptp.hAPP _let_1 _let_4 (tptp.hAPP _let_1 (tptp.fun _let_1 _let_4) (tptp.product_Pair _let_1 _let_1) A_3) B_2)) (tptp.hAPP _let_3 _let_5 (tptp.bijR tptp.int tptp.int) (tptp.hAPP tptp.int _let_3 tptp.zcongm Ma)))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int _let_3 tptp.zcong (tptp.hAPP _let_1 tptp.int _let_2 A_3)) (tptp.hAPP _let_1 tptp.int _let_2 B_2)) Ma))))))))) (forall ((A_3 $$unsorted) (P_2 $$unsorted) (P_1 $$unsorted) (D_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) (tptp.zero_zero tptp.int)) D_2)) (=> (exists ((Z_2 $$unsorted)) (forall ((X_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.bool) (tptp.ord_less tptp.int) Z_2) X_2)) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X_2)))))) (=> (forall ((X_2 $$unsorted)) (=> (forall ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (forall ((Xb $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xb) A_3)) (not (= (tptp.ti tptp.int X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xb) Xa))))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.plus_plus tptp.int) X_2) D_2)))))) (=> (forall ((X_2 $$unsorted) (K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.int))) (= (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X_2)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.minus_minus tptp.int) X_2) (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int _let_1 (tptp.times_times tptp.int) K_1) D_2))))))) (= (exists ((X1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 X1))) (or (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_2) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_2 X_2))))) (exists ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) X_2) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.one_one tptp.int)) D_2))) (exists ((Xa $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (and (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.int (tptp.fun _let_1 tptp.bool) (tptp.member tptp.int) Xa) A_3)) (tptp.hBOOL (tptp.hAPP tptp.int tptp.bool P_1 (tptp.hAPP tptp.int tptp.int (tptp.hAPP tptp.int (tptp.fun tptp.int tptp.int) (tptp.minus_minus tptp.int) Xa) X_2)))))))))))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_b tptp.bool))) (let ((_let_3 (tptp.product_prod _let_1 _let_2))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_1 (tptp.fun _let_2 _let_3) (tptp.product_Pair _let_1 _let_2) A_3) B_2)) (tptp.hAPP (tptp.fun X_a _let_2) _let_4 (tptp.bijR X_a X_b) P_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_a) A_3)))))))) (forall ((X_a $$unsorted) (X_b $$unsorted) (A_3 $$unsorted) (B_2 $$unsorted) (P_1 $$unsorted)) (let ((_let_1 (tptp.fun X_b tptp.bool))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (let ((_let_3 (tptp.product_prod _let_2 _let_1))) (let ((_let_4 (tptp.fun _let_3 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.hAPP _let_3 (tptp.fun _let_4 tptp.bool) (tptp.member _let_3) (tptp.hAPP _let_1 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_1 _let_3) (tptp.product_Pair _let_2 _let_1) A_3) B_2)) (tptp.hAPP (tptp.fun X_a _let_1) _let_4 (tptp.bijR X_a X_b) P_1))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 X_b) B_2)))))))) (forall ((L $$unsorted) (F $$unsorted)) (let ((_let_1 (tptp.filter tptp.nat))) (let ((_let_2 (tptp.fun _let_1 tptp.bool))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real F N_2)) (tptp.hAPP tptp.nat tptp.real F (tptp.hAPP tptp.nat tptp.nat tptp.suc N_2))))) (=> (forall ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.nat tptp.real F N_2)) L))) (=> (forall ((E $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) E)) (exists ((N_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP 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(tptp.hAPP X_c _let_1 (tptp.at X_c) A_2))) (let ((_let_3 (tptp.fun X_c X_b))) (let ((_let_4 (tptp.fun X_c X_a))) (let ((_let_5 (tptp.fun X_a X_b))) (let ((_let_6 (tptp.fun _let_1 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_5 (tptp.fun X_a tptp.bool) (tptp.isCont X_a X_b) G) L)) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a _let_6 (tptp.hAPP _let_4 (tptp.fun X_a _let_6) (tptp.tendsto X_c X_a) F) L) _let_2)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_6 (tptp.hAPP _let_3 (tptp.fun X_b _let_6) (tptp.tendsto X_c X_b) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_5 (tptp.fun _let_4 _let_3) (tptp.combb X_a X_b X_c) G) F)) (tptp.hAPP X_a X_b G L)) _let_2))))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((F $$unsorted) (X_1 $$unsorted) (L $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun X_a _let_1) 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(let ((_let_1 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_1 (tptp.fun tptp.real tptp.bool) (tptp.isCont tptp.real tptp.real) (tptp.hAPP tptp.nat _let_1 tptp.root N_1)) X_1))))) (forall ((X_1 $$unsorted)) (=> (not (= (tptp.hAPP tptp.real tptp.real tptp.cos X_1) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real tptp.bool) (tptp.isCont tptp.real tptp.real) tptp.tan) X_1)))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_field X_a) (forall ((F $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (let ((_let_2 (tptp.fun X_a X_a))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.hAPP _let_2 (tptp.fun X_a _let_1) (tptp.deriv X_a) F) X_1) D_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.isCont X_a X_a) F) X_1)))))))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real tptp.bool) (tptp.isCont tptp.real tptp.real) tptp.cos) X_1))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real tptp.bool) (tptp.isCont tptp.real tptp.real) tptp.arctan) X_1))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real tptp.bool) (tptp.isCont tptp.real tptp.real) tptp.sqrt) X_1))) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real tptp.bool) (tptp.isCont tptp.real tptp.real) tptp.sin) X_1))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_normed_field X_a) (tptp.banach X_a)) (forall ((X_1 $$unsorted)) (tptp.hBOOL (tptp.hAPP 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(tptp.fun X_a X_b))) (let ((_let_4 (tptp.isCont X_a X_b))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 F) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 G) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_b _let_1 X_a) (tptp.minus_minus X_b)) F)) G)) A_2)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((G $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.isCont X_a X_b))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 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X_b))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.isCont X_a X_b) (tptp.hAPP X_b _let_1 (tptp.combk X_b X_a) K)) A_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((A_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP (tptp.fun X_a X_a) (tptp.fun X_a tptp.bool) (tptp.isCont X_a X_a) (tptp.combi X_a)) A_2))))) (forall ((X_b $$unsorted) (X_c $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.topological_space X_c) (tptp.topological_space X_b)) (forall ((G $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 _let_4 (tptp.isCont X_a X_b) F) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_3 (tptp.fun X_b tptp.bool) (tptp.isCont X_b X_c) G) (tptp.hAPP X_a X_b F A_2))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_4 (tptp.isCont X_a X_c) (tptp.hAPP _let_2 _let_1 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_1) (tptp.combb X_b X_c X_a) G) F)) A_2))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.real))) (let ((_let_2 (tptp.fun X_a X_b))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.isCont X_a X_b) F) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.isCont X_a tptp.real) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b tptp.real) (tptp.fun _let_2 _let_1) (tptp.combb X_b tptp.real X_a) (tptp.norm_norm X_b)) F)) A_2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.power X_b) (tptp.real_normed_algebra X_b)) (forall ((N_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat X_b))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.isCont X_a X_b))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 F) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP tptp.nat _let_3 (tptp.hAPP _let_2 (tptp.fun tptp.nat _let_3) (tptp.combc X_a tptp.nat X_b) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_b _let_1 X_a) (tptp.power_power X_b)) F)) N_1)) A_2))))))))))) (forall ((X_a $$unsorted)) (=> (and (tptp.real_algebra_1 X_a) (tptp.real_normed_vector X_a)) (forall ((A_2 $$unsorted)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real X_a) (tptp.fun tptp.real tptp.bool) (tptp.isCont tptp.real X_a) (tptp.of_real X_a)) A_2))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_n2089651433ebra_1 X_b)) (forall ((F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.fun X_a tptp.real))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_2 _let_3 (tptp.isCont X_a tptp.real) F) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_3 (tptp.isCont X_a X_b) (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun tptp.real X_b) (tptp.fun _let_2 _let_1) (tptp.combb tptp.real X_b X_a) (tptp.of_real X_b)) F)) A_2))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.isCont X_a X_b))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 F) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_1 _let_1) (tptp.combb X_b X_b X_a) (tptp.uminus_uminus X_b)) F)) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.topological_space X_a) (forall ((F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.real))) (let ((_let_2 (tptp.isCont X_a tptp.real))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 F) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun _let_1 _let_1) (tptp.combb tptp.real tptp.real X_a) (tptp.abs_abs tptp.real)) F)) A_2))))))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((X_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.isCont X_a X_a) (tptp.hAPP X_a _let_1 (tptp.times_times X_a) X_1)) A_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.real_normed_algebra X_a) (forall ((Y_1 $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.fun X_a _let_1))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 (tptp.fun X_a tptp.bool) (tptp.isCont X_a X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP _let_2 _let_2 (tptp.combc X_a X_a X_a) (tptp.times_times X_a)) Y_1)) A_2))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_algebra X_b)) (forall ((G $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.isCont X_a X_b))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 F) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 G) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_b _let_1 X_a) (tptp.times_times X_b)) F)) G)) A_2)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_algebra X_b)) (forall ((G $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.isCont X_a X_b))) (let ((_let_5 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 F) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 G) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_5 _let_4 (tptp.hAPP _let_3 _let_3 (tptp.hAPP _let_2 (tptp.fun _let_3 _let_3) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_b _let_1) (tptp.fun _let_3 _let_2) (tptp.combb X_b _let_1 X_a) (tptp.times_times X_b)) F)) G)) A_2)))))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.isCont X_a X_b))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 F) A_2)) (=> (not (= (tptp.hAPP X_a X_b F A_2) (tptp.zero_zero X_b))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 (tptp.hAPP _let_1 _let_1 (tptp.hAPP (tptp.fun X_b X_b) (tptp.fun _let_1 _let_1) (tptp.combb X_b X_b X_a) (tptp.sgn_sgn X_b)) F)) A_2)))))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_n1866405975lgebra X_b)) (forall ((F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_b))) (let ((_let_2 (tptp.isCont X_a X_b))) (let ((_let_3 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_1 _let_3 _let_2 F) A_2)) (=> 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_let_1 (tptp.fun tptp.real tptp.bool) (tptp.isCont tptp.real X_a) (tptp.hAPP X_a _let_1 (tptp.hAPP (tptp.fun tptp.real (tptp.fun X_a X_a)) (tptp.fun X_a _let_1) (tptp.combc tptp.real X_a X_a) (tptp.scaleR_scaleR X_a)) X_1)) A_2)))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.topological_space X_a) (tptp.real_normed_vector X_b)) (forall ((G $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_b))) (let ((_let_2 (tptp.fun X_a _let_1))) (let ((_let_3 (tptp.fun X_a tptp.real))) (let ((_let_4 (tptp.fun X_a X_b))) (let ((_let_5 (tptp.isCont X_a X_b))) (let ((_let_6 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 _let_6 (tptp.isCont X_a tptp.real) F) A_2)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 G) A_2)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_4 _let_6 _let_5 (tptp.hAPP _let_4 _let_4 (tptp.hAPP _let_2 (tptp.fun _let_4 _let_4) (tptp.combs X_a X_b X_b) (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun tptp.real _let_1) (tptp.fun _let_3 _let_2) (tptp.combb tptp.real _let_1 X_a) (tptp.scaleR_scaleR X_b)) F)) G)) A_2))))))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_1 (tptp.fun tptp.real tptp.bool) (tptp.isCont tptp.real tptp.real) (tptp.hAPP tptp.nat _let_1 tptp.root N_1)) (tptp.zero_zero tptp.real)))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) X_1) (tptp.zero_zero tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.isCont tptp.real tptp.real) (tptp.hAPP tptp.nat _let_1 tptp.root N_1)) X_1))))))) (forall ((X_1 $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.nat tptp.bool (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.bool) (tptp.ord_less tptp.nat) (tptp.zero_zero tptp.nat)) N_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_1 _let_2 (tptp.isCont tptp.real tptp.real) (tptp.hAPP tptp.nat _let_1 tptp.root N_1)) X_1))))))) (forall ((X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.real_normed_vector X_a) (tptp.topological_space X_b)) (forall ((F $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun _let_1 tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 (tptp.fun X_a tptp.bool) (tptp.isCont X_a X_b) F) X_1)) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_b _let_4 (tptp.hAPP _let_3 (tptp.fun X_b _let_4) (tptp.tendsto X_a X_b) (tptp.hAPP _let_2 _let_3 (tptp.hAPP _let_3 (tptp.fun _let_2 _let_3) (tptp.combb X_a X_b X_a) F) (tptp.hAPP X_a _let_2 (tptp.plus_plus X_a) X_1))) (tptp.hAPP X_a X_b F X_1)) (tptp.hAPP X_a _let_1 (tptp.at X_a) (tptp.zero_zero X_a)))))))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 X_1) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) _let_1 (tptp.isCont tptp.real tptp.real) tptp.arccos) X_1))))))) (forall ((X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 (tptp.hAPP tptp.int tptp.real (tptp.number_number_of tptp.real) tptp.min_1)) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 X_1) (tptp.one_one tptp.real))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) _let_1 (tptp.isCont tptp.real tptp.real) tptp.arcsin) X_1))))))) (forall ((X_c $$unsorted) (X_b $$unsorted) (X_a $$unsorted)) (=> (and (tptp.metric_space X_a) (tptp.topological_space X_b) (tptp.topological_space X_c)) (forall ((G $$unsorted) (L $$unsorted) (F $$unsorted) (A_2 $$unsorted)) (let ((_let_1 (tptp.filter X_a))) (let ((_let_2 (tptp.fun X_a X_c))) (let ((_let_3 (tptp.fun X_a X_b))) (let ((_let_4 (tptp.fun X_b X_c))) (let ((_let_5 (tptp.fun _let_1 tptp.bool))) (let ((_let_6 (tptp.filter X_b))) (let ((_let_7 (tptp.fun _let_6 tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP _let_3 (tptp.fun X_a tptp.bool) (tptp.isCont X_a X_b) F) A_2)) (=> (tptp.hBOOL (tptp.hAPP _let_6 tptp.bool (tptp.hAPP X_c _let_7 (tptp.hAPP _let_4 (tptp.fun X_c _let_7) (tptp.tendsto X_b X_c) G) L) (tptp.hAPP X_b _let_6 (tptp.at X_b) (tptp.hAPP X_a X_b F A_2)))) (=> (exists ((D_3 $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_3)) (forall ((X_2 $$unsorted)) (=> (and (not (= (tptp.ti X_a X_2) (tptp.ti X_a A_2))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.hAPP X_a tptp.real (tptp.hAPP X_a (tptp.fun X_a tptp.real) (tptp.dist_dist X_a) X_2) A_2)) D_3))) (not (= (tptp.hAPP X_a X_b F X_2) (tptp.hAPP X_a X_b F A_2))))))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_c _let_5 (tptp.hAPP _let_2 (tptp.fun X_c _let_5) (tptp.tendsto X_a X_c) (tptp.hAPP _let_3 _let_2 (tptp.hAPP _let_4 (tptp.fun _let_3 _let_2) (tptp.combb X_b X_c X_a) G) F)) L) (tptp.hAPP X_a _let_1 (tptp.at X_a) A_2)))))))))))))))) (forall ((F $$unsorted) (B_1 $$unsorted) (X_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) B_1) X_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP tptp.real (tptp.fun _let_1 tptp.bool) (tptp.member tptp.real) X_2) (tptp.hAPP tptp.real _let_1 (tptp.hAPP tptp.real (tptp.fun tptp.real _let_1) (tptp.ord_gr676655987ssThan tptp.real) B_1) X_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real F X_2)))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) _let_1 (tptp.isCont tptp.real tptp.real) F) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.zero_zero tptp.real)) (tptp.hAPP tptp.real tptp.real F X_1)))))))) (forall ((B_1 $$unsorted) (A_2 $$unsorted) (F $$unsorted) (G $$unsorted) (X_1 $$unsorted) (D_2 $$unsorted)) (let ((_let_1 (tptp.deriv tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (let ((_let_3 (tptp.fun tptp.real _let_2))) (let ((_let_4 (tptp.fun tptp.real tptp.real))) (let ((_let_5 (tptp.ord_less tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_4 _let_3 _let_1 F) (tptp.hAPP tptp.real tptp.real G X_1)) D_2)) (=> (not (= D_2 (tptp.zero_zero tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_5 A_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_5 X_1) B_1)) (=> (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.ord_less tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) Y_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 Y_2) B_1))) (= (tptp.hAPP tptp.real tptp.real F (tptp.hAPP tptp.real tptp.real G Y_2)) Y_2))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_4 _let_2 (tptp.isCont tptp.real tptp.real) G) X_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.hAPP _let_4 _let_3 _let_1 G) X_1) (tptp.hAPP tptp.real tptp.real (tptp.inverse_inverse tptp.real) D_2))))))))))))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted)) (=> (and (tptp.topological_space X_b) (tptp.real_normed_vector X_c)) (forall ((F $$unsorted) (X_1 $$unsorted) (A_3 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_b _let_1))) (let ((_let_3 (tptp.fun X_b X_c))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (let ((_let_5 (tptp.fun _let_4 X_c))) (let ((_let_6 (tptp.fun X_b _let_5))) (=> (tptp.hBOOL (tptp.hAPP _let_4 tptp.bool (tptp.finite_finite_1 X_a) A_3)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP _let_2 tptp.bool (tptp.hAPP X_a (tptp.fun _let_2 tptp.bool) (tptp.member X_a) X_2) A_3)) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_1 (tptp.fun X_b tptp.bool) (tptp.isCont X_b X_c) (tptp.hAPP X_a _let_1 F X_2)) X_1)))))) (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP _let_3 (tptp.fun X_b tptp.bool) (tptp.isCont X_b X_c) (tptp.hAPP _let_4 _let_3 (tptp.hAPP _let_6 (tptp.fun _let_4 _let_3) (tptp.combc X_b _let_4 X_c) (tptp.hAPP _let_2 _let_6 (tptp.hAPP (tptp.fun _let_1 _let_5) (tptp.fun _let_2 _let_6) (tptp.combb _let_1 _let_5 X_b) (tptp.big_co1399186613setsum X_a X_c)) (tptp.hAPP (tptp.fun X_a _let_3) _let_2 (tptp.combc X_a X_b X_c) F))) A_3)) X_1))))))))))))) (forall ((G $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_1)) (=> (forall ((Z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (= (tptp.hAPP tptp.real tptp.real G (tptp.hAPP tptp.real tptp.real F Z_2)) Z_2))) (=> (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.isCont tptp.real tptp.real) F) Z_2)))))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) _let_1 (tptp.isCont tptp.real tptp.real) G) (tptp.hAPP tptp.real tptp.real F X_1)))))))) (forall ((X_1 $$unsorted) (F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 (tptp.ord_less tptp.real) A_2) B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 X_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) _let_1 (tptp.isCont tptp.real tptp.real) F) X_2)))))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 X_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) (tptp.zero_zero tptp.real))))))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_1)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_1) B_1)) (= (tptp.hAPP tptp.real tptp.real F X_1) (tptp.hAPP tptp.real tptp.real F A_2)))))))))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) A_2) B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 X_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) _let_1 (tptp.isCont tptp.real tptp.real) F) X_2)))))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 X_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) (tptp.zero_zero tptp.real))))))) (= (tptp.hAPP tptp.real tptp.real F B_1) (tptp.hAPP tptp.real tptp.real F A_2)))))) (forall ((F $$unsorted) (A_2 $$unsorted) (B_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) A_2) B_1)) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.ord_less_eq tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 X_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP (tptp.fun tptp.real tptp.real) _let_1 (tptp.isCont tptp.real tptp.real) F) X_2)))))) (=> (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.ord_less tptp.real))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 _let_2 X_2) B_1))) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.hAPP (tptp.fun tptp.real tptp.real) (tptp.fun tptp.real _let_1) (tptp.deriv tptp.real) F) X_2) (tptp.zero_zero tptp.real))))))) (forall ((X_2 $$unsorted)) (let ((_let_1 (tptp.ord_less_eq tptp.real))) (let ((_let_2 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 A_2) X_2)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_2 _let_1 X_2) B_1))) (= (tptp.hAPP tptp.real tptp.real F X_2) (tptp.hAPP tptp.real tptp.real F A_2)))))))))) (forall ((G $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_1)) (=> (forall ((Z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (= (tptp.hAPP tptp.real tptp.real G (tptp.hAPP tptp.real tptp.real F Z_2)) Z_2))) (=> (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.isCont tptp.real tptp.real) F) Z_2)))))) (exists ((E $$unsorted)) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) E)) (forall ((Y_2 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) Y_2) (tptp.hAPP tptp.real tptp.real F X_1))))) (let ((_let_2 (tptp.ord_less tptp.real))) (let ((_let_3 (tptp.fun tptp.real tptp.bool))) (=> (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 (tptp.zero_zero tptp.real)) _let_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_3 _let_2 _let_1) E))) (= (tptp.hAPP tptp.real tptp.real F (tptp.hAPP tptp.real tptp.real G Y_2)) Y_2)))))))))))) (forall ((G $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_1)) (=> (forall ((Z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (= (tptp.hAPP tptp.real tptp.real G (tptp.hAPP tptp.real tptp.real F Z_2)) Z_2))) (=> (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.isCont tptp.real tptp.real) F) Z_2)))))) (exists ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real F Z_2)) (tptp.hAPP tptp.real tptp.real F X_1)))))))))) (forall ((G $$unsorted) (F $$unsorted) (X_1 $$unsorted) (D_1 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less tptp.real) (tptp.zero_zero tptp.real)) D_1)) (=> (forall ((Z_2 $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.bool) (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (= (tptp.hAPP tptp.real tptp.real G (tptp.hAPP tptp.real tptp.real F Z_2)) Z_2))) (=> (forall ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (let ((_let_2 (tptp.fun tptp.real tptp.real))) (=> (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real _let_2 (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP _let_2 _let_1 (tptp.isCont tptp.real tptp.real) F) Z_2)))))) (exists ((Z_2 $$unsorted)) (let ((_let_1 (tptp.fun tptp.real tptp.bool))) (and (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less_eq tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.abs_abs tptp.real) (tptp.hAPP tptp.real tptp.real (tptp.hAPP tptp.real (tptp.fun tptp.real tptp.real) (tptp.minus_minus tptp.real) Z_2) X_1))) D_1)) (tptp.hBOOL (tptp.hAPP tptp.real tptp.bool (tptp.hAPP tptp.real _let_1 (tptp.ord_less tptp.real) (tptp.hAPP tptp.real tptp.real F X_1)) (tptp.hAPP tptp.real tptp.real F Z_2)))))))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.int tptp.bool))) (let ((_let_2 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat _let_2 (tptp.ord_atMost tptp.nat) N_1) (tptp.hAPP _let_1 _let_2 (tptp.hAPP (tptp.fun tptp.int tptp.nat) (tptp.fun _let_1 _let_2) (tptp.image tptp.int tptp.nat) tptp.nat_1) (tptp.hAPP tptp.int _let_1 (tptp.hAPP tptp.int (tptp.fun tptp.int _let_1) (tptp.ord_atLeastAtMost tptp.int) (tptp.zero_zero tptp.int)) (tptp.hAPP tptp.nat tptp.int (tptp.semiring_1_of_nat tptp.int) N_1))))))) (forall ((N_1 $$unsorted) (V_1 $$unsorted)) (let ((_let_1 (tptp.hAPP tptp.int tptp.int (tptp.number_number_of tptp.int) (tptp.hAPP tptp.int tptp.int tptp.pred V_1)))) (let ((_let_2 (tptp.ord_max tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat tptp.nat))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 _let_4) (tptp.hAPP tptp.int tptp.nat (tptp.number_number_of tptp.nat) V_1)) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 (tptp.hAPP tptp.bool (tptp.fun tptp.nat _let_3) (tptp.if tptp.nat) (tptp.hAPP tptp.int tptp.bool tptp.nat_neg _let_1)) _let_4) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_3 _let_2 N_1) (tptp.hAPP tptp.int tptp.nat tptp.nat_1 _let_1)))))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.finite_finite_1 tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.ord_atMost tptp.nat) K))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (Z_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_min X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_max X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 Y) Z_1)) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Z_1) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (Z_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 Y) Z_1)) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Z_1) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_min X_a) X))) (let ((_let_3 (tptp.ord_max X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X))) (let ((_let_3 (tptp.ord_min X_a))) (= (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.ord_min X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X) Y)) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.ord_min X_a) X) Y)) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.ord_max X_a) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.ord_min X_a) (tptp.hAPP X_a X_a _let_1 X)) (tptp.hAPP X_a X_a _let_1 Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linord219039673up_add X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.uminus_uminus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.ord_min X_a) X) Y)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 (tptp.ord_max X_a) (tptp.hAPP X_a X_a _let_1 X)) (tptp.hAPP X_a X_a _let_1 Y)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 (tptp.ord_min X_a) X))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) (tptp.hAPP X_a X_a _let_3 Z_1))) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (let ((_let_2 (tptp.hAPP X_a _let_1 (tptp.ord_max X_a) X))) (let ((_let_3 (tptp.ord_min X_a))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) (tptp.hAPP X_a X_a _let_2 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 Y) Z_1))) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 _let_3 (tptp.hAPP X_a X_a _let_2 Y)) (tptp.hAPP X_a X_a _let_2 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (= (tptp.ord_max X_a) (tptp.hAPP (tptp.fun X_a (tptp.fun X_a tptp.bool)) (tptp.fun X_a (tptp.fun X_a X_a)) (tptp.max X_a) (tptp.ord_less_eq X_a))))) (forall ((N_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat _let_1 (tptp.hAPP tptp.nat (tptp.fun tptp.nat _let_1) (tptp.ord_atLeastAtMost tptp.nat) (tptp.zero_zero tptp.nat)) N_1) (tptp.hAPP tptp.nat _let_1 (tptp.ord_atMost tptp.nat) N_1)))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X_1) Y_1)) Z)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) Z))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X_1) Y_1))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (X $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)))))))) (forall ((K $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP tptp.nat _let_1 (tptp.ord_lessThan tptp.nat) (tptp.hAPP tptp.nat tptp.nat tptp.suc K)) (tptp.hAPP tptp.nat _let_1 (tptp.ord_atMost tptp.nat) K)))) (forall ((N_1 $$unsorted) (Ma $$unsorted)) (let ((_let_1 (tptp.ord_max tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun _let_2 _let_2))) (let ((_let_4 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 _let_4) Ma) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_3 (tptp.nat_case tptp.nat) _let_4) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_3 (tptp.combb tptp.nat tptp.nat tptp.nat) tptp.suc) (tptp.hAPP tptp.nat _let_2 _let_1 N_1))) Ma))))))) (forall ((Ma $$unsorted) (N_1 $$unsorted)) (let ((_let_1 (tptp.ord_max tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (let ((_let_3 (tptp.fun tptp.nat _let_2))) (let ((_let_4 (tptp.fun _let_2 _let_2))) (let ((_let_5 (tptp.hAPP tptp.nat tptp.nat tptp.suc N_1))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 Ma) _let_5) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP _let_2 _let_2 (tptp.hAPP tptp.nat _let_4 (tptp.nat_case tptp.nat) _let_5) (tptp.hAPP _let_2 _let_2 (tptp.hAPP _let_2 _let_4 (tptp.combb tptp.nat tptp.nat tptp.nat) tptp.suc) (tptp.hAPP tptp.nat _let_2 (tptp.hAPP _let_3 _let_3 (tptp.combc tptp.nat tptp.nat tptp.nat) _let_1) N_1))) Ma)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) X) (tptp.ti X_a X))))) (forall ((N $$unsorted) (M $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.plus_plus tptp.nat) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.minus_minus tptp.nat) N) M)) M) (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_1 (tptp.ord_max tptp.nat) N) M)))) (forall ((X_a $$unsorted)) (=> (tptp.ordered_ab_group_add X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.minus_minus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_max X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.ordere236663937imp_le X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.plus_plus X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_max X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 X) Y)) Z_1) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Z_1)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_max tptp.nat) N) (tptp.zero_zero tptp.nat)) N)) (forall ((N $$unsorted)) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat (tptp.fun tptp.nat tptp.nat) (tptp.ord_max tptp.nat) (tptp.zero_zero tptp.nat)) N) N)) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.ord_atMost X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (= (tptp.hAPP X_a _let_2 _let_1 X_1) (tptp.hAPP X_a _let_2 _let_1 Y_1)) (= (tptp.ti X_a X_1) (tptp.ti X_a Y_1)))))))) (forall ((M $$unsorted) (N $$unsorted)) (let ((_let_1 (tptp.ord_max tptp.nat))) (let ((_let_2 (tptp.fun tptp.nat tptp.nat))) (= (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 (tptp.hAPP tptp.nat tptp.nat tptp.suc M)) (tptp.hAPP tptp.nat tptp.nat tptp.suc N)) (tptp.hAPP tptp.nat tptp.nat tptp.suc (tptp.hAPP tptp.nat tptp.nat (tptp.hAPP tptp.nat _let_2 _let_1 M) N)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 Y)) Z_1) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) Z_1))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a _let_3 B)) C) (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) C))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted) (Z_1 $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 X))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 Y))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 Z_1)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 Z_1)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.hAPP X_a _let_2 _let_1 B))) (let ((_let_4 (tptp.hAPP X_a _let_2 _let_1 A_1))) (= (tptp.hAPP X_a X_a _let_3 (tptp.hAPP X_a X_a _let_4 C)) (tptp.hAPP X_a X_a _let_4 (tptp.hAPP X_a X_a _let_3 C)))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 Y))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1))) (let ((_let_2 (tptp.hAPP X_a X_a _let_1 B))) (= (tptp.hAPP X_a X_a _let_1 _let_2) _let_2)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 X) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 Y) X))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 B) A_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) A_1) (tptp.ti X_a A_1))))) (forall ((U_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (= (tptp.hAPP _let_1 tptp.nat (tptp.finite_card tptp.nat) (tptp.hAPP tptp.nat _let_1 (tptp.ord_atMost tptp.nat) U_1)) (tptp.hAPP tptp.nat tptp.nat tptp.suc U_1)))) (forall ((S $$unsorted)) (= (tptp.hBOOL (tptp.hAPP (tptp.fun tptp.nat tptp.bool) tptp.bool (tptp.finite_finite_1 tptp.nat) S)) (exists ((K_1 $$unsorted)) (let ((_let_1 (tptp.fun tptp.nat tptp.bool))) (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP _let_1 (tptp.fun _let_1 tptp.bool) (tptp.ord_less_eq _let_1) S) (tptp.hAPP tptp.nat _let_1 (tptp.ord_atMost tptp.nat) K_1))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (B $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)) X)) (not (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) X)) (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) X))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (D $$unsorted) (A_1 $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.ord_max X_a))) (let ((_let_2 (tptp.fun X_a X_a))) (let ((_let_3 (tptp.ord_less_eq X_a))) (let ((_let_4 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 A_1) C)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 B) D)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_4 _let_3 (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 A_1) B)) (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_2 _let_1 C) D)))))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Z_1 $$unsorted) (Y $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Z_1) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) Y) Z_1)) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (A_1 $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 A_1) X)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 B) X)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)) X))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) X)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) Y) (tptp.ti X_a X)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) Y)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) Y) (tptp.ti X_a Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((A_1 $$unsorted) (X $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 B)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((B $$unsorted) (X $$unsorted) (A_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X))) (=> (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 A_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) A_1) B)))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted) (Z $$unsorted)) (let ((_let_1 (tptp.ord_less_eq X_a))) (let ((_let_2 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X_1) Y_1)) Z)) (and (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 X_1) Z)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_2 _let_1 Y_1) Z))))))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X_1 $$unsorted) (Y_1 $$unsorted)) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X_1) Y_1)) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X_1) Y_1) (tptp.ti X_a Y_1)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Y $$unsorted) (X $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Y) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((X $$unsorted) (Y $$unsorted)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) X) (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X) Y)))))) (forall ((X_a $$unsorted)) (=> (tptp.linorder X_a) (forall ((Z $$unsorted) (X_1 $$unsorted) (Y_1 $$unsorted)) (let ((_let_1 (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.ord_less_eq X_a) Z))) (= (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 (tptp.hAPP X_a X_a (tptp.hAPP X_a (tptp.fun X_a X_a) (tptp.ord_max X_a) X_1) Y_1))) (or (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 X_1)) (tptp.hBOOL (tptp.hAPP X_a tptp.bool _let_1 Y_1)))))))) (forall ((X_a $$unsorted)) (=> (tptp.ord X_a) (forall ((I $$unsorted) (K $$unsorted)) (let ((_let_1 (tptp.fun X_a tptp.bool))) (= (tptp.hBOOL (tptp.hAPP _let_1 tptp.bool (tptp.hAPP X_a (tptp.fun _let_1 tptp.bool) (tptp.member X_a) I) (tptp.hAPP X_a _let_1 (tptp.ord_atMost X_a) K))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a _let_1 (tptp.ord_less_eq X_a) I) K))))))) (forall ((X_b $$unsorted)) (=> (and (tptp.number X_b) (tptp.ord X_b)) (forall ((U $$unsorted) (V $$unsorted)) (let ((_let_1 (tptp.number_number_of X_b))) (let ((_let_2 (tptp.hAPP tptp.int X_b _let_1 U))) (let ((_let_3 (tptp.hAPP tptp.int X_b _let_1 V))) (let ((_let_4 (tptp.hAPP X_b X_b (tptp.hAPP X_b (tptp.fun X_b X_b) (tptp.ord_max X_b) _let_2) _let_3))) (let ((_let_5 (tptp.hBOOL (tptp.hAPP X_b tptp.bool (tptp.hAPP X_b (tptp.fun X_b tptp.bool) (tptp.ord_less_eq X_b) _let_2) _let_3)))) (and (=> _let_5 (= _let_4 _let_3)) (=> (not _let_5) (= _let_4 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(tptp.real_field tptp.complex) (tptp.dist_norm tptp.complex) (tptp.division_ring tptp.complex) (tptp.comm_semiring tptp.complex) (tptp.t2_space tptp.complex) (tptp.semiring_char_0 tptp.complex) (tptp.number_semiring tptp.complex) (tptp.ab_group_add tptp.complex) (tptp.zero_neq_one tptp.complex) (tptp.monoid_mult tptp.complex) (tptp.comm_ring_1 tptp.complex) (tptp.monoid_add tptp.complex) (tptp.semiring_1 tptp.complex) (tptp.semiring_0 tptp.complex) (tptp.field_char_0 tptp.complex) (tptp.group_add tptp.complex) (tptp.mult_zero tptp.complex) (tptp.comm_ring tptp.complex) (tptp.ring_char_0 tptp.complex) (tptp.number_ring tptp.complex) (tptp.semiring tptp.complex) (tptp.inverse tptp.complex) (tptp.uminus tptp.complex) (tptp.ring_1 tptp.complex) (tptp.minus tptp.complex) (tptp.field tptp.complex) (tptp.power tptp.complex) (tptp.zero tptp.complex) (tptp.plus tptp.complex) (tptp.banach tptp.complex) (tptp.ring tptp.complex) (tptp.idom tptp.complex) (tptp.number tptp.complex) (tptp.one tptp.complex) (tptp.dvd tptp.complex) (forall ((T_2 $$unsorted) (T_1 $$unsorted)) (=> (and (tptp.finite_finite T_1) (tptp.finite_finite T_2)) (tptp.finite_finite (tptp.product_prod T_2 T_1)))) (tptp.ordere223160158up_add tptp.code_code_numeral) (tptp.ordere236663937imp_le tptp.code_code_numeral) (tptp.linord893533164strict tptp.code_code_numeral) (tptp.linord20386208strict tptp.code_code_numeral) (tptp.ordere779506340up_add tptp.code_code_numeral) (tptp.ordere216010020id_add tptp.code_code_numeral) (tptp.cancel146912293up_add tptp.code_code_numeral) (tptp.ordere453448008miring tptp.code_code_numeral) (tptp.ordere1490568538miring tptp.code_code_numeral) (tptp.cancel_semigroup_add tptp.code_code_numeral) (tptp.linordered_semiring tptp.code_code_numeral) (tptp.linordered_semidom tptp.code_code_numeral) (tptp.ab_semigroup_mult tptp.code_code_numeral) (tptp.comm_monoid_mult tptp.code_code_numeral) (tptp.ab_semigroup_add tptp.code_code_numeral) (tptp.ordered_semiring tptp.code_code_numeral) (tptp.no_zero_divisors tptp.code_code_numeral) (tptp.comm_monoid_add tptp.code_code_numeral) (tptp.comm_semiring_1 tptp.code_code_numeral) (tptp.comm_semiring_0 tptp.code_code_numeral) (tptp.semiring_div tptp.code_code_numeral) (tptp.comm_semiring tptp.code_code_numeral) (tptp.semiring_char_0 tptp.code_code_numeral) (tptp.zero_neq_one tptp.code_code_numeral) (tptp.preorder tptp.code_code_numeral) (tptp.linorder tptp.code_code_numeral) (tptp.monoid_mult tptp.code_code_numeral) (tptp.monoid_add tptp.code_code_numeral) (tptp.semiring_1 tptp.code_code_numeral) (tptp.semiring_0 tptp.code_code_numeral) (tptp.mult_zero tptp.code_code_numeral) (tptp.order tptp.code_code_numeral) (tptp.semiring tptp.code_code_numeral) (tptp.ord tptp.code_code_numeral) (tptp.minus tptp.code_code_numeral) (tptp.power tptp.code_code_numeral) (tptp.zero tptp.code_code_numeral) (tptp.plus tptp.code_code_numeral) (tptp.number tptp.code_code_numeral) (tptp.one tptp.code_code_numeral) (tptp.dvd tptp.code_code_numeral) (tptp.ordere223160158up_add tptp.quickcheck_code_int) (tptp.ordere236663937imp_le tptp.quickcheck_code_int) (tptp.linord893533164strict tptp.quickcheck_code_int) (tptp.linord20386208strict tptp.quickcheck_code_int) (tptp.ordere779506340up_add tptp.quickcheck_code_int) (tptp.ordere216010020id_add tptp.quickcheck_code_int) (tptp.cancel146912293up_add tptp.quickcheck_code_int) (tptp.ordere453448008miring tptp.quickcheck_code_int) (tptp.ordere1490568538miring tptp.quickcheck_code_int) (tptp.cancel_semigroup_add tptp.quickcheck_code_int) (tptp.linordered_semiring tptp.quickcheck_code_int) (tptp.linordered_semidom tptp.quickcheck_code_int) (tptp.ab_semigroup_mult tptp.quickcheck_code_int) (tptp.comm_monoid_mult tptp.quickcheck_code_int) (tptp.ab_semigroup_add tptp.quickcheck_code_int) (tptp.ordered_semiring tptp.quickcheck_code_int) (tptp.no_zero_divisors tptp.quickcheck_code_int) (tptp.comm_monoid_add tptp.quickcheck_code_int) (tptp.comm_semiring_1 tptp.quickcheck_code_int) (tptp.comm_semiring_0 tptp.quickcheck_code_int) (tptp.semiring_div tptp.quickcheck_code_int) (tptp.comm_semiring tptp.quickcheck_code_int) (tptp.semiring_char_0 tptp.quickcheck_code_int) (tptp.zero_neq_one tptp.quickcheck_code_int) (tptp.preorder tptp.quickcheck_code_int) (tptp.linorder tptp.quickcheck_code_int) (tptp.monoid_mult tptp.quickcheck_code_int) (tptp.monoid_add tptp.quickcheck_code_int) (tptp.semiring_1 tptp.quickcheck_code_int) (tptp.semiring_0 tptp.quickcheck_code_int) (tptp.mult_zero tptp.quickcheck_code_int) (tptp.order tptp.quickcheck_code_int) (tptp.semiring tptp.quickcheck_code_int) (tptp.ord tptp.quickcheck_code_int) (tptp.minus tptp.quickcheck_code_int) (tptp.power tptp.quickcheck_code_int) (tptp.zero tptp.quickcheck_code_int) (tptp.plus tptp.quickcheck_code_int) (tptp.number tptp.quickcheck_code_int) (tptp.one tptp.quickcheck_code_int) (tptp.dvd tptp.quickcheck_code_int) (forall ((T $$unsorted) (A $$unsorted)) (let ((_let_1 (tptp.ti T A))) (= (tptp.ti T _let_1) _let_1))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.bool (tptp.fun X_a _let_1) (tptp.if X_a) tptp.fTrue) X) Y) (tptp.ti X_a X)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (let ((_let_1 (tptp.fun X_a X_a))) (= (tptp.hAPP X_a X_a (tptp.hAPP X_a _let_1 (tptp.hAPP tptp.bool (tptp.fun X_a _let_1) (tptp.if X_a) tptp.fFalse) X) Y) (tptp.ti X_a Y)))) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((X_a $$unsorted) (P $$unsorted) (X $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool P X))) (tptp.hBOOL (tptp.hAPP (tptp.fun X_a tptp.bool) tptp.bool (tptp.fEx X_a) P)))) (forall ((P $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P))) (not (tptp.hBOOL P)))) (forall ((P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool tptp.fNot P)))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_a X_c))) (let ((_let_2 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_2 _let_1 (tptp.hAPP (tptp.fun X_b X_c) (tptp.fun _let_2 _let_1) (tptp.combb X_b X_c X_a) P) Q) R) (tptp.hAPP X_b X_c P (tptp.hAPP X_a X_b Q R)))))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (= (tptp.hAPP X_a X_c (tptp.hAPP X_b _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun X_b _let_2) (tptp.combc X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) Q))))) (forall ((X_a $$unsorted) (P $$unsorted)) (= (tptp.hAPP X_a X_a (tptp.combi X_a) P) (tptp.ti X_a P))) (forall ((X_b $$unsorted) (X_a $$unsorted) (P $$unsorted) (Q $$unsorted)) (= (tptp.hAPP X_b X_a (tptp.hAPP X_a (tptp.fun X_b X_a) (tptp.combk X_a X_b) P) Q) (tptp.ti X_a P))) (forall ((X_a $$unsorted) (X_c $$unsorted) (X_b $$unsorted) (P $$unsorted) (Q $$unsorted) (R $$unsorted)) (let ((_let_1 (tptp.fun X_b X_c))) (let ((_let_2 (tptp.fun X_a X_c))) (let ((_let_3 (tptp.fun X_a X_b))) (= (tptp.hAPP X_a X_c (tptp.hAPP _let_3 _let_2 (tptp.hAPP (tptp.fun X_a _let_1) (tptp.fun _let_3 _let_2) (tptp.combs X_a X_b X_c) P) Q) R) (tptp.hAPP X_b X_c (tptp.hAPP X_a _let_1 P R) (tptp.hAPP X_a X_b Q R))))))) (tptp.hBOOL tptp.fTrue) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL P))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fconj P) Q))) (tptp.hBOOL Q))) (forall ((Q $$unsorted) (P $$unsorted)) (or (not (tptp.hBOOL P)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fdisj P) Q))) (tptp.hBOOL P) (tptp.hBOOL Q))) (not (tptp.hBOOL tptp.fFalse)) (forall ((P $$unsorted)) (let ((_let_1 (tptp.ti tptp.bool P))) (or (= _let_1 tptp.fTrue) (= _let_1 tptp.fFalse)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y))) (= (tptp.ti X_a X) (tptp.ti X_a Y)))) (forall ((X_a $$unsorted) (X $$unsorted) (Y $$unsorted)) (or (not (= (tptp.ti X_a X) (tptp.ti X_a Y))) (tptp.hBOOL (tptp.hAPP X_a tptp.bool (tptp.hAPP X_a (tptp.fun X_a tptp.bool) (tptp.fequal X_a) X) Y)))) (forall ((Q $$unsorted) (P $$unsorted)) (or (tptp.hBOOL P) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL Q)) (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q)))) (forall ((P $$unsorted) (Q $$unsorted)) (or (not (tptp.hBOOL (tptp.hAPP tptp.bool tptp.bool (tptp.hAPP tptp.bool (tptp.fun tptp.bool tptp.bool) tptp.fimplies P) Q))) (not (tptp.hBOOL P)) (tptp.hBOOL Q))) _let_16 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 17.64/17.89 )
% 17.64/17.89 % SZS output end Proof for NUM924+8
% 17.64/17.89 % cvc5---1.0.5 exiting
% 17.64/17.90 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------